Download A Survey of Molecules With Large Nuclear

Wesleyan University The Honors College A SURVEY OF MOLECULES WITH LARGE NUCLEAR QUADRUPOLES AND OTHER PROJECTS by Eric A. Arsenault Class of 2017 A thesis (or essay) submitted to the faculty of Wesleyan University in partial fulfillment of the requirements for the Degree of Bachelor of Arts with Departmental Honors in Chemistry Middletown, Connecticut April, 2017 “Let me show ya something.” —Old Gregg For Dr. Dan Obenchain. i Acknowledgements As a member of the Novick/Pringle/Cooke research group, I have grown fantastically. With this group, I experienced my first flight and I became a published scientist. There are quite a few people to thank: I want to thank Professor Stew Novick, Professor Wallace “Pete” Pringle, and Professor Steve Cooke for all of their support, wisdom, and guidance and for allowing me to join their research group despite the fact that at the time, I had not the slightest idea of what the hell they were doing. Over the past three years, Professor Novick has been exceptionally important in shaping the researcher that I am now and the one that I aspire to be. Thank you. I want to thank Dr. Dan Obenchain for his perpetual support, patience, encouragement, and for showing me my first episode of The Mighty Boosh. I also would like to thank Dr. Dan for editing and re-editing my work, for listening to practice presentation after practice presentation, for his questions (“Where are the numbers?”), and for continuously answering my questions. Thank you. I want to thank the many scientists that I was fortunate to collaborate with during my time in the Novick/Pringle/Cooke group, especially Dr. Thomas Blake, Professor Karen Peterson, and Professor Wei Lin. I also want to give many thanks to the current and former members of the Novick/Pringle/Cooke group that helped to make my experience what is was, including Dr. Brittany Long, Derek Frank, Yoon Jeong Choi, Angela Chung, Will Orellana, Robert Melchreit, and Dr. Sue Stephens. Outside of the laboratory, I would like to acknowledge the many professors ii that I have interacted with on a daily basis during my time at Wesleyan, especially Professor Joseph Knee. Outside both the laboratory and the classroom, I am so grateful for my family and friends. Shout-outs to Mom, Dad, Emily, Luke, Grandma, Charlie, and Roxy (meow ). Thank you to Isabel for teaching me about the present and life beyond equations. I also want to thank the Wesleyan Cross Country team, specifically the many teammates that ran thousands and thousands of miles alongside me over the past few years. Lastly, a hat tip to the residents of 52 Home Avenue. iii Contents 1 Introduction 1.1 1 Microwave Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 The Rigid Rotor . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Centrifugal Distortion . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Hyperfine Interactions . . . . . . . . . . . . . . . . . . . . 4 1.1.4 Nuclear Quadrupole Interaction . . . . . . . . . . . . . . . 5 1.1.5 Nuclear Spin-Rotation Interaction . . . . . . . . . . . . . . 7 1.1.6 The Full Hamiltonian . . . . . . . . . . . . . . . . . . . . . 8 2 A Study of 2-Iodobutane by Rotational Spectroscopy 10 2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.2 Quantum Chemical Calculations . . . . . . . . . . . . . . . 14 2.3.3 Spectral Assignments . . . . . . . . . . . . . . . . . . . . . 16 2.3.4 Hyperfine Structure . . . . . . . . . . . . . . . . . . . . . . 18 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.1 Structural Determination . . . . . . . . . . . . . . . . . . . 22 2.4.2 Nuclear Quadrupole Coupling Tensor of Iodine . . . . . . . 25 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.7 Supplemental Information . . . . . . . . . . . . . . . . . . . . . . 30 2.4 iv 3 A Study of the Conformational Isomerism of 1-Iodobutane by High Resolution Rotational Spectroscopy 33 3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.1 Quantum Chemical Calculations . . . . . . . . . . . . . . . 36 3.3.2 Spectral Assignments . . . . . . . . . . . . . . . . . . . . . 36 3.3.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.7 Supplemental Material . . . . . . . . . . . . . . . . . . . . . . . . 49 4 Nuclear Quadrupole Coupling in SiH2 I2 due to the Presence of Two Iodine Nuclei 53 4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4 Spectral Assignments . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.5.1 Structural Determination . . . . . . . . . . . . . . . . . . . 60 4.5.2 Nuclear Quadrupole Coupling Tensor of Iodine . . . . . . . 60 4.5.3 Chemical Nature of the Si−I Bond . . . . . . . . . . . . . 62 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.7 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.8 Supplemental Material . . . . . . . . . . . . . . . . . . . . . . . . 64 5 Assorted Projects 72 6 Appendix A 84 v Chapter 1 Introduction 1.1 Microwave Spectroscopy This section will provide a brief synopsis of the theory behind microwave spectroscopy. Information pertaining to instrumentation, experimental setup, and spectral analysis will be left to the following chapters, where the presentation of these details has been tailored to the project under discussion. Microwave spectroscopy is the study of the interaction between microwave radiation, which spans the 300 MHz to 300 GHz portion of the electromagnetic spectrum, and matter, typically in the gas phase[1]. In the simplest case, this leads to the observation of a pure rotational spectrum, although in practice many complexities arise. For brevity, a mere outline of the theory behind microwave spectroscopy will be presented here. Molecular Rotation Spectra by H. W. Kroto, Microwave Spectroscopy by C. H. Townes and A. L. Schawlow, and Microwave Molecular Spectra by Walter Gordy and R. L. Cook can serve the reader as a more comprehensive set of resources for the concepts presented below[4–6]. 1 1.1.1 The Rigid Rotor To investigate the origin of the rigid rotor Hamiltonian, it is best to start with the classical expression for pure rotational kinetic energy given by 1 Tr = ω † Iω 2 where  I 0 0  aa  I =  0 Ibb 0  0 0 Icc (1.1)      (1.2) is the diagonalized inertia tensor, I, which, by definition, is a projection of the tensor in the principal axis system of the molecule under investigation[2]. Similarly,  ωa      ω =  ωb    ωc (1.3) is the angular velocity about the principal axes of the molecule. The derivation for Tr itself can be found in most texts on classical dynamics[3]. Next, defining the angular momentum, P , as P = Iω (1.4) leads to the rearrangement of Tr such that 1 1 1 Tr = ω † Iω = (Iω)† I −1 (Iω) = P † I −1 P . 2 2 2 (1.5) When expressed in this way, Tr can be used directly to formulate the classical rigid rotor Hamiltonian 1 † −1 1 Pa2 Pb2 Pc2 Ĥ = P I P = ( + + ). 2 2 Iaa Ibb Icc (1.6) By replacing the general angular momentum operator, P , with the corresponding conjugate (quantum mechanical) angular momentum operator, J , the quantum mechanical rigid rotor Hamiltonian can be easily determined to be of the form J2 J2 1 J2 ĤR = ( a + b + c ) 2 Iaa Ibb Icc 2 (1.7) Table 1.1: Classes of rigid rotors A=B=C spherical top B=C linear molecule A>B=C prolate symmetric top A=B>C oblate symmetric top A>B>C asymmetric rotor [4–6]. By convention, so that the components of J are expressed in units of ~, ĤR is written as ĤR = AJa2 + BJb2 + CJc2 where A, B, and C, are the principal rotational constants given by ~2 , 2Icc (1.8) 2 ~2 , ~ , 2Iaa 2Ibb and respectively. Also by convention, IA ≤ IB ≤ IC such that A ≥ B ≥ C. These distinctions lead to several specific classes of rigid rotors, which are presented in Table 1.1. Lastly, the eigenstates of ĤR , for the most general rotor, which correspond to the rotational energy levels, are labeled by quantum numbers J KA can have values of J to 0 and KC KA KC , where can have values of 0 to J. For each class of rigid rotor, specific selection rules determine the allowed transitions between rotational energy levels, however, these rules will not be presented here. 1.1.2 Centrifugal Distortion In experiment, observed rotational transitions rarely conform to the predictions yielded by the final form of ĤR in (1.8), as this Hamiltonian is based on the approximation that the nuclear framework of the molecule is fixed. In practice, centrifugal force produced by molecular rotation causes a distortion in the geometry of the molecule, which is to say that it is best to treat molecular systems as semi-rigid rotors. The consequence of this is that the principal moments of inertia are not longer constant parameters, rather they depend on the 3 rotational state of the molecule. The effects of centrifugal distortion are treated as a perturbation to ĤR so that the resulting Hamiltonian becomes Ĥ = ĤR + ĤCD (1.9) where ĤCD is the Hamiltonian accounting for centrifugal distortion. The firstorder perturbation correction to HˆR is given by (1) ĤCD = ~4 X ταβγδ Jα Jβ Jγ Jδ 4 (1.10) α,β,γ,δ where α, β, γ, δ = a, b, or c. After some manipulation this becomes ĤCD = −DJ J 4 − DJK J 2 Jz2 − Dk Jz4 + d1 J 2 (J+2 + J−2 ) + d2 (J+4 + J−4 ) (1.11) where DJ , DJK , Dk , d1 , and d2 are the quartic centrifugal distortion constants, which are functions of ταβγδ [5, 7]. It should be noted that this form of ĤCD is general and depending on the molecule and therefore the choice of basis Jz = Ja , Jb , or Jc [5, 7]. For the work presented in subsequent chapters, ĤCD was chosen to be in the symmetric rotor basis and therefore Jz was taken to be Ja or Jc depending upon whether the basis set was prolate or oblate. Additionally, ĤCD can be treated by higher levels of perturbation theory, which would return higher-order centrifugal distortion coefficients. That being said, only quartic centrifugal distortion terms are pertinent to the work that will be presented in the subsequent chapters. Lastly, the eigenstates of (1.9) are still labeled by the quantum numbers J KA KC . 1.1.3 Hyperfine Interactions Many of the molecules to be discussed contain nuclei with intrinsic nuclear spins, I (not be confused with the moments of inertia in this context), greater than 12 . The presence of these nuclei in the molecular framework of a species can 4 give rise to many additional interactions. Nuclei with I > 1 2 have a magnetic dipole moment and an electric quadrupole moment, both of which can further complicate the rotational spectrum of a molecule. 1.1.4 Nuclear Quadrupole Interaction An atomic nucleus with I > 1 2 has a non-spherical distribution of nuclear charge and therefore a non-spherical distribution of electronic charge around the nucleus. When such a nucleus is introduced into a molecular system, the nuclear spin couples with the rotational angular momentum of the molecule causing perturbations and splittings in the rotational energy levels. The coupling scheme for the nuclear quadrupole interaction is F =I +J (1.12) where F is the total angular momentum. The new total angular momentum quantum numbers then become F = J + I, J + I − 1, ..., |J − I| (1.13) such that the rotational energy energy levels are labeled by the quantum numbers J KA KC F . In the case of a species with two quadrupolar nuclei, with spins of I1 and I2 , the coupling scheme becomes F1 = I1 + J (1.14) F2 = I2 + F1 (1.15) where the rotational energy levels are labeled by J KA KC F1 F2 . In this manner, n quadrupolar nuclei could be accounted for (yet assigning the rotational spectrum of such a species would be a different beast). To first order, for cylindrically symmetric molecules, the nuclear quadrupole interaction is given by EQ = eQqJ 2J + 3 Y (J, I, F ) J 5 (1.16) where Y (J, I, F ) = 3 C(C 4 + 1) − I(I + 1)J(J + 1) 2I(2I − 1)(2J − 1)(2J + 3) (1.17) with C = F (F + 1) − J(J + 1) − I(I + 1) (1.18) is Casimir’s function (Y (J, I, F )), e is the charge of a proton, Q is the nuclear quadrupole moment (due to non-spherical nuclear charge), and qJ is the electric field gradient at the nucleus (due to non-spherical electronic charge around the nucleus)[4–6]. In this general form X 2 qJ = qgg Jg2 (J + 1)(2J + 3) (1.19) 2 Jg = J K A K C |Jg2 |J K A K C (1.20) g=a,b,c where [4–6]. However, as will be the case in many of the studies to come, the molecule is not cylindrically symmetric (χbb 6= χcc ) and off-diagonal elements of the nuclear quadrupole coupling Hamiltonian, ĤQ , are not negligible. It therefore becomes necessary to also include the second order and higher corrections in perturbation theory to EQ (or to not rely on perturbation theory at all and diagonalize the full Hamiltonian). Upon this inclusion, ĤQ becomes ĤQ = X 1 χαβ [I , I ] α β + 2I(2I − 1) (1.21) α,β where α, β = a, b, or c, [Iα , Iβ ]+ = Iα Iβ + Iβ Iα , and χαβ are elements of the traceless nuclear quadrupole coupling tensor  χ χ χ  aa ab ac  χ =  χba χbb χbc  χca χcb χcc      (1.22) such that the final form of this Hamiltonian is[4–6, 8] ĤQ = 3 1 1 1 { χaa [Ia2 − I 2 ] + (χbb − χcc )[I+2 + I−2 ] + χab [Ia Ib + Ib Ia ] 2I(2I − 1) 2 3 4 +χac [Ia Ic + Ic Ia ] + χbc [Ib Ic + Ic Ib ]}. (1.23) 6 In the case of two (or more) quadrupolar nuclei, the quadrupolar interaction can be treated in two ways: a) if I1 > I2 then ĤQ2 is treated as a perturbation to ĤQ1 or b) if I1 is of equal or similar magnitude to I2 then the characteristic equation must be solved. The latter case is considerably more complex and was characterized in-depth by Robinson et al. and Meyers et al.[9, 10]. 1.1.5 Nuclear Spin-Rotation Interaction Nuclei with I ≥ 1 2 exhibit (often subtle) magnetic hyperfine interactions (nuclear spin-rotation interactions) that further perturb the rotational energy levels of a system. Classically, the interaction between a dipole moment and a magnetic field is given by ĤM = −µ· H. (1.24) In this context, the dipole moment, µ, is the nuclear spin magnetic moment µI , which is given by the nuclear magneton, βI , the gyromagnetic ratio of the nucleus, gI , and the nuclear spin, I, such that µ = µI = βI gI I (1.25) and H is the magnetic field created via molecular rotation. As the frequency of molecular rotation is so much greater than the the precession of the nuclear spin, µI is approximated to interact only with the average of the magnetic field generated by the angular momentum of the molecule in the direction of J . Considering this HJ J Hef f = p J(J + 1) (1.26) and ĤSR = −βI gI I· Hef f −βI gI HJ = p I· J . J(J + 1) (1.27) After some manipulation, for the most general rotor, ĤSR = CJ KA KC I· J 7 (1.28) where CJ KA KC X 1 Cgg Jg2 . = J(J + 1) (1.29) g=a,b,c It is important to note here that the CJ KA KC ’s depend on a specific rotational state and during spectral analysis process, these are the values used to calculate the Cgg ’s. Again after some rearrangement, to first-order, the nuclear-spin rotation Hamiltonian is given by ĤSR = Caa Ia Ja + Cbb Ib Jb + Ccc Ic Jc (1.30) where Caa , Cbb , and Ccc are the nuclear spin-rotation coupling constants respective to the a-, b-, and c-principal axes[4–6]. In the case of a species that has more than one nuclei with I ≥ 21 , ĤSR total = ĤSR 1 + ĤSR 2 + ... + ĤSR n . (1.31) It should be noted that no additional quantum numbers are necessary to account specifically for the nuclear spin-rotation interaction, as it is merely a perturbative interaction. Additionally, this outline of the nuclear spin-rotation interaction is P specifically for molecules in 1 states. 1.1.6 The Full Hamiltonian The full Hamiltonian, for a species that exhibits all of the aforementioned interactions, as will be the case for the molecules to be discusses, then has the form Ĥ = AJa2 + BJb2 + CJc2 − DJ J 4 − DJK J 2 Jz2 − Dk Jz4 + d1 J 2 (J+2 + J−2 ) +d2 (J+4 + J−4 ) + 1 1 3 { χaa [Ia2 − I 2 ] 2I(2I − 1) 2 3 1 + (χbb − χcc )[I+2 + I−2 ] + χab [Ia Ib + Ib Ia ] (1.32) 4 +χac [Ia Ic + Ic Ia ] + χbc [Ib Ic + Ic Ib ]} +Caa Ia Ja + Cbb Ib Jb + Ccc Ic Jc . 8 References [1] J. E. Wollrab, Rotational Spectra and Molecular Structure: Physical Chemistry: a Series of Monographs, volume 13, Academic Press, 2016. [2] R. G. Mortimer, Physical chemistry. 3rd, 2008. [3] D. T. Greenwood, Classical dynamics, Courier Corporation, 1977. [4] H. W. Kroto, Molecular Rotation Spectra, Dover, 1992. [5] W. Gordy, R. L. Cook, Microwave Molecular Spectra, Wiley, New York, 1984. [6] C. H. Townes, A. L. Schawlow, Microwave Spectroscopy, Courier Corporation, 2013. [7] J. K. Watson, The Journal of Chemical Physics 46 (1967) 1935–1949. [8] E. Hirota, J. M. Brown, J. Hougen, T. Shida, N. Hirota, Pure Appl. Chem. 66 (1994) 571–576. [9] G. W. Robinson, C. Cornwell, The Journal of Chemical Physics 21 (1953) 1436–1442. [10] R. J. Myers, W. D. Gwinn, The Journal of Chemical Physics 20 (1952) 1420– 1427. 9 Chapter 2 A Study of 2-Iodobutane by Rotational Spectroscopy This chapter has been published in the Journal of Physical Chemistry A prior to the compilation of this thesis. The author list is as follows: Eric A. Arsenault, Daniel A. Obenchain, Yoon Jeong Choi, Thomas A. Blake, S. A. Cooke, and Stewart E. Novick. The publication is E. A. Arsenault, D. A. Obenchain, Y. J. Choi, T. A. Blake, S. A. Cooke, S. E. Novick, J. Phys. Chem. A 120 (2016) 7145–7151. 2.1 Abstract The rotational transitions belonging to 2-iodobutane (sec-butyl-iodide, CH3 CHICH2 CH3 ) have been measured over the frequency range 5.5-16.5 GHz via jet-pulsed Fourier transform microwave (FTMW) spectroscopy. The complete nuclear quadrupole coupling tensor of iodine, χ, has been obtained for the gauche (g)-, anti (a)-, and gauche0 (g0 )-conformers, as well as the four 13 C isotopologues of the gauche species. Rotational constants, centrifugal distortion constants, quadrupole coupling constants, and nuclear spin-rotation constants were determined for each species. Changes in the χ of the iodine nucleus, resulting from conformational and isotopic differences, will be discussed. Isotopic 10 substitution of g-2-iodobutane allowed for a rs structure to be determined for the carbon backbone. Additionally, isotopic substitution, in conjunction with an ab initio structure, allowed for a fit of various r0 structural parameters belonging to g-2-iodobutane. 2.2 Introduction The electrophilic addition of hydrogen halides to alkenes is a fundamental two-step reaction discussed in most introductory organic texts[1]: first a carbonium ion is formed with the transfer of the proton from the hydrogen halide to the alkene, and second the halide ion bonds to the carbonium ion. Where on the carbon backbone the halide ion attaches is dictated by the relative stability of the carbonium ion formed in the first step. An ion formed at a tertiary carbon position is more stable than that at a secondary position, which in turn is more stable than an ion formed at a primary carbon position. These relative stabilities lead to Markovnikov’s empirical rule explaining the preponderance of one product isomer formed relative to another in hydrogen halide additions to alkenes. The overall energetics of these reactions are further complicated by conformational equilibria.[1, 2] Our interest is in examining the structures of these haloalkane conformers and, eventually, their relationship to the carbonium ion transition state. Halobutanes represent a sufficiently complex, yet tractable, conformer system to study using free-jet supersonic cooling and Fourier transform microwave spectroscopy. We begin here by examining the conformers of 2-iodobutane. Iodine, with its large nuclear quadrupole moment and possible spin-rotation coupling, makes the resulting microwave spectrum more complex and challenging to assign and fit, but it affords the opportunity of gathering more detailed information about the molecule’s electronic wave function parameters.[3] The first spectroscopic investigation of 2-iodobutane belonged to a larger infrared (IR) study of 2-haloalkanes carried out by Benedetti and Cecchi[4] over 11 40 years ago. The IR spectra for each haloalkane revealed the presence of three conformational isomers, related via a rotation about the C2 −C3 bond of the four carbon chain. The conformations of 2-iodobutane, found in this work, agree with the conclusions of Benedetti and Cecchi. Additionally, the 13 C isotopologues of g-2-iodobutane were observed in natural abundance, leading to a more rigorous determination of the structure of this particular conformation. The nuclear quadrupole coupling constants (NQCCs) belonging to the spectroscopically observed 2-iodobutane species in the present work will be compared with each other and to previously investigated iodoalkanes, in order to gain insight into how substitution affects the electronic environment at the nucleus of the iodine atom. 2.3 2.3.1 Experimental Instrumentation The initial rotational spectrum of 2-iodobutane was collected over a frequency range of 7-13 GHz, shown in Figure 2.1, on a chirp-pulsed Fourier transform microwave (FTMW) spectrometer. This instrument is based on the design by Pate and coworkers[5] and has been outlined in detail elsewhere[6]. The circuitry of this instrument will be described briefly. An 8, 10, or 12 GHz microwave center frequency, ν, is mixed with a 6 µs linear frequency sweep, from DC to 1 GHz. The successive microwave radiation, ν ± 1 GHz, is amplified and then broadcast through a microwave horn antenna into the molecular beam. The radiation then induces a polarization in the coincident supersonic expansion of the gas-phase molecular sample. Following a 1 µs delay, a second microwave horn antenna collects the free induction decay (FID). The FID is fast Fourier transformed and directly digitized on a Tektronix TDS6124C Digital Oscilloscope. 800,000 points of the FID are collected over a time period of 20 µs, where one point is obtained every 25 ps. Measured rotational transitions have an average 12 line width of 80 kHz with an uncertainty of ± 8 kHz in the center frequency. Transitions for all four 13 C isotopologues, as well as ancillary transitions for all of the conformers, were measured with a Balle-Flygare type spectrometer[7]. This instrument has also been formerly described in detail[8, 9]. In short, microwave radiation, lasting 0.9 µs, polarizes the sample concurrently undergoing supersonic expansion. After a delay of 26 µs, the FID of the polarized sample is collected for 102.4 µs and digitized. Between a few hundred and a few thousand averages were collected for each molecular transition, in order to improve the signal-to-noise ratio. The measured transitions have an average line width of 5 kHz with an uncertainty of ± 3 kHz in the center frequency. The sample was purchased from Sigma-Aldrich (≥ 98% CH3 CHICH2 CH3 ) and used without further purification. The volatile liquid sample (boiling point 119-120 ◦ C) was pipetted into a glass U-form tube containing copper beads as a stabilizer. One atmosphere of dry argon (99.999%, Airgas) was bubbled through the sample. This mixture was then pulsed through a solenoid valve into the chamber of the spectrometer, which is held at a pressure of ∼ 10−6 Torr. The molecules in the gas pulse undergo supersonic expansion, leaving them rotationally cold (1-2 K) and in only the lowest energy conformations, but yet, g-, a-, and g0 -conformers were observed. Sample treatment, as described above, was identical for both instruments. 13 Figure 2.1: The experimental rotational spectrum of 2-iodobutane is shown above the baseline and the simulated spectra of the various conformers are shown below. This portion of spectrum illustrates the heavy overlap of the hyperfine structure due to the iodine nucleus in each of the three conformers. The predicted gauche-, anti-, and gauche0 -2-iodobutane transitions are represented by purple, red, and green, respectively. Theoretical transition intensities have been scaled using the relative ab initio energies. 2.3.2 Quantum Chemical Calculations Figure 2.2: Illustrations of the three ab initio structures. The C1 −C2 −C3 −C4 dihedral angles for the a-, g0 -, and g-conformers are 64◦ , -62◦ , and 171◦ , respectively. Quantum chemical calculations were performed using the GAUSSIAN09 Revision A suite[10] to obtain ab initio structures for CH3 CHICH2 CH3 . A coordinate scan at the APFD/321G* level was first employed, in order to determine likely ground state molecular geometries. From this scan, multiple low-energy structures were found. However, only two structures from this calculation were observed in the spectra, which have been labeled as the g- and g0 -conformers. The subsequent structures were optimized at the MP2 level of theory using a 14 6-311G* basis set for the iodine atom, which was imported from the EMSL Basis Set Library[11, 12] and a 6-311G++(2d,2p) basis set for the remaining hydrogen and carbon atoms. An additional calculation for the a-conformer, not obtained in the coordinate scan, was performed at the same level of theory as the other optimizations. Zero point energy (ZPE) corrections were calculated for each optimized structure. Results from the ZPE corrections did not contain any imaginary frequencies, which indicates that these three structures are all true local minima on the potential energy surface. Images of these three ab initio structures are presented in Figure 2.2 and the results of the calculation are presented in Table 2.1. The rotational constants, belonging to the a-, g0 -, and g-conformers, are in basic agreement with the experimental results. Table 2.1: Ab initio results of 2-iodobutane at the MP2 level of theory Parameters a g g0 A (MHz) 6072 3612 4273 B (MHz) 1160 1645 1479 C (MHz) 1014 1189 1248 χaa a (MHz) -812 -684 -650 χbb (MHz) 395 272 287 χcc (MHz) 417 411 363 χab (MHz) -256 -441 -416 χac (MHz) -207 -212 -311 χbc (MHz) -43 -85 -118 ∆Eb (cm−1 ) 166 0 210 ∆EZP E c (cm−1 ) 174 0 237 Dihedral Angle (◦ ) 64 171 -62 a NQCCs resulting from the presence of iodine. b Energies relative to lowest energy conformer. c Energies relative to lowest energy conformer with ZPE corrections. 15 2.3.3 Spectral Assignments The microwave assignments for the three conformers and all four 13 C isotopologues of gauche-2-iodobutane were completed with the aid of Pickett’s SPFIT/SPCAT[13] software. All of the conformers were fit initially from broadband spectra gathered on the chirp-pulse FTMW instrument, where the AABS package[14] was used jointly with Pickett’s programs. Tables 2.2 and 2.3 contain the final spectroscopic constants for the three conformations observed and for the gauche species and its four 13 C isotopologues, respectively. It can be noted that there is approximately a 4% difference between all of the ab initio and experimental rotational constants. The ab initio NQC tensors of iodine are all quite a bit different than the experimental results. The only agreement is in the trend in relative magnitude of the diagonal and off-diagonal NQCCs. The rather poor prediction of the NQC tensor is due to the fact that a core potential was used to estimate the interaction energies of the many core electrons of iodine. For consistency, the experimentally determined off-diagonal NQCCs are presented with signs in agreement with the ab initio values. However, the only certainty that exists about the signs of the off-diagonal terms is that the product of the three off-diagonal elements must be negative[15]. The g-conformer, an asymmetric top with κ = −0.62, contains a dipole moment that projects onto the a-, b-, and c-principal axes. Both the a- and g0 species are near prolate, with κ = −0.94 and κ = −0.85, and also contain a dipole moment with three projections in the principal axis system. Due to the asymmetry and large quadrupolar nuclei present in each species, a rich variety of transition types were observed. Spectral assignments for the a-conformer were based on Q- and R- branch transitions. For the g0 - species, Q-, R-, and S-branch transitions (∆J=+2) were also observed. The fit for the g-conformer included P-, Q-, R-, and S-branch transitions. Figure 2.3 presents an a-type S-branch transition belonging to g-2-iodobutane. The assignments for the four gauche-13 C isotopologues, all present in nat- 16 ural abundance, were based primarily on a-type R-branch transitions. A few b-type R-branch transitions and a S-branch transition, also included in the spectral fits for each species, helped significantly to better determine the A rotational constant. All four of these fits consist of fifteen parameters. However, six parameters, namely the centrifugal distortion constants, DK , d1 , and d2 , and the nuclear spin-molecular rotation constants, Caa , Cbb , and Ccc , were held constant to the parent values. These terms were unable to be fit from the small number of observed transitions belonging to the lowest energy conformation, the g-13 C isotopologues. 13 C isotopologues belonging to the two other conformers were not assigned. The transitions belonging to these species were both lacking in intensity and heavily tangled in a slew of other transitions. 17 Figure 2.3: The Doppler doublet of the a-type S-branch transition, 404 3 2 ← 221 1 2, of the parent conformer of g-2-iodobutane is shown, where the average of each peak is taken to be the transition frequency, 11011.621 MHz. Labels on the y-axis of the plot were omitted, since the intensity of the transition is arbitrary. The transition was measured on a Balle-Flygare type spectrometer with 100 averages, with a signal-to-noise ratio of 76. 2.3.4 Hyperfine Structure The I = 5 2 nuclear spin of iodine, results in the presence of hyperfine structure in the rotational spectrum of 2-iodobutane. The observed hyperfine structure is a result of nuclear quadrupole and spin-rotation coupling. The Hamiltonian that accounts for these complications is of the form[16–18]: 18 Ĥ = ĤR + ĤCD + ĤQ + ĤSR . (2.1) ĤR and ĤCD are the Hamiltonian terms accounting for molecular rotation and centrifugal distortion, respectively. ĤQ is the nuclear quadrupole coupling Hamiltonian, which can be written[19]: X 1 χαβ [I , I ] ĤQ = α β + 2I(2I − 1) (2.2) α,β and then, with some manipulation, this can be written in a form appropriate for use with Pickett’s SPFIT/SPCAT[13]: ĤQ = 1 3 1 1 { χaa [Ia2 − I 2 ] + (χbb − χcc )[I+2 + I−2 ] + χab [Ia Ib + Ib Ia ] 2I(2I − 1) 2 3 4 +χac [Ia Ic + Ic Ia ] + χbc [Ib Ic + Ic Ib ]} (2.3) where the χij terms correspond to the components of the nuclear electric quadrupole coupling tensor. ĤSR , the Hamiltonian that accounts for nuclear spin-rotation coupling can be expanded as[20]: ĤSR = Caa Ia Ja + Cbb Ib Jb + Ccc Ic Jc (2.4) where Cii are the diagonal nuclear spin-rotation constants. Rotational 0 0 00 00 transitions are labeled by quantum numbers of the form JK ← JK 0 0F 00 00 F , a Kc a Kc where F is the total angular momentum quantum number that includes the coupling of spin angular momentum with the rotational angular momentum of the molecule, given by F = I + J . 19 Table 2.2: Spectroscopic parameters of three conformations of 2-iodobutane Experimental a ab initio Parameters a g g0 a g g0 A (MHz) 6276.1041(8)a 3726.51649(11) 4433.8638(7) 6072 3612 4273 B (MHz) 1200.61256(18) 1706.60968(12) 1520.53128(26) 1160 1645 1479 C (MHz) 1049.42041(11) 1231.19182(7) 1287.89606(38) 1014 1189 1248 DJ (kHz) 0.0908(16) 0.3488(14) 0.3546(29) – – – DJK (kHz) – – -0.618(18) – – – DK (kHz) -6.12(25) 1.034(7) 4.54(7) – – – d1 (kHz) -0.0141(11) -0.1256(10) -0.088(4) – – – d2 (kHz) – -0.01970(35) – – – – χaa b (MHz) -1550.634(13) -1329.651(2) -1256.176(6) -812 -684 -650 χbb (MHz) 779.401(12) 582.497(14) 569.007(11) 395 272 287 χcc (MHz) 771.233(17) 747.154(14) 687.169(12) 417 411 363 χab c (MHz) -497.892(35) -822.076(20) -792.17(4) -256 -441 -416 χac (MHz) -452.170(28) -456.84(5) -615.34(6) -207 -212 -311 χbc (MHz) -92.25(7) -176.840(32) -227.51(4) -43 -85 -118 Caa (kHz) 4.0(7) 2.85(11) 2.7(5) – – – Cbb (kHz) 3.74(22) 4.69(12) 4.18(30) – – – Ccc (kHz) 4.47(24) 3.65(7) 3.52(27) – – – Nd 102 212 72 – – – RMSe (kHz) 3.8 2.7 3.0 – – – Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b NQCCs c The resulting from the presence of iodine. relative signs of the off-diagonal NQCCs can not be determined. It is only known that the product of the three, χab , χac , and χbc , must be negative. These terms are presented with signs in agreement with the ab initio results. d Number e Root of transitions used in the fit. r P h mean square deviation of the fit, i (obs − calc)2 /N . 20 Table 2.3: Spectroscopic parameters for g-2-iodobutane Parameters Predictiona g-Parent 13 A (MHz) 3612 3726.51649(11)b 3606.32964(26) 3710.83914(30) 3722.6838(8) 3659.4255(8) B (MHz) 1645 1706.60968(12) 1697.90412(9) 1697.83972(12) 1677.48112(18) 1674.57492(14) C (MHz) 1189 1231.19182(7) 1213.32896(9) 1225.72244(13) 1216.26864(20) 1207.29040(14) 0.3478(24) C1 13 C2 13 C3 13 C4 DJ (kHz) – 0.3488(14) 0.3386(15) 0.3441(20) 0.3385(32) DK (kHz) – 1.034(7) [1.034]g [1.034] [1.034] [1.034] d1 (kHz) – -0.1256(10) [-0.1256] [-0.1256] [-0.1256] [-0.1256] d2 (kHz) – -0.01970(35) [-0.0197] [-0.0197] [-0.0197] [-0.0197] χaa c (MHz) -684 -1329.651(2) -1356.097(13) -1339.391(6) -1323.515(23) -1291.649(17) χbb (MHz) 272 582.497(14) 609.264(14) 589.897(11) 578.842(27) 544.173(20) χcc (MHz) 411 747.154(14) 746.833(19) 749.494(13) 744.672(36) 747.476(27) χab d (MHz) -441 -822.076(20) -789.72(13) -814.05(12) -826.10(33) -864.80(20) χac (MHz) -212 -456.84(5) -460.40(31) -452.34(31) -461.4(7) -451.6(5) χbc (MHz) -85 -176.840(32) -169.526(30) -173.04(17) -180.07(44) -187.00(28) Caa (kHz) – 2.85(11) [2.85] [2.85] [2.85] [2.85] Cbb (kHz) – 4.69(12) [4.69] [4.69] [4.69] [4.69] Ccc (kHz) – 3.65(7) [3.65] [3.65] [3.65] [3.65] Ne – 212 39 58 38 40 f – 2.7 0.8 1.7 1.6 1.2 RMS (kHz) a From MP2 level calculation. b Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. c NQCCs resulting from the presence of iodine. d The relative signs of the off-diagonal NQCCs can not be determined. It is only known that the product of the three, χab , χac , and χbc , must be negative. These terms are presented with signs in agreement with the ab initio results. e f g Number of transitions used in the fit. r P h i 2 Root mean square deviation of the fit, (obs − calc) /N . Numbers in square brackets indicate values held constant to those obtained for parent. 21 2.4 2.4.1 Discussion Structural Determination The five unique sets of rotational constants for g-2-iodobutane, from the parent species and four 13 C isotopologues, allowed for structural determination via isotopic substitution. With the aid of the STRFIT structural fitting program[21], eight selected geometric parameters were obtained using these fifteen spectroscopic rotational constants, where ab initio coordinates served as an initial structure. Table 2.4 lists the four bond lengths, two bond angles, and two dihedral angles that give the structure of the carbon backbone and C−I bond. The C1 C2 -C3 -C4 dihedral angle was determined to be 172.7(16)◦ , thus indicating that the carbon chain is non-planar. The r0 coordinates obtained from this structural fit were used in later calculations, namely when performing a rotation of the quadrupole tensor into the C−I bond. A Kraitchman analysis[22] yielded rs coordinates for the carbon chain, with respect to the principal axes of g-2-iodobutane. This analysis was performed to serve as a confirmation that the positions of the assigned carbons are correct. A comparison between these experimentally derived coordinates and ab initio coordinates is presented in Table 2.5. It should be noted that the c-coordinate for C1 is an imaginary number. Although this coordinate is included in Table 2.5, it is best to assume that it is simply near zero. Table 2.5 also offers a comparison between the Kraitchman analysis and ab initio results, which are in good agreement. 22 Table 2.4: STRFIT r0 structural parameters of gauche-2-iodobutane Bond Length (Å) C1 -C2 1.536(12)a C2 -C3 1.497(6) C3 -C4 1.548(6) I-C2 2.166(4) Bond Angle (◦ ) ∠(C1 -C2 -C3 ) 112.9(10) ∠(C2 -C3 -C4 ) 114.17(23) Dihedral (◦ ) (C1 -C2 -C3 -C4 ) 172.7(16) (I-C2 -C3 -C4 ) -63.85(31) Structural Fit Error a χ2 0.0024 σ 0.018 Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. 23 24 a 2.2422(7) 2.3616(6) C3 C4 1.6019(9) 0.132(11) 0.6646(23) 2.1389(7) |b| 0.113(13) 0.354(4) 0.370(4) 0.052(29)i |c| Values in parentheses give absolute Costain errors of the least significant figure. 1.1801(13) C2 a 1.2170(12) |a| Kraitchman Coordinates C1 Atoms 2.4 2.3 1.2 1.2 a -1.6 -0.15 0.67 2.2 b 0.13 -0.36 0.37 -0.023 c ab initio Gauche Coordinates Table 2.5: Kraitchman versus ab initio coordinates for gauche-2-iodobutane 2.4.2 Nuclear Quadrupole Coupling Tensor of Iodine Upon inspection of Tables 2.2 and 2.3, it is immediately obvious that the elements of the NQC tensor are quite different for each species of 2-iodobutane. These differences are a result of the different orientations of the principal inertial axes in the conformations and isotopologues with respect to the C−I bond. In order to make a meaningful comparison of these tensors, they should all be expressed in individual coordinate systems that are not dependent upon the conformations or the isotopic variations. One such set of frames are those in which the χ tensors themselves are diagonalized. Utilizing Kisiel’s program, QDIAG[23], the complete NQC tensor of iodine was diagonalized for each species of 2-iodobutane. Diagonalization transforms the NQC tensor from the inertial axis system of the molecule to the principal axis system of the quadrupolar nucleus, iodine, in this case. Table 2.6: Conformational comparison of the diagonalized NQC tensor of iodine in 2-iodobutane a Parameters a g g0 χzz (MHz) -1737.458(21)a -1731.291(23) -1730.09(4) χyy (MHz) 881.337(18) 888.384(20) 862.95(4) χxx (MHz) 856.121(20) 842.907(28) 867.14(5) ηχ b 0.014513(16) 0.026268(20) -0.00242(4) Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b ηχ is a measure of the asymmetry of the nuclear quadrupole coupling tensor, where ηχ = χxx −χyy . χzz A comparison of the diagonalized quadrupole tensor, χ, for iodine in each of the three observed conformations is presented in Table 2.6. Comparing values of η χ , which is a measure of the asymmetry of the tensor, in Table 2.6 reveals subtle changes in the electronic nature of the C−I bond, or more specifically, 25 changes in the electric field gradient at the nucleus of the iodine atom, due to conformational differences. A NQC tensor with an η χ of 0 would indicate a cylindrically symmetric tensor. Values of η χ for the a-, g-, and g0 -conformers were 0.014513(16), 0.026268(20), and -0.00242(4), respectively. This parameter indicates that the g0 -conformer is 6 times more “symmetric” than the a-conformer, which is just under twice as “symmetric” as the g-conformer. Interestingly, the order in increasing symmetry between χ for the three conformers follows the trend in the increasing relative ab initio energies between the three conformers. The affect of geometric changes on the NQC tensor can also be seen upon a comparison of χzz between the three conformers. After comparing the final values of χzz for each conformer, at most, only a 0.4% difference was observed. However, more powerful conclusions can be drawn from the values of χzz obtained for 2-iodobutane upon contrasting this work with a series of previous studies on iodoalkanes. Table 2.7 presents a selection of such work. There is a notable trend, namely that the magnitude of χzz decreases with increasing carbon substitution in the iodoalkane. This change in magnitude is more pronounced when the degree of substitution increases on the carbon directly bonded to the iodine atom. More simply put, |χzz | is less for an iodine atom bonded to a secondary carbon than it is for an iodine atom bonded to a primary carbon. This diagonalization is only possible because the complete tensor was determined, which, in turn, was only possible because the iodine χ was large enough that even the off-diagonal terms had spectroscopic consequences. There is only a 0.23% difference between χzz of a-2-iodobutane and isopropyl iodide, which is just under three times less than the difference between χzz of g0 -2-iodobutane and isopropyl iodide, 0.65%. This factor of three can be rationalized by comparing geometric differences between these species. The g0 -conformer simply differs more from isopropyl iodide geometrically than the a-conformer does. These comparisons serve quite nicely to show the sensitivity of the nuclear quadrupole of the iodine atom and its ability to serve as a probe of subtle chemically relevant differences. However, even more subtle changes in the NQC tensor of iodine can be 26 Table 2.7: Comparison of the diagonalized NQC tensor of iodine 2-iodobutane with other iodoalkanes Molecule χzz (MHz) Reference CH3 I -1934.080(10) Wlodarczak et al. [24] CH3 CH2 I -1815.693(210) Boucher et al. [25] trans-CH3 CH2 CH2 I -1814.55(55) Fujitake and Hayashi [26] gauche-CH3 CH2 CH2 I -1805.16(56) Fujitake and Hayashi [26] CH3 CHICH3 -1741.47(75) Ikeda et al. [27] a−CH3 CH2 CHICH3 -1737.458(21) This work g−CH3 CH2 CHICH3 -1731.291(33) This work g0 -CH3 CH2 CHICH3 -1730.09(4) This work noticed by comparing χ of the parent species of g-2-iodobutane with its four 13 C isotopologues. This can be seen in Table 2.8. A comparison of ηχ between these five isotopic species reveals agreement, at least within range of their respective errors. 13 C isotopic substitution seems to have no noticeable affect on the asymmetry of the NQC tensor of iodine in g-2-iodobutane. Although there may be no affect in this regard, the values of χzz seem to suggest a change in the projection of the NQC tensor along the z-axis of the iodine nucleus when the directly bonded to iodine is substituted with a the difference in χzz between the parent and 13 13 12 C nucleus C nucleus. When comparing C2 isotopologue, the change in χzz is 200 kHz. This is just over a factor of two greater than the largest change observed for any of the other isotopologues, where the values of χzz between the parent and 13 C1 , 13 C3 , and 13 C4 isotopologues only vary by 40 to 80 kHz. Multi- ple causes for this discrepancy were investigated in order to rationalize this very small difference. First, the presence of additional nuclear spin-rotation interactions, due to the the magnetic moment of the 13 C nucleus, were investigated. However, the 27 Table 2.8: Rotation of the diagonalized NQC tensor of iodine into the principal axis system of g-2-iodobutane a 13 13 C1 13 C2 13 Parameters g-Parent C3 C4 χzz (MHz) -1731.291(23)a -1731.21(14) -1731.49(13) -1731.24(34) -1731.25(23) χyy (MHz) 888.384(20) 888.34(8) 888.61(9) 888.60(24) 888.51(16) χxx (MHz) 842.907(28) 842.88(14) 842.89(14) 842.63(35) 842.74(25) ηχ b 0.026268(20) 0.02626(9) 0.02640(10) 0.02655(25) 0.02644(17) Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b ηχ is a measure of the asymmetry of the nuclear quadrupole coupling tensor, where ηχ = χxx −χyy . χzz inclusion of these terms in the Hamiltonian of this isotopologue both did not fit or counterbalance the change in χzz of the 13 C2 isotopologue. Further evidence against the presence of this interaction was provided by the fact that the other three isotopic species yielded values of χzz nearly identical to the parent value without the addition of these terms in their respective Hamiltonians. Second, an additional spin-spin interaction between (I = 52 ) may be present. No change in χzz of the 13 13 C (I = 12 ) and 127 I C2 isotopologue ensued as a result of including this term in the Hamiltonian. The term was deemed negligible, as it did not fit well and was only on the order of 2 kHz. After a missing term in the Hamiltonian of the 13 C2 isotopologue was eliminated as a cause for this change, the discrepancy in χzz , between the parent species and this isotopologue, can be attributed to the most obvious effect, the increased mass of the carbon atom directly bonded to the iodine. Upon 13 C isotopic substitution, the vibrationally averaged C−I bond length should decrease. The fact that the z-axis of the diagonalized nuclear electronic quadrupole tensor is under 2◦ from the C−I bond axis certainly helped to make such an observation possible. A further ab initio study was performed, to determine the normal mode vibration frequencies of g-2-iodobutane. The bond length was scaled using the normal mode frequency that is closest to the “pure” C−I stretch, 599 cm−1 , and 28 the approximation that the reduced mass of the stretch was the reduced mass of 12 C − 127 I or 13 C − 127 I. A decrease in bond length of 1.8 mÅ was found, which was used to scale the 13 C − 127 I bond length. An energy calculation was then performed on this slightly altered structure, at the same level of theory as all previous quantum chemical calculations, to predict the change in the NQCCs. Table 2.9 presents χ for each of the two species in question with more significant figures than are typically presented because the comparison being made is only among ab initio values, so the errors in the magnitudes cancels out to first order. A decrease in χzz of 300 kHz was determined for a bond length decrease of 1.8 mÅ. Thus our measured decrease of 199(13) kHz suggests a C−I bond length decrease of approximately 1.2 mÅ upon 13 C isotopic substitution. Table 2.9: Changes in the ab initio NQC tensor due to isotopic substitution Parent 2.5 13 C Bond Length Correction χzz (MHz) -896.4 -896.7 χyy (MHz) 444.5 444.7 χxx (MHz) 451.9 452.1 Conclusion Utilizing high-resolution rotational spectroscopy, an intensive investigation of three conformers and four 13 C isotopologues of 2-iodobutane allowed for many chemically relevant parameters of this haloalkane to be determined. The observed hyperfine structure led to the complete determination of the NQC tensor of iodine in seven different species of 2-iodobutane. In this way, iodine served as a probe of the subtle differences in these species, resulting from both isotopic and geometric differences. 29 2.6 Acknowledgements The authors thank Wallace (Pete) Pringle for many useful discussions. The cluster at Wesleyan University is supported by the NSF under CNS-0619508. The Pacific Northwest National Laboratory is operated for the United States Department of Energy by the Battelle Memorial Institute under contract DEAC05-76RLO 1830. 2.7 Supplemental Information Final fit outputs for the a-, g-, and g0 -parent species, in addition to the four 13 C isotopologues of the g0 -conformer, can be found at doi:10.1021/acs.jpca.6b06938. References [1] R. T. Morrison, R. N. Boyd, Organic Chemistry, 3 ed., Allyn and Bacon, Inc., Boston, 1973. [2] W. E. Steinmetz, F. Hickernell, I. K. Mun, L. H. Scharpen, J. Mol. 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Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian-09 revision d.01, 2013. Gaussian Inc. Wallingford, CT 2009. [11] D. Feller, J. Comput. Chem. 17 (1996) 1571–1586. [12] K. L. Schuchardt, B. T. Didier, T. Elsethagen, L. Sun, V. Gurumoorthi, J. Chase, J. Li, T. L. Windus, J. Chem. Inf. Model. 47 (2007) 1045–1052. [13] H. M. Pickett, J. Mol. Spectrosc. 148 (1991) 371–377. [14] Z. Kisiel, L. Pszczólkowski, I. R. Medvedev, M. Winnewisser, F. C. De Lucia, E. Herbst, J. Mol. Spectrosc. 233 (2005) 231–243. [15] U. Spoerel, H. Dreizler, W. Stahl, Zeitschrift für Naturforschung A 49 (1994) 645–646. [16] P. Thaddeus, L. Krisher, J. Loubser, J. Chem. Phys. 40 (1964) 257–273. [17] D. Posener, Austr. J. Phys. 11 (1958) 1–17. 31 [18] D. Boucher, J. Burie, D. Dangoisse, J. Demaison, A. Dubrulle, J. Chem. Phys. 29 (1978) 323–330. [19] E. Hirota, J. M. Brown, J. Hougen, T. Shida, N. Hirota, Pure Appl. Chem. 66 (1994) 571–576. [20] W. Gordy, R. L. Cook, Microwave Molecular Spectra, Wiley, New York, 1984. [21] Z. Kisiel, J. Mol. Spectrosc. 218 (2003) 58–67. [22] J. Kraitchman, Am. J. Phys. 21 (1953) 17–24. [23] Z. Kisiel, Prospe–programs for rotational spectroscopy, 2000. [24] G. Wlodarczak, D. Boucher, R. Bocquet, J. Demaison, J. Mol. Spectrosc. 124 (1987) 53–65. [25] D. Boucher, A. Dubrulle, J. Demaison, J. Mol. Spectrosc. 84 (1980) 375–387. [26] M. Fujitake, M. Hayashi, J. Mol. Spectrosc. 127 (1988) 112–124. [27] C. Ikeda, T. Inagusa, M. Hayashi, J. Mol. Spectrosc. 135 (1989) 334–348. 32 Chapter 3 A Study of the Conformational Isomerism of 1-Iodobutane by High Resolution Rotational Spectroscopy This chapter has been published in the Journal of Molecular Spectroscopy prior to the compilation of this thesis. The author list is as follows: Eric A. Arsenault, Daniel A. Obenchain, Thomas A. Blake, S. A. Cooke, and Stewart E. Novick. The publication is E. A. Arsenault, D. A. Obenchain, T. A. Blake, S. A. Cooke, S. E. Novick, J. Mol. Spec. (2017). doi:10.1016/j.jms.2017.03.014. 3.1 Abstract The first microwave study of 1-iodobutane, performed by Steinmetz et al. in 1977, led to the determination of the B + C parameter for the antianti- and gauche-anti-conformers. Nearly 40 years later, this reinvestigation of 1-iodobutane, by high-resolution microwave spectroscopy, led to the determination of rotational constants, centrifugal distortion constants, nuclear quadrupole coupling constants (NQCCs), and nuclear-spin rotation constants belonging to 33 both of the two previously mentioned conformers, in addition to the gauchegauche-conformer, which was observed in this frequency regime for the first time. Comparisons between the three conformers of 1-iodobutane and other iodo- and bromoalkanes are made, specifically through an analysis of the nuclear quadrupole coupling constants belonging to the iodine and bromine atoms in the respective chemical environments. 3.2 Introduction It has been commonly accepted that the electric field gradient of a nucleus remains unchanged in most simple molecules even as they take on different conformations or as they form van der Waals complexes. A field gradient caused by a charge is proportional to 1/r3 , where r is the distance from the charge to the nucleus. It is presented by Townes and Dailey[1] and outlined in Gordy and Cook[2], how the field gradient found at a nucleus can be assumed to have been produced by the bonds made by that atom. This analysis was originally for bonding p orbitals, but was later extended to include hybrid orbital contributions by Novick in 2011[3]. This unchanging nature of a field gradient was recently used to correctly determine the structure of HOD−N2 O[4]. The assumption that the field gradient will remain unchanged upon the formation of a complex, conformational change, or isotopic substitution has, of course, exceptions. Choosing N2 O and the complexes it forms as an example[5– 16], it was shown repeatedly that there are sublte changes in the electronic environment of near atoms as complexes are formed. For HCCH· · · N2 O[5, 7], as studied by Leung and coworkers, it was shown that in forming the complex there is a significant change in the electric field gradient of the central nitrogen, while the field gradient at terminal nitrogen remained unchanged. Through molecular multipole analysis, the authors showed that this change is caused by redistribution of electrons about the central nitrogen. To observe changes in electronic structure from perturbations smaller in 34 magnitude than those observed upon forming a van der Waals complex, such as conformational changes, a more sensitive nucleus is required to act as a probe for this change. Iodine, with its large nuclear electric quadrupole moment, −69.6(12) f m2 [17] for 127 I, compared to the 14 N value of 2.001(10) f m2 [18], makes the observed nuclear quadrupole coupling constants significantly more sensitive to small changes in electron distribution near the iodine nucleus. For example, in a recent study of iodobenzene and the Ne-iodobenzene complex[19], there is a < 0.3% change in the iodine NQCC upon forming the complex with neon. We have recently reported a small, but significant, change in electronic structure from carbon-13 isotopic substitution in 2-iodobutane[20]. Continuing a series of studies on the subtle changes in electric structure determined by changes in nuclear quadrupole coupling constants, we report here on the conformational effects on a terminal iodine group in a hydrocarbon chain. 3.3 Experimental The high-resolution rotational spectrum of 1-iodobutane was measured from 7-13 GHz with a chirped-pulse Fourier transform microwave (FTMW) spectrometer. Detailed specifications of this spectrometer, which is based on the design of Pate and coworkers[21], have been presented previously[22]. In short, a chosen microwave center frequency, ν, and a 6 µs linear frequency sweep are mixed from DC to 1 GHz. The resulting radiation, ν ± 1 GHz, is broadcast directly into a vacuum chamber through a microwave horn antenna. This transmitted radiation then induces a polarization in the coincident molecular beam. A second microwave horn antenna collects the free induction decay (FID) after a 1 µs delay. With the aid of a Tektronix TDS6124C Digital Oscilloscope, the FID is fast Fourier transformed and directly digitized. A total of 800,000 points, over a time of 20 µs, are collected from the FID. On average, the molecular rotational transitions have a line width of 80 kHz with an uncertainty of |8| kHz in the center 35 frequency. R The sample was acquired from Sigma-Aldrich (≥ 99% CIH2 CH2 CH2 CH3 ). Further purification was not necessary. The sample (bp 130-131 ◦ C) was contained in a glass U-form tube at room temperature and one atmosphere of dry R argon (99.999%, Airgas ) was bubbled directly through the liquid. The final mixture of carrier gas and sample was pulsed through a solenoid valve into the chamber, held at an ambient pressure of 10−6 Torr, allowing the molecules to undergo supersonic expansion, where the molecules become rotationally cold (1-2 K). 3.3.1 Quantum Chemical Calculations Using a 321G* basis set at the APFD level of theory, a coordinate scan of the C−C−C−C and C−C−C−I dihedral angles was performed, in order to identify the most probable ground state molecular geometries. Three of the lowest energy structures from the scan were optimized at the MP2 level of theory. A 6311G* basis set was imported from the EMSL Basis Set Library[23, 24] specifically chosen to handle the iodine atom, while a 6311G++(2d,2p) basis set was used for the remaining carbon and hydrogen atoms. All calculations were performed with the GAUSSIAN09 Revision D suite[25]. Results from the ab initio optimizations are presented in Table 3.1. Illustrations of the corresponding structures can be found in Figure 3.1. More on predicting the NQCCs will be discussed in the subsequent sections. 3.3.2 Spectral Assignments All three of the lowest energy conformers obtained from the ab initio investigation were successfully assigned from the rotational spectrum collected in the frequency range of 7-13 GHz. A 70 MHz portion of this spectrum is shown in Figure 3.2. The three broadband assignments were accomplished with the help of both the AABS package[26] and Pickett’s programs, SPFIT/SPCAT[27, 28]. The 36 Table 3.1: Rotational constants and NQCCs for three conformers of 1-iodobutane as determined from ab initio optimization at the MP2 level of theory Parameters gg ga aa A (MHz) 6033 7388 15123 B (MHz) 1077 937 706 C (MHz) 1013 867 686 -397 -274 -682 χbb (MHz) 74 -167 223 χcc (MHz) 322 441 459 χab (MHz) -570 -670 -511 χac (MHz) -330 -109 0b χbc (MHz) -226 -104 0 ∆Ea (cm−1 ) 385 160 0 127 I χaa (MHz) 127 I 127 I 127 I 127 I 127 I a Relative energies from MP2 optimizations. b χac and χbc are zero by symmetry. Figure 3.1: Calculated structures of the anti-anti (aa)-, gauche-anti (ga)-, and gauchegauche (gg)-conformers of 1-iodobutane from an ab initio optimization. The C−C−C−C and C−C−C−I dihedral angles for the aa-, ga-, and gg-species were calculated to be 180◦ , 180◦ ; 179◦ , 66◦ ; and -65◦ , -63◦ . 37 Figure 3.2: A small portion of the experimental spectrum of 1-iodobutane is shown in black, with the final simulated spectra for the aa-, ga-, and gg-conformers shown below in green, purple, and red, respectively. The quantum numbers associated with each rotational transition 00 0 00 0 ← JK are also presented above the experimental spectrum, in the form JK 00 00 F . 0 0F a Kc a Kc Figure 3.3: A 100 MHz portion of three different predictions of the rotational spectrum of aa-1-iodobutane. The top orange spectrum is based on a hybrid tensor (discussed in Spectral Assignments) and ab initio rotational constants, the middle blue spectrum is the prediction using the experimental results belonging to the aa-conformer, and the bottom orange spectrum is based completely on ab initio results. 38 Table 3.2: Spectroscopic parameters of 1-iodobutane a Parameters gg ga aa A (MHz) 5917.262(13)a 7532.3121(18) 15052.043(9) B (MHz) 1162.2040(14) 970.51215(26) 732.93002(18) C (MHz) 1082.7921(12) 896.60780(18) 711.34567(20) DJ (kHz) 0.816(10) 0.2058(24) 0.0459(11) DK (kHz) 34.9(38) 45.8(4) – DJK (kHz) -7.18(5) -4.450(18) -2.867(17) d1 (kHz) -0.133(12) -0.0302(6) – d2 (kHz) – 0.0122(14) – χaa (MHz) -752.593(28) -521.973(12) -1294.041(34) χbb (MHz) 157.01(5) -337.242(15) 380.05(6) χcc (MHz) 595.58(6) 859.216(19) 913.99(7) χab b (MHz) -1116.74(13) -1331.251(23) -1070.28(6) χac (MHz) -692.17(19) -226.66(13) 0e χbc (MHz) -460.66(12) -235.95(6) 0 Caa (kHz) – 6.4(15) 15(4) Cbb (kHz) 3.43(7) 0.89(27) 1.8(8) Ccc (kHz) – 1.66(26) 2.7(8) Nc 74 198 136 RMSd (kHz) 6.4 7.3 6.4 Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b The signs of the off-diagonal nuclear quadrupole coupling constants can not be exactly determined. It is only known that the product of the three, χab , χac , and χbc , must be negative. These terms are presented with signs in accordance with the ab initio results. c Number d Root eχ ac of transitions used in the fit. r P h i (obs − calc)2 /N . mean square deviation of the fit, and χbc are zero by symmetry. 39 final rotational constants, centrifugal distortion constants, NQCCs, and nuclear spin-rotation constants for each conformer can be found in Table 3.2. Although there is a large discrepancy between the ab initio and experimental NQC tensors belonging to the iodine atom in each of the three species, there is at most only a 7% difference between the rotational constants obtained from the ab initio study and those determined experimentally. This seems to suggest that the actual geometries of the three conformers present in the molecular beam are quite similar to those that were calculated, whereas the only agreement in the NQCCs was in the trend of their respective magnitudes. The poor ab initio NQCC values made the first assignment, of the gaconformer, quite challenging. In order to make the assignment process more efficient and less tedious, alternate methods of prediction were employed. Taking advantage of the fact that changes in the geometry of the butane chain have a very small effect on the electric field gradient at the iodine nucleus (more on this to come later), the experimental NQC tensor of iodine in the ga-conformer was used to make predictions of the NQC tensors of iodine in both of the two remaining unassigned conformers. This predictive process was simply an exercise in tensor rotation. Using QDIAG[29], the ab initio tensors of the two unassigned conformers were diagonalized. In doing this, the rotation matrices, specific to the ab initio geometries of these species, were obtained. Then, these respective rotation matrices were used to transform the experimental NQC tensor of the ga-conformer into the inertial axes systems of the gg- and aa-conformers. The resulting hybrid tensors were based on ab initio geometries, specific to the unassigned conformers, and experimental NQCCs, belonging to the already assigned ga-conformer. To best illustrate the power of this method, the NQC tensor predictions of the aa-conformer will used as an example. Equation (1) contains the ab initio tensor belonging to the aa-conformer, Equation (2) contains the hybrid tensor, and Equation (3) contains the experimental tensor based only on rotational transitions belonging to the aa-conformer. It is perhaps immediately obvious that the hybrid tensor, again based on the ab initio geometry of the aa-conformer and 40 the rotated experimental NQC tensor of the ga-conformer, offers a much better prediction than the purely ab initio tensor. To further highlight this point, Figure 3.3 presents small portions of the rotational spectra corresponding to these respective tensors. It is worth noting here that the similarities between the NQC tensors of iodine in various iodoalkanes, such as iodoethane, t-1-iodopropane, and aa-1-iodobutane, which will be discussed later, suggest that this method can be applied to quite a large range of problems. This method, based on straightforward linear algebra, can lead to very accurate predictions without the need for expensive computations. It should be noted there are other methods used to make accurate predictions of NQQCs, especially for species with large quadrupoles, as shown by Professor W. C. Bailey[30]. Post-analysis, we received calculations from Professor Bailey, which can be found in Table 3.3 alongside the predictions from our hybrid approach[31, 32]. These calculations involve the calibration of a specific combination of level of theory and basis set, by linear regression, of the calculated electric field gradients versus the experimental NQCCs of a selected group of molecules. Once calibrated, the specific combination of level of theory and basis set can be applied to other systems. Upon comparison of Table 3.2 and Table 3.3, it can be seen that this method yields excellent results. The differences between the hybrid method explained previously and these calculations are small. Although it is clear that these calculations are quite accurate, the hybrid method can rapidly provide good predictions based on very computationally inexpensive optimizations.  −682 −511 0      χM P 2 =  −511 223 0    0 0 459   −1346 −1019 0     χhybrid =  −1019 462 0    0 0 884 41 (3.1) (3.2)  χexp −1294.041(34) −1070.28(6) 0   =  −1070.28(6) 380.05(6) 0  0 0 913.99(7)      (3.3) Table 3.3: Comparison of the two methods of prediction for the NQC tensors in 1-iodobutane MP2/6311+G(d,p)a gg ga aa gg gab aa -757 -546 -1317 -706 – -1346 χbb (MHz) 164 -314 400 104 – 462 χcc (MHz) 593 860 917 602 – 884 χab (MHz) -1119 -1336 -1062 -1025 – -1019 χac (MHz) -702 -234 0c -632 – 0c χbc (MHz) -464 -238 0 -367 – 0 Parameters 127 I χaa (MHz) 127 I 127 I 127 I 127 I 127 I a Hybrid Method These calculations were performed by Professor W. C. Bailey with the calibrated MP2/6311+G(d,p) combination[31, 32]. b These values were not predicted via the hybrid method, as the experimental NQC tensor of the ga-conformer was used to make the predictions for the other two conformers. Rather, the NQC tensor presented in Table 1 was used. c Zero by symmetry. 3.3.3 Theory The hyperfine structure in the rotational spectrum of 1-iodobutane is a consequence of the nuclear spin of iodine (I = 52 ), which allows for the observation of both nuclear quadrupole coupling and nuclear spin-rotation coupling. The respective Hamiltonians, which account for these interactions, were combined with both the rigid rotor and centrifugal distortion Hamiltonians. The final form of the Hamiltonian then becomes[20, 33–35]: Ĥ = ĤR + ĤCD + ĤQ + ĤSR . 42 (3.4) Quantum labels for the rotational transitions belonging to 1-iodobutane 00 0 00 0 are as follows: JK 0 F ← JK 00 K 00 F , where F = I + J . The quantum number F 0 a c a Kc is the total angular momentum quantum number that accounts for the coupling between the nuclear spin of iodine and the rotational angular momentum of the molecule. 3.4 Discussion Table 3.4: Comparison of this work with the previous study of 1-iodobutane Parameters a This work. Steinmetz et al.[36] ga B + C (MHz) 1867.11995(32) 1868.4(30)a aa B + C (MHz) 1444.27569(27) 1445.3(4) gg B + C (MHz) 2244.9961(18) Not observed. Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. For the first time since 1977, 1-iodobutane was reinvestigated via microwave spectroscopy. Table 3.4 presents a comparison between this study and the work of Steinmetz et al.[36] In the previous low-resolution microwave study, the B + C parameter was measured for the ga- and aa-conformers. Between studies, the measured values of B + C are within 0.07% for both the ga-conformer and aa-conformer. In this study, the gg-conformer was spectroscopically detected in this frequency range for the first time, although previous work[36] did indicate that this species should likely be present in low abundance, as the highest energy conformer of the three. Due to the flexible nature of this molecule, the three observed conformers possess quite different rotational constants. This is most evident upon noting that the difference between the A rotational constant of the heavy atom planar aa-conformer and the highly asymmetric ga-conformer is over 9100 MHz, as seen in Table 3.2. As expected, the large structural differences between these 43 Table 3.5: NQC tensor of iodine in 1-iodobutane Parameters gg ga aa Energies (cm−1 )a 385 160 0 χzz (MHz) -1758.57(14)b -1804.133(35) -1815.72(6) -3.15%c -0.64% – 1182.40(19) 920.04(9) 901.73(7) +31.13% +2.03% – 576.17(16) 884.09(11) 913.99(7) -36.96% -3.27% – 0.34473(15) 0.01993(8) -0.00675(6) χyy (MHz) χxx (MHz) ηχ d a From Table 1. b Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. c Percentage change relative to the corresponding component of the lowest energy aa-conformer. d ηχ is a measure of the asymmetry of the nuclear quadrupole coupling tensor, where ηχ = χxx −χyy . χzz 44 Table 3.6: NQC tensor of bromine in 1-bromobutane[37] Parameters 79 Br 79 Br 79 Br gg ga aa χzz (MHz) 536.2(5)a 539.7(6) 543.45(34) χyy (MHz) -264.9(6) -264.9(20) -269.5(6) χxx (MHz) -271.29(36) -274.8(15) -274.0(9) -0.0119(13) -0.018(5) -0.0083(21) χzz (MHz) 448.3(47) 451.1(9) 453.95(35) χyy (MHz) -222.0(19) -220.2(23) -225.5(7) χxx (MHz) -226.3(39) -231.0(19) -228.4(9) -0.01(1) -0.024(7) -0.0065(24) ηχ b 81 Br 81 Br 81 Br ηχ a Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b ηχ is a measure of the asymmetry of the nuclear quadrupole coupling tensor, where ηχ = χxx −χyy . χzz three conformational isomers, resulting from differences in the I−C−C−C and C−C−C−C dihedral angles, do not translate to substantial variations in the chemical environment at the iodine nucleus. The most meaningful quantification of the differences between these chemical environments or more specifically, the electric field gradient at the iodine nucleus, can be made through a comparison of the various diagonalized nuclear quadrupole coupling tensors, χ, where χ is a projection of the NQC tensor in the principal axis system of the quadrupolar nucleus (e.g. iodine), as opposed to a projection of the tensor in the inertial axis system of the molecule. The advantage of comparing these diagonalized tensors is that they are all projections into an axis system which is independent of the conformation. Table 3.5 presents the diagonalized χ tensor of iodine in each conformer. Diagonalization was performed with QDIAG[29]. It should be noted that the χzz element is the best means of comparison because it is the projection of χ onto the z-axis of the nuclear quadrupole, which is pointed nearly along the 45 Table 3.7: A comparison of this work with similar haloalkanes 127 I 127 I 127 I iodoethane[38] t-1-iodopropane[39] aa-1-iodobutane χzz (MHz) -1815.22(85)a -1814.55(55) -1815.72(6) χyy (MHz) 901.71(81) 900.44(47) 901.73(7) χxx (MHz) 913.50(26) 914.12(44) 913.99(7) -0.0065(6) -0.0075(5) -0.00675(6) bromoethane[38] t-1-bromopropane[40] aa-1-bromobutane[37] χzz (MHz) 544.03(168) 541.6(7) 543.45(34) χyy (MHz) -270.32(166) -267.8(7) -269.5(6) χxx (MHz) -273.71(17) -273.79(4) -274.0(9) -0.0062(34) -0.0111(12) -0.0083(21) bromoethane[38] t-1-bromopropane[40] aa-1-bromobutane[37] χzz (MHz) 453.91(203) 451.9(7) 453.95(35) χyy (MHz) -225.25(201) 223.1(7) -225.5(7) χxx (MHz) -228.65(18) -228.77(4) -228.4(9) -0.0075(48) -0.0125(16) -0.0065(24) ηχ b 79 Br 79 Br 79 Br ηχ 81 Br 81 Br 81 Br ηχ a Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b ηχ is a measure of the asymmetry of the nuclear quadrupole coupling tensor, where ηχ = χxx −χyy . χzz 46 C−I bond, whereas the orientation of the x- and y-axis are not known. While the differences in the rotated NQC tensor elements of the three conformers are small, they are never the less significant, as can be seen in Table 3.5. Upon inspection, only a 3.15% difference between χzz of the gg- and aa-species is observed, even though the geometry of the alkane chain is drastically different in each case. Even smaller differences in χzz , of 2.56% and 0.64%, are present when comparing the remaining two pairs of conformers, namely the gg- versus the ga-species, and the ga- versus the aa-species, respectively. This is purely a reflection of the fact that the two latter pairs of conformers possess more similar geometries than the first pair that was mentioned. This indicates that there is hardly a change in the electric field gradient at the iodine nucleus upon rather significant conformational changes. Similar comparisons, based on a study by Kim et al., between the χzz element of χ belonging to both 79 Br and 81 Br in the gg-, ga-, and aa-species of 1bromobutane were made[37]. These tensors are presented in Table 3.6. At most, a 0.7% difference between the 81 Br gg- and aa-species was determined, which is just over four and a half times less than the percent difference found between the iodine gg- and aa-species. The greater differences between the χzz elements of the 1-iodobutane conformers is as expected and can be explained simply by the fact that iodine is both larger and more polarizable than bromine[41]. Additional comparisons were made between progressively longer haloalkanes, namely iodoethane, t-1-iodopropane, aa-1-iodobutane, and the corresponding bromine analogs. These NQCCs are presented in Table 3.7. In order to complete Table 3.7, the NQCCs belonging to t-1-bromopropane were measured by highresolution microwave spectroscopy because these values could not be found in the previous work on this species by Sarachman[42]. Table 3.7 shows clearly that the NQC tensors of iodine in each of these progressively longer haloalkanes are identical, within experimental error. Unsurprisingly, additional terminal carbon atoms seem to have a very small effect on the electric field gradient at the iodine nucleus. Upon investigating the differences in the bromine analogs, the same 47 conclusion can be realized. Although this does not necessarily present itself as a surprise, one curious trend did emerge. If closer attention is payed to Table 3.7, it can be seen that although the tensors amongst alkanes with identical halogen substituents are the same, within experimental error, the tensors belonging to iodine, 79 Br, and 81 Br are in better agreement between the ethane and butane chains than between the ethane and propane chains or the propane and butane chains. However, this trend remains inconclusive because the NQCCs belonging to 35 Cl and 37 Cl in aa-1-chlorobutane have yet to be obtained. Additionally, NQC tensors belonging to longer iodine- and bromine-containing alkanes have also yet to be measured, due to the fact that collecting and measuring spectra for progressively longer haloalkanes becomes more and more challenging. 3.5 Conclusion The reinvestigation of 1-iodobutane by high-resolution microwave spectroscopy in the frequency range of 7-13 GHz led to the determination of rotational constants, centrifugal distortion constants, nuclear quadrupole coupling constants, and nuclear-spin rotation constants for three low energy conformations. The full NQC tensor of iodine in each conformation was obtained, which allowed for comparisons to be made between the chemical environments of these conformers, as well as other similar haloalkanes. 3.6 Acknowledgments The authors thank Professor Wallace (Pete) Pringle for many useful discussions and Professor W. C. Bailey for the calculations that he shared. This work was supported at Wesleyan University by NSF grant CHE-1565276. 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Novick, Private communication, 2016. [41] E. V. Anslyn, D. A. Dougherty, Modern Physical Organic Chemistry, University Science Books, 2006. [42] T. Sarachman, in: International Symposium on Molecular Spectroscopy, Ohio State University, 1968, p. N7. 52 Chapter 4 Nuclear Quadrupole Coupling in SiH2I2 due to the Presence of Two Iodine Nuclei 4.1 Abstract The rotational spectrum of diiodosilane was measured with a jet-pulsed, cavity Fourier transform microwave (FTMW) spectrometer over the frequency range 8.8 GHz to 15 GHz and assigned for the first time. The complete nuclear quadrupole coupling (NQC) tensors for both iodine nuclei were obtained for the 28 Si, 29 Si, and 30 Si isotopologues of diiodosilane. In addition to the nuclear quadrupole coupling constants (NQCCs), rotational constants, centrifugal distortion constants, and nuclear spin-rotation constants were determined for each silicon isotopologue. Subtle, yet unmistakable, changes in the NQCCs of iodine upon isotopic substitution were observed and will be discussed. A r0 structure of diiodosilane was also fit via isotopic substitution, which led to the determination of bond lengths and angles: r0 (Si−I) = 2.4236(19) Å, r0 (Si−H) = 1.475(21) Å, ∠(I−Si−I) = 111.27(13)◦ , and ∠(I−Si−H) = 105.9(19)◦ . These molecular parameters will be compared to the results of a previous gas electron diffraction 53 study. 4.2 Introduction Halosilanes of the form SiY4−n Xn , with Y = HF ; X = ClBrI ; n = 2, 3, remain vastly understudied by microwave, millimeter wave, and submillimeter wave spectroscopy, especially when compared to the carbon analogs, CY4−n Xn , of these species. To date, five halosilanes that meet this criteria have been studied, none of which include even one iodine atom[1–11]. However, over the same time period, thirteen halomethanes with at least two quadrupole-containing halogen substituents (these include: Cl, Br, and I[12]) have been the subject of over 50 studies by similar spectroscopic techniques[13–69]. Additionally, out of all eighteen of the previously mentioned halosilanes and halomethanes, only a select few were found to be the focus of spectroscopic studies in the terahertz, far infrared, and infrared frequency regimes[70–76]. Perhaps more notably, fewer than half a dozen molecules that contain both a silicon and an iodine atom have been studied by microwave spectroscopy throughout the 64 years previous to the work presented in this paper[77–86]. This work aims to fill that gap. The molecule that is the focus of this paper, diiodosilane, is the first halosilane with two iodine substituents and the third molecule with two iodine substituents, the first being diiodomethane[66] and the second being difluorodiiodomethane[69], to be studied by high-resolution microwave spectroscopy. High-resolution microwave studies of iodine-containing silanes allow for the measurement of complete 127 I nuclear quadrupole coupling (NQC) tensors. These tensors contain an abundance of information about the Si−I bond, as will be discussed throughout the course of this paper. One method of deducing the chemical nature of the Si−I bond through these tensors is the Townes-Dailey analysis[87–89], the implications of which will be examined for the mono-, di-, and tetraiodosilane series. Alongside this analysis, twelve spectroscopic parameters for 54 each silicon isotopologue of diiodosilane and a r0 structure for this molecule will be presented. 4.3 Experiment R The diiodosilane sample (Sigma-Aldrich ) was held in a glass U-form tube R and 760 torr of dry argon (99.999 %, Airgas ) was bubbled through the liquid. The resulting mixture was pulsed through a solenoid valve into the chamber of a Balle-Flygare type spectrometer, which freatures a Fabry-Perot cavity[90, 91]. A microwave pulse of 0.9 µs duration then polarized the sample. Following a 26 µs delay, the free induction decay (FID) was collected for 102.4 µs and digitized. A few hundred to a few thousand averages were collected for each each rotational transition, in order to achieve a satisfactory signal-to-noise ratio. The average line width of a transition is 5 kHz and the uncertainty in the center frequency is |3| kHz. Further details on this instrument can be found elsewhere[92, 93]. 4.4 Spectral Assignments In order to assign the complex hyperfine structure belonging to SiH2 I2 , an amalgam of predictive techniques, including scaling, quantum chemical calculations, and tensor rotations were employed. Rotational constants, based on the r0 gas phase structure obtained by Altabef et al.[94], were calculated using the Gaussian 09 Revision A suite[95] at the MP2 level of theory. A 6-311G* basis set, imported from the EMSL Basis Set Library[96, 97], was used for the iodine atom and a 6-311G++(2d,2p) basis set was used for the remaining silicon and hydrogen atoms. Scaled NQCCs were predicted using the ratio presented in equation (1). It is important to note here that scaling was performed with the elements of the diagonalized 127 I NQC tensors, χ, in each of the three species, CH3 I, CH2 I2 , and SiH3 I, to ensure that the tensors were all independent of specific molecular 55 geometries[98]. Table 4.1 presents the values used for scaling, as well as the resulting prediction of the NQC tensor of iodine in SiH2 I2 . χCH3 I χSiH3 I = χCH2 I2 χSiH2 I2 (4.1) Table 4.1: Results obtained from equation (4.1) CH3 I[99] CH2 I2 [66] SiH3 I[80]b SiH2 I2 a χzz (MHz) -1934.1306(51) -2030.1(5) -1245.1 -1306.9 χyy (MHz) 967.0635(36) 1036.66(9) 622.55 667.3 χxx (MHz) 967.0635(36) 993.4(10) 622.55 600.9 Parameters 127 I 127 I 127 I a Method of prediction described in detail in section on Spectral Assignments. These are not ab initio predictions. b No error reported. The scaled NQC tensor was then projected into the inertial axis frame of the r0 gas phase structure by using the rotation matrix obtained through diagonalization of the NQC tensor from the MP2 optimization. Diagonalization was performed with QDIAG[100]. The results of this prediction can be found in Table 4.2. Spectral assignments, in the frequency range of 8.8 GHz to 15 GHz, were completed with the AABS package[101] and Pickett’s programs, SPFIT/SPCAT[102, 103]. The coupling scheme used to assign the hyperfine structure was F1 = I1 + J and F2 = I2 + F1 where I1 and I2 are both 52 , the nuclear spin of iodine, and 0 0 0 00 00 00 quantum labels took on the form: JK ← JK 0 0F F 00 00 F1 F2 . Rotational cona Kc 1 2 a Kc stants, centrifugal distortion constants, nuclear quadrupole coupling constants (χij where i, j = a, b, c), and nuclear-spin rotation constants (Cij where i, j = a, b, c) were fit for each of the three silicon isotopologues of diiodosilane. An additional term, χK aa , was included in the fit to handle K-dependent centrifugal distortion in χaa . As a result of this small perturbation, the term χaa ef f = χaa + K2 χK aa replaced χaa in the nuclear quadrupole coupling Hamiltonian[66, 104]. Table 4.2 contains the final collection of these spectroscopic parameters. In total, 56 Table 4.2: Spectroscopic parameters of three silicon isotopologues of diiodosilane Parameters Prediction 28 SiI2 H2 Experimental 28 29 SiI2 H2 30 SiI2 H2 SiI2 H2 A (MHz) 8550a 8574.52263(20)b 8363.96765(18) 8165.3310(48) B (MHz) 499 496.1275(5) 496.1410(7) 496.1493(14) C (MHz) 474 471.42779(34) 470.7846(6) 470.1462(8) DJ (kHz) – 0.0362(10) 0.0343(9) [0.0343]c DJK (kHz) – -3.96(17) -3.86(28) [-3.86] -773e -693.754(1) -693.777(1) -693.791(9) 127 I χaa d (MHz) 127 I χbb (MHz) 133 36.871(1) 36.890(1) 36.908(7) 127 I χcc (MHz) 601 656.883(1) 656.887(2) 656.884(11) |χab | (MHz) 877 856.2242(19) 856.2266(17) 856.237(11) – 20.1(7) 19.6(7) [19.6] Caa f (kHz) – 4.60(9) 4.37(9) [4.37] Cbb (kHz) – 0.567(31) 0.43(4) [0.43] Ccc (kHz) – 0.906(21) 0.845(29) [0.845] Ng – 189 147 27 RMSh (kHz) – 0.5 0.5 0.6 127 I 127 I K χaa (kHz) a Calculated rotational constants based on GED study[94]. b Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. c Brackets denote that the term was held constant to the value measured for 29 d χaa , χbb , χcc , χab , and χK aa are identical for each iodine nucleus. However, the sign of χab SiI2 H2 . can not be exactly determined. It is only known that χab (127 I1 ) = -χab (127 I2 )[64, 66]. e Method of prediction described in detail in section on Spectral Assignments. f Caa , Cbb , and Ccc are identical for each iodine nucleus. g Number of transitions used in the fit. r P h i 2 h Root mean square deviation of the fit, (obs − calc) /N . 57 363 b-type R-branch rotational transitions were measured for the three silicon isotopologues of diiodosilane. Of the measured transitions, 189 belonged to the isotopologue (92.21% natural abundance), 147 belonged to the (4.70% natural abundance) and only 27 belonged to the 30 29 28 Si Si isotopologue Si isotopologue (3.09% natural abundance)[105]. Although fewer transitions were measured for the 30 Si isotopologue, due mainly to low natural abundance, enough were measured such that the rotational constants and the 127 I NQC tensor could be determined, which were necessary for the purposes of structural analysis and NQC tensor comparison. However, not enough transitions were measured to determine the centrifugal distortion constants or nuclear spin-rotation constants for 30 SiH2 I2 , so in the fit, these parameters were held constant to those measured for the most similar isotopologue, in terms of mass, 29 SiH2 I2 . In Table 4.2, the results of the predicted NQC tensor of iodine in the 28 Si isotopologue are provided next to the experimentally determined tensor of this species. The predicted tensor elements, χaa , χcc , and χab , are all within less than 6% of the experimental values. However, χbb was predicted to be three and a half times larger in magnitude than the final spectroscopic value. This discrepancy is attributed to small imperfections in the rotation matrix, which was used to transform χpredicted into the principal axis system of the predicted structure (based on molecular parameters from the GED study[94]). The predicted NQC tensor is in even better agreement with experimental results when the respective diagonalized NQC tensors are compared. Of course, this makes sense as, once again, the diagonalized tensors are independent of specific molecular geometries. Table 4.3 contains the experimental NQC tensor, diagonalized with QDIAG[100], and the predicted NQC tensor of iodine in the 28 Si isotopologue. At most, there is only a 1.8% difference between the elements of χ in the predicted tensor versus the experimental tensor. 58 Table 4.3: NQC tensor of iodine in diiodosilane Parameters Prediction 28 127 I 127 I 127 I a SiH2 I2 a Experimental 28 SiH2 I2 29 SiH2 I2 30 SiH2 I2 χzz (MHz) -1306.9 -1259.3406(20)b -1259.3530(20) -1259.367(7) χyy (MHz) 667.3 656.8830(10) 656.8870(20) 656.8840(11) χxx (MHz) 600.9 602.4576(20) 602.4660(20) 602.484(6) ηχ c 0.05 0.0432174(18) 0.0432134(22) 0.043196(5) θzb d (◦ ) – 56.55 56.55 56.55 Method of prediction described in detail in section on Spectral Assignments. These are not ab initio predictions. b Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. c ηχ is a measure of the asymmetry of the nuclear quadrupole coupling tensor, where ηχ = d χxx −χyy . χzz Angle between the quadrupolar z-axis and the inertial b-axis. 59 4.5 4.5.1 Discussion Structural Determination Utilizing STRFIT (STRucture FITting program)[106], an r0 structure of diiodosilane was determined via isotopic substitution. Using the twelve available experimental rotational constants, four chemically relevant molecular parameters, namely the Si−I and Si−H bond lengths and the ∠(I−Si−I) and ∠(I−Si−H) bond angles, were fit. These parameters are presented in Table 4.4 alongside previous work by Altabef et al.[94] on the r0 gas phase structure of diiodosilane. Upon comparison, it can be concluded that the results of these two studies are nearly identical, as most parameters agree within experimental error. The only discrepancy is in the value of the ∠(I−Si−I) angle, but the disparity is reasonable and only on the order of 0.14◦ . This can be attributed to the fact that the r0 structure determined from this spectroscopic study only included isotopic substitution data for the central silicon atom. Overall, the agreement between the two experimentally determined r0 structures is acceptable and serves as further evidence that the spectral assignments presented in this work are correct. More on the Si−I bond length will be discussed in the subsequent sections. 4.5.2 Nuclear Quadrupole Coupling Tensor of Iodine In addition to providing structural information, the observation of all three silicon isotopologues allowed for comparisons between χ, measured for each species, to be made. As shown in-depth by Arsenault et al.[107], subtle changes in χzz between the CH3 12 CHICH2 CH3 and CH3 13 CHICH2 CH3 species of g-2-iodobutane can be attributed to small changes in the C−I bond length due to isotopic substitution. Changes in the C−I bond length upon isotopic substitution, observed through χzz , can also be found in a study of iodobenzene by Neill et al., although this difference was not explicitly mentioned in the text[108]. A comparison of χzz (see Table 4.3), the projection of χ nearly along the 60 Table 4.4: r0 structure versus GED of diiodosilane a Parameters This work GED[94] Si−I (Å) 2.4236(19)a 2.423(1)b Si−H (Å) 1.475(21) 1.470(11) ∠(I−Si−I) (◦ ) 111.27(13) 110.8(2) ∠(I−Si−H) (◦ ) 105.9(19) 107.3(13) χ2 0.0012 – σ 0.0016 – For this work, numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b Numbers in parentheses for GED results give 1σ standard errors in units of the least significant figure, which were converted from the provided 3σ standard errors. Si−I bond (angle between Si−I bond and quadrupolar z-axis is less than 1◦ ), between the three silicon isotopologues of diiodosilane shows that in fact, small changes in the electric field gradient at the iodine nucleus result from isotopic substitution of the central silicon atom. The magnitude of χzz increases by 12 kHz as a direct result of isotopic substitution, namely the replacement of a nucleus with a 29 28 Si Si nucleus. This trend continues as a 14 kHz increase in the magnitude of χzz is observed upon the isotopic substitution of a 29 Si nucleus with a 30 Si nucleus. Estimating the change in bond length that corresponds to these changes in χzz is not as straightforward as in the case of 2-iodobutane. For one thing, diiodosilane is of C2v symmetry, which requires that both Si−I bond lengths must change in an identical fashion. Many possible interactions between any combination of the iodine and silicon atoms leaves an accurate estimation of the Si−I bond length change very hard to make. In g-2-iodobutane, the C−I bond was estimated to decrease by 1.8 mÅ upon 13 C substitution, where the percent increase in the mass of 13 C from 12 C is about 8%[105, 107]. Based on this previous 61 study and the fact that the percent increase in the mass of of 30 Si from 29 29 Si from 28 Si and Si is only about 3.5%, it is expected that the Si−I bond should decrease by less than 1.8 mÅ upon the isotopic substitution of silicon[105]. With this understood, the Si−I bond length change is most likely on the order of 1 mÅ or less. Regardless, it is understood that upon 29 Si or 30 Si substitution, the vibrationally averaged Si−I bond length should decrease. Perhaps information about the NQC tensors of iodine in iodosilane, specifically in either 29 SiH3 I or 30 SiH3 I, would help illuminate the trends in Si−I bond length changes resulting from isotopic substitution, but these tensors have yet to be measured. 4.5.3 Chemical Nature of the Si−I Bond As summarized by Noll[109], Si−X bonds are understood to include ionic, covalent, and double bond character. Beginning with the Si−I bond in iodosilane, evidence of ionic and double bond character was shown by Gordy and Cook through a Townes-Dailey analysis[87–89], where the ionic character of the σ bond, iσ , was estimated to be 32% and the π character, πc , of the bond was found to be approximately 28%. These estimations neglect the possibility that the iodine atom is hybridized and assume that the negative pole, δ − , of the σ bond is on the halogen. Gordy and Cook also performed this analysis on tetraiodosilane where iσ and πc were determined to be 29% and 26%, respectively. It was concluded by Gordy and Cook that the π character of the Si−I bond in these species is evidence for (p→d)π bonding and the contributions of hyperconjugation to the π character, although likely present, were assumed to be small and ignored[88]. With the aim of linking that which was found for the Si−I bond in iodosilane and tetraiodosilane, a Townes-Dailey analysis[87–89] was performed for diiodosilane. Here, it was also assumed that the iodine atom is not hybridized. For diiodosilane, iσ was estimated to be 31%. The π character, πc , of the bond was found to be approximately 12% if hyperconjugation effects were taken into account, as in the case of dihalomethanes[88]. If this possibility was neglected, πc 62 was found to be approximately 28%, a value which is in better agreement with the trend in πc that was established for iodosilane and tetraiodosilane. The latter value makes the most sense because it is to be expected that the Si−I bond in tetraiodosilane would have the least amount of π character, as the silicon atom in this molecule should have the highest degree of sp3 hybridization. This can be extrapolated from the work by Donald et al.[110] on the bonding parameters and structure of halosilanes and from the experimental work by Kolotis et al.[111] on the gas-electron diffraction structure of tetraiodosilane. The theoretical study of fluorine-, chlorine-, and bromine-containing silanes by Donald et al. showed maximum and minimum sp3 hybridization at the central silicon atom occurred in species of the form SiX4 and SiH3 X1 (X = FClBr). Although no in-depth theoretical study of this sort has been done on X = I, it can be predicted that the same trend should hold. This trend is not surprising, however, as molecules composed of a central atom and four equivalent substituent atoms can be of Td symmetry, where the four equivalent σ bonds would be sp3 hybridized[112]. Of course, tetraiodosilane is of Td symmetry, which was shown experimentally by Kolotis et al.[111] where the ∠(I−Si−I), based on a ra structure, was determined to be 109.4(1)◦ . To conclude, the Si−I bond in SiI4 has the highest degree of sp3 hybridization and therefore the least π character, by approximately 2-3%, as was supported by a Townes-Dailey analysis. However, some π character is still present in SiI4 due to (p→d)π bonding. This increase in sp3 hybridization at the silicon atom from SiH3 I to SiI4 is due directly to an increase in the number of relatively more electronegative substituents. As more electronegative substituents (i.e. iodine atoms) are added, the central silicon atom rehybridizes such that the percent of p character in the Si−I bond increases and the percent of s character in the Si−H bond increases.[110, 113]. This simultaneously causes an increase in hybridization and a decrease in π character. Incidentally, this is also why the Si−I bond length (r0 ) in diiodosilane (2.4236(19)Å) is 15 mÅ less than the Si−I bond length in iodosilane (2.43835(59)Å[114]). This phenomenon, although opposite to intuition, has been 63 widely observed and was well summarized long ago by Bent[113]. 4.6 Conclusion Rotational transitions belonging to diiodosilane were measured for the first time, which allowed for nuclear quadrupole coupling constants, rotational constants, centrifugal distortion constants, and nuclear spin-rotation constants to be fit for each silicon isotopologue. A r0 structure of diiodosilane was also fit via isotopic substitution and was found to be in agreement with a previously determined r0 gas phase structure. An in-depth analysis of the NQCCs belonging to iodine in each isotopologue revealed small changes in the Si−I bond length that resulted from isotopic substitution. The NQCCs of iodine in this species were compared to those measured for iodine in similar molecules, allowing for insights into the chemical nature of the Si−I bond to be made. 4.7 Acknowledgments The authors thank Professor Wallace (Pete) Pringle for many useful discussions and Angela Y. Chung and Yoon Jeong Choi for their involvement on this project. This work was supported at Wesleyan University by NSF grant CHE1565276. The cluster at Wesleyan University is supported by the NSF under CNS-0619508. 4.8 Supplemental Material The final fit outputs for 28 SiH2 I2 , Chapter 6. 64 29 SiH2 I2 , and 30 SiH2 I2 are presented in References [1] M. Mitzlaff, R. Holm, H. Hartmann, Z. Naturforsch. A 23 (1968) 1819. [2] M. Mitzlaff, R. Holm, H. Hartmann, Z. Naturforsch. A 23 (1968) 65. [3] R. Holm, M. Mitzlaff, Z. Naturforsch. A 22 (1967) 288–289. [4] M. Mitzlaff, R. Holm, H. Hartmann, Z. Naturforsch. A 22 (1967) 1415. [5] R. Holm, M. Mitzlaff, H. Hartmann, Z. Naturforsch. A 22 (1967) 1287. [6] R. 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Ocola, J. Laane, W. C. Pringle, S. A. Cooke, J. Phys. Chem. A 120 (2016) 8686–8690. 72 Journal of Molecular Structure 1107 (2016) 344 Contents lists available at ScienceDirect Journal of Molecular Structure journal homepage: http://www.elsevier.com/locate/molstruc Corrigendum Corrigendum to “Conformations of the semifluorinated n-alkane H(CF2)8-H investigated using Fourier transform microwave spectroscopy and quantum chemical calculations” [J. Mol. Struct. 1093 (2015) 77e81] Weixin Wu a, Eric A. Arsenault b, B.E. Long b, S.A. Cooke a, * a b School of Natural and Social Sciences, Purchase College SUNY, 735 Anderson Hill Rd, Purchase, NY 10577, USA Department of Chemistry, Wesleyan University, Hall-Atwater Laboratories, 52 Lawn Ave, Middletown, CT 06459-0180, USA The authors regret to inform that the investigator, Eric A. Arsenault, was inadvertently left off the author list of this published work. S. A. Cooke would like to apologize for the inconvenience caused. DOI of original article: http://dx.doi.org/10.1016/j.molstruc.2015.03.031. * Corresponding author. E-mail address: [email protected] (S.A. Cooke). http://dx.doi.org/10.1016/j.molstruc.2015.11.028 0022-2860/© 2015 Elsevier B.V. All rights reserved. 73 Journal of Molecular Structure 1093 (2015) 77–81 Contents lists available at ScienceDirect Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc Conformations of the semifluorinated n-alkane H–(CF2)8–H investigated using Fourier transform microwave spectroscopy and quantum chemical calculations Weixin Wu a, B.E. Long b, S.A. Cooke a,⇑ a b School of Natural and Social Sciences, Purchase College SUNY, 735 Anderson Hill Rd, Purchase, NY 10577, USA Department of Chemistry, Wesleyan University, Hall-Atwater Laboratories, 52 Lawn Ave, Middletown, CT 06459-0180, USA h i g h l i g h t s g r a p h i c a l a b s t r a c t 209 pure rotational transitions of 1H,8H-perfluorooctane recorded between 7.8 GHz and 16.2 GHz. Precise rotational constants have been obtained for the first time. Quantum chemical calculations support the experimental measurements. a r t i c l e i n f o Article history: Received 3 February 2015 Received in revised form 13 March 2015 Accepted 21 March 2015 Available online 27 March 2015 Keywords: C8H2F16 Oligomer Structure determination Microwave spectra a b s t r a c t The three lowest energy conformations of the title compound have been investigated using quantum chemical calculations and the lowest energy conformer has been observed using pure rotational spectroscopy. The lowest energy conformer possesses C 2 symmetry, a helical CF2 backbone, with the hydrogens nearly eclipsing one another when looking down the long axis of the molecule. The technique of Fourier transform microwave spectroscopy in conjunction with quantum chemical calculations is demonstrated as a complimentary method to X-ray diffraction for structural determinations of small oligomers for which the location of hydrogen atoms may be important. Ó 2015 Elsevier B.V. All rights reserved. Introduction Structural studies on the perfluoroalkane chain (–CF2)n are of interest due to the simplicity of the repeating unit and the importance of the structural motif to modern materials chemistry. In contrast to the paraffins it is well known that the most stable ⇑ Corresponding author. E-mail address: [email protected] (S.A. Cooke). URL: http://www.openscholar/purchase/cooke (S.A. Cooke). http://dx.doi.org/10.1016/j.molstruc.2015.03.031 0022-2860/Ó 2015 Elsevier B.V. All rights reserved. 74 conformation for a perfluoroalkane chain is that of a slowly twisting helix in which each C–C–C–C dihedral is approximately 17° from the planar trans position [1]. The source of this helicity has been investigated in several studies [2–4], most recently by Jang et al. [5] who conclude that the dominant source of helicity is electrostatics. Experimental methods pertaining to structure determination of helical polymers were reviewed in 2010 by Yashima [6]. Yashima notes that the ‘‘exact helical structures of most of the already prepared synthetic helical polymers remain unsolved’’. Current methods for structure determination of helical 78 W. Wu et al. / Journal of Molecular Structure 1093 (2015) 77–81 Fig. 1. The PBE0/6-311++G(d,p) geometry of three low energy conformers of 1H,8H-perfluorooctane. From left to right the panels show the conformers in the ac plane, the bc plane, the bc plane with fluorines removed to highlight the positions of the hydrogen atoms, and the bc plane in which two lines replace the terminal C–H bonds and the dihedral angle between these bonds is shown. Table 1 Experimentala and PBE0/6-311++G(d,p) calculated spectroscopic parameters, and related quantities, for H–(CF2)8–H. Parameter Experimental A/MHz B/MHz C/MHz 695.72346(20)b 117.704735(72) 113.846756(73) DJ /Hz DK /Hz dJ /Hz 0.299(58) 6.2(19) 0.074(12) P aa /u Å2 P bb /u Å2 P cc /u Å2 4003.1628 435.9539 290.4540 la /D lb /D lc /D Relative energies/cm1c Nd 209 RMSe 0.994 Calculated Cis Transoid Skew 697.035 117.324 113.504 662.957 120.663 117.916 697.899 115.718 114.166 4017.517 435.023 290.019 3855.986 429.953 332.357 4034.954 391.758 332.385 0.0 0.0 2.9 0 1.3 0.6 0.8 201 0.0 1.6 1.0 318 a Using a Watson A reduction. The first group of constants are the three rotational constants, followed by the centrifugal distortion constants, then the three second moments, and then the components of the dipole moment along the principal axes. b Numbers in parentheses give standard errors (1r, 67% confidence level) in units of the least significant figure. c Energies calculated using an MP2/6-311++G(d,p) method using the geometry optimized at the PBE0/6-311++G(d,p) level. d Number of observed transitions used in the fit. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P h i 2 e Root mean square deviation of the fit, ððobs calcÞ=errorÞ =Nlines . polymers include liquid crystalline X-ray diffraction, atomic force microscopy, theoretical/experimental circular dichroism, and notably X-ray analysis of uniform oligomers. In this latter technique the complex problem of polymer structure determination is simplified through the preparation and study of small oligomers using, for example, size exclusion chromatography. Uniform oligomers as small as pentamers have been used to determine the nature of the helix for some polymers [7]. Microwave spectroscopy has been demonstrated to have the resolution and sensitivity to determine the structure of oligomers possessing similar numbers of repeating units to those examined with the above mentioned X-ray diffraction method [8–10]. Two of the few shortcomings of X-ray diffraction concern the solid state nature of the experiment and the difficulty of locating hydrogen atoms. Fourier transform microwave spectroscopy coupled with quantum chemical calculations and/or simple models may serve as a complimentary technique in this regard as the sample molecules are studied once stabilized within a rapidly expanding puff of argon gas. This ensures that the target molecule is observed in the absence of solvent or lattice effects and furthermore the lower energy conformers are often, but not always, the dominant species observed. In this study we apply Fourier transform broadband microwave spectroscopy to the study of H–(CF2)8–H, also known as 1H,8Hperfluorooctane, 1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8-hexadecafluorooctane, or a, x-dihydroperfluorooctane. This compound contains the repeating CF2 unit but has the added challenge that complete structural determination requires the location of two hydrogens within a molecule with an atomic mass of 402 Da. Experimental The target molecule, H–(CF2)8–H, was purchased from Synquest Labs (97% purity) and was used without further purification. The compound is a liquid at room temperature with a boiling point of 432–436 K and a vapor pressure of 0.01 bar at 298 K [11]. The liquid sample was placed in a 1/4 in. tube about 40 cm behind a solenoid valve. Argon held at backing pressures of 1.5 bar was bubbled through the liquid prior to passage through the solenoid valve and into a vacuum chamber held at approximately 108 bar. This process resulted in a rotationally cold, 2 K, pulse of the target molecule stabilized within a matrix of supersonically expanded argon. Expansions in neon or helium were not attempted. 75 W. Wu et al. / Journal of Molecular Structure 1093 (2015) 77–81 79 Fig. 2. Top: an approximately 20 MHz portion of the experimental spectrum. The spectrum was recorded in 2 GHz sections between 7 GHz and 13 GHz. Transitions are labeled as J0ka kc J00ka kc . Bottom: simulated spectrum using the constants determined in Table 1. Table 2 Helical angles derived from the calculated structures of H–(CF2)8–H. See Fig. 3 for the dihedral angle labeling scheme. Dihedral Cis Transoid Skew /1 /2 /3 /4 /5 /6 /7 62.8 161.4 162.1 162.4 162.1 161.4 62.8 63.1 161.5 162.2 162.1 161.9 163.1 169.6 62.6 161.4 162.5 162.1 161.6 170.8 49.5 A Fourier transform microwave spectrometer utilizing chirps of radiation was then used to record the spectra of the target molecules between the frequency regions of 7.8 GHz and 16.2 GHz. This instrument has been described elsewhere [12,13] and is based upon the chirped experiment previously introduced by Pate and coworkers [14]. Briefly, the instrument mixes a microwave pulse of frequency m with a fast (4 ls) linear frequency sweep of DC1 GHz generating a m ± 1 GHz broadband pulse. The pulse was then amplified (5 W) using a solid state amplifier and broadcast onto the supersonically expanding gas sample through a horn antenna. Following a delay of 100 ns a second antenna horn received the resulting free induction decay (FID). The signal was then passed through an amplification stage and proceeded to be directly digitized at a rate of 25 picoseconds per point for 800,000 points. Transition line widths were 80 kHz with line centers possessing an uncertainty of 8 kHz. Geometry calculations were performed using quantum chemical calculations at the PBE0/6-311G++(d,p) level of theory [15–19]. This hybrid functional has been shown to perform well with perfluorinated systems [20]. The energies of three lowest energy optimized structures, shown in Fig. 1, were recalculated using the MP2/6-311G++(d,p) level of theory [21]. The Gaussian 03 software package was used for all quantum chemical calculations [22]. Calculated properties for the three lowest energy conformers are given in Table 1. Results The observed rotational spectrum of H–(CF2)8–H consisted of c-type transitions in a pattern expected of a nearly prolate, asymmetric rotor. Initially Q-branch progressions were located, an example of which, near 8.7 GHz, is shown in Fig. 2. These Q-branches are separated by 1159 MHz from one another, which was taken to be the value of 2A ðB þ CÞ. Secondly, doublets such as those shown near 8.68 GHz in Fig. 2 were found to repeat approximately every 230 MHz, which was taken to be the approximate value of B þ C. From these assumptions a spectrum was predicted using an A; B; C of 694.5 MHz, 116 MHz and 114 MHz, respectively. This predicted spectrum produced patterns close enough to the observed spectrum that transition quantum Fig. 3. Figure indicating the 7 dihedral angles for 1H,8H-perfluorooctane. 76 80 W. Wu et al. / Journal of Molecular Structure 1093 (2015) 77–81 Fig. 4. A simple molecular model for 1H,8H-perfluorooctane. numbers could be assigned. Three types of transition sequence were observed these being c Q 1;2 (25 transitions), c Q 1;0 (29 transitions), and c R1;0 (155 transitions). No unassigned lines remained in the spectrum. A standard, iterative least squares analysis of all observed transitions led to the spectroscopic constants given in Table 1 and the residuals Dm ¼ mobs mcalc of the fit reported in the supplementary data. Pickett’s SPCAT/SPFIT suite of programs [23,24] were used for the least squares analysis. To simplify the analytical procedure we have written a program called SpecFitter [25] that serves as a spectral viewer and graphical user interface to the SPCAT/SPFIT programs. The Hamiltonian employed was the familiar semi-rigid asymmetric top in the Watson A reduction [26]. Not all of the quartic centrifugal distortion (CD) constants were required to produce a satisfactory fit, with the most successful combination being DJ ; DK , and dJ . The criterion for success being the least number of CD constants required to produce the lowest root mean square deviation of the fit while maintaining relatively small uncertainties on the resulting constants. Discussion In regards to the structure of the observed conformer comparison of experimental and calculated properties is most usefully made through the second moments: X 1 ðI b þ I c I a Þ ¼ mi a2i 2 i X 1 2 mi bi P b ¼ ðI c þ I a I b Þ ¼ 2 i X 1 mi c2i P c ¼ ðI a þ I b I c Þ ¼ 2 i Pa ¼ ð1Þ ð2Þ the higher, C 2 symmetry of this conformer in contrast to the other two conformers. The conformers differ mainly in the magnitude of their terminal H–C–C–C dihedral angles. The location of the hydrogen atoms as being in the designated cis conformation can also be demonstrated through an appeal to a very simple moment of inertia model. In the first application of this model we have used the familiar formula for the moment of inertia of a solid cylinder: mR2 2 2 ml mR2 ¼ þ 12 4 Ia ¼ ð4Þ Ib;c ð5Þ in which the radius, R, and length, l, of the cylinder, were treated as adjustable parameters with the mass, m fixed at 438 Da, i.e. the mass of the fully fluorinated octane, C8F18. The radius and length of the cylinder were adjusted to best reproduce the experimentally observed moments of inertia for H–(CF2)8–H. The radius and length determined were 1.92 Å and 11.385 Å, respectively. These values produced second moments for the model cylinder of Pa = 4731.1 u Å2 and Pb = Pc = 403.7 u Å2. At this point two separate, negative 18 Da point masses were allowed to ‘‘roam’’ the cylinder with b-coordinates fixed at zero but adjustable a and c-coordinates. The best agreement between this models second moments and the experimental second moments occured when the negative 18 Da point masses, i.e. the hydrogens, were symmetrically located ±4.5 Å from the cylinder origin, both 1.5 Å from the c axis corresponding to the cis conformer. This model is illustrated in Fig. 4 where the angle between the negative 18 point masses h = 0° produces best agreement between the models second moments and those experimentally observed for H–(CF2)8–H. ð3Þ which are given in Table 1. It is clear that the second moments of the observed species match very closely the calculated structure of the cis conformer, differing by, at most 0.4%. Furthermore, the observed spectrum consisted of only c-type transitions consistent with the calculated dipole moment of the cis conformer also given in Table 1. The dipole moments of the transoid and skew conformers are sizable and the lack of observation of transitions from these conformers is likely the result of the experimental conditions only populating the lowest energy conformer. The calculated dihedral angles for all three low energy conformers of H–(CF2)8–H are presented in Table 2. All three conformers show the typical ‘‘trans minus’’ angle common to perfluoroalkane chains [5]. The dihedral angles for the cis conformer nicely display Conclusions Fourier transform microwave spectroscopy in concert with both quantum mechanical calculations and a simple molecular model has been demonstrated to provide useful insights into the structure of an a, x-dihydrogenated perfluoroalkyl oligomer. The lowest three conformers of H–(CF2)8–H have been identified an the lowest conformer experimentally observed through its pure rotational spectrum. The three conformers differ primarily in the position of the terminal hydrogens. The rotational spectroscopic constants, together with the quantum chemical calculations demonstrate that the lowest energy conformer possesses C 2 symmetry with the terminal hydrogen atoms eclipsing one another when looking down the long axis of the molecule. 77 W. Wu et al. / Journal of Molecular Structure 1093 (2015) 77–81 Acknowledgements We gratefully acknowledge financial support from the Petroleum Research Foundation administered by the American Chemical Society, award number 53451-UR6. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.molstruc.2015.03. 031. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] C.W. Bunn, E.R. Howells, Nature 174 (1954) 549–551. D.A. Dixon, J. Phys. Chem. 96 (1992) 3698–3701. G.D. Smith, R.L. Jaffe, D.Y. Yoon, Macromolecules 27 (1994) 3166–3173. U. Rothlisberger, K. Laasonen, M.L. Klein, M.J. Sprik, Chem. Phys. 104 (1996) 3692–3700. S.S. Jang, M. Blanco, W.A. Goddard III, G. Caldwell, R.B. Ross, Macromolecules 36 (2003) 5331–5341. E. Yashima, Polym. J. 42 (2010) 3–16. Y. Ito, T. Ohara, R. Shima, M. Suginome, J. Am. Chem. Soc. 118 (1996) 9188– 9189. J.A. Fournier, R.K. Bohn, J.A. Montgomery Jr., M. 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Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian 03, Gaussian, Inc., 340 Quinnipiac Street, Building 40, Wallingford, CT, 06492, 2003, copyright Ó 1994–2003. [23] H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371–377. [24] SPFIT/SPCAT package. <http://spec.jpl.nasa.gov>. [25] S.A. Cooke, SpecFitter. <http://specfitter.droppages.com/>, 2014. [26] J.K.G. Watson, in: J.R. Durig (Ed.), Vibrational Spectra and Structure, vol. 6, 1977, p. 1. Article pubs.acs.org/JPCA Microwave Spectra, Structure, and Ring-Puckering Vibration of Octafluorocyclopentene B.E. Long,§,† Eric A. Arsenault,† Daniel A. Obenchain,⊥,† Yoon Jeong Choi,‡ Esther J. Ocola,¶ Jaan Laane,¶ Wallace C. Pringle,† and S.A. Cooke*,‡ † Department of Chemistry, Wesleyan University, Hall-Atwater Laboratories, 52 Lawn Avenue, Middletown, Connecticut 06459, United States ‡ School of Natural and Social Sciences, Purchase College SUNY, 735 Anderson Hill Road, Purchase, New York 10577, United States ¶ Department of Chemistry, Texas A & M University, College Station, Texas 77840, United States S Supporting Information * ABSTRACT: The rotational spectra of octafluorocyclopentene (C5F8) has been measured for the first time using pulsed jet Fourier transform microwave spectroscopy in a frequency range of 6 to 16 GHz. As in the molecule cyclopentene, the carbon ring is nonplanar, and inversion through the plane results in an inversion pair of ground state vibrational energy levels with an inversion splitting of 18.4 MHz. This large amplitude motion leads to the vibration−rotation coupling of energy levels. The symmetric double minimum ring-puckering potential function was calculated, resulting in a barrier of 222 cm−1. The rotational constants A0 = 962.9590(1) MHz, B0 = 885.1643(4) MHz, C0 = 616.9523(4) MHz, A1 = 962.9590(1) MHz, B1 = 885.1643(4) MHz, C1 = 616.9528(4) MHz, and two centrifugal distortion constants for each state were determined for the parent species and all 13C isotopologues. A mixed coordinate molecular structure was determined from a least-squares fit of the ground state rotational constants of the parent and each 13C isotopologue combined with the equilibrium bond lengths and angles from quantum chemical calculations. ■ ■ INTRODUCTION The ring-puckering of small ring molecules has been studied for more than 50 years by both microwave1,2 and far-infrared spectroscopy.3−5 In many cases, four-membered ring molecules such as cyclobutane possess two equivalent energy minima separated by low-lying barriers. Similarly, five-membered rings containing a double bond (“pseudo-four-membered rings”) such as cyclopentene (C5H8) have the same type of double minimum potential energy function for the ring puckering. Such potential functions give rise to an inversion splitting often less than 1 cm−1. The microwave spectrum of C5H8 was first reported by Rathjens, Jr.6 in 1962 and was further analyzed by Butcher and Costain,7 who determined the ring-puckering inversion frequency to be 27 GHz. In 1967, Laane and Lord8 reported the far-infrared spectrum of cyclopentene and determined its ring-puckering potential energy function, which had a barrier to inversion of 232 cm−1. In the present paper, we present the microwave spectrum of the fully fluorinated cyclopentene molecule and investigate its structure and ring-puckering potential energy function. These will be compared to cyclopentene results. The infrared and Raman spectra of this molecule have been previously studied by Harris and Longshore.9 Microwave spectra have been previously reported for fluorocyclobutane10 and 1-chloro-cyclopentene,11 and inversion frequencies were determined for both. © 2016 American Chemical Society EXPERIMENTAL SECTION The rotational spectra of octafluorocyclopentene was initially collected from 6 to 16 GHz on a chirped Fourier transform microwave spectrometer (FTMW). This spectrometer, which has been described previously,12 is based on the instrument designed by Pate et al.13 The desired microwave center frequency is first mixed with a linear frequency sweep, lasting 6 μs, from DC to 1 GHz. The resultant microwave radiation, ν ± 1 GHz, is then broadcast directly into the vacuum chamber via a microwave horn antenna. The incident radiation then induces a polarization in the concurrent supersonic expansion of the gas sample. After a ≈1 μs delay, a second horn antenna collects the free induction decay (FID), which is then fast Fourier transformed and directly digitized on a Tektronix TDS6124C digital oscilloscope. The FID is collected for 20 μs, resulting in 800 000 points at 25 ps per point. The average line width of a transition measured on this instrument is approximately 80 kHz with an uncertainty in the center frequency of ±8 kHz. Additional rotational transitions for the parent and all three unique 13C isotopologues were measured with a Balle−Flygare type spectrometer.14 Received: July 27, 2016 Revised: September 12, 2016 Published: October 4, 2016 8686 79 DOI: 10.1021/acs.jpca.6b07554 J. Phys. Chem. A 2016, 120, 8686−8690 Article The Journal of Physical Chemistry A Figure 1. Ab initio structure obtained from MP2/cc-pVTZ calculation. level. Considering previous work,15−20 a scaling factor of 0.985 was used because all of the approximated frequencies were below 1800 cm−1. The energy levels for the ring-puckering potential energy function, shown in Figure 2, were calculated using the Meinander−Laane Da1OPTN1 program.21 The gas sample was purchased from SynQuest Laboratories (97% C5F8) and used without further purification. Utilizing a flow control system, a 1.7% tank of sample in approximately 20 atm of dry argon (99.999%, Airgas) was mixed. Experiments ran with a final sample concentration of 0.75% in 2 atm argon carrier gas. ■ ■ RESULTS The spectral assignment for octafluorcyclopentene, an asymmetric top with κ = 0.55, was completed using Pickett’s SPFIT/ CALCULATIONS Quantum chemical calculations were utilized to obtain an ab initio structure for C5F8. Shown in Figure 1 is the resultant Table 1. Fit Comparison of Parent Species ab initioa states fit separately v=0 A (MHz) B (MHz) C (MHz) DJ (kHz) dJ (kHz) Fbc (MHz) ΔE01 (MHz) Nd RMSe (kHz) 965.0 889.0 623.1 −c − − − states fit together v=1 962.9590(1) 962.9590(1)b 885.1643(4) 885.1643(4) 616.9523(4) 616.9528(4) 0.0229(3) 0.0223(3) 0.0052(1) 0.0050(1) 12.508(5) 18.404(5) 176 4.1 962.9590(1) 885.1666(9) 616.9503(9) 0.0226(4) 0.0051(2) 12.483(9) 18.401(6) 176 5.7 a From MP2 level calculation. Results given are re values. bNumbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. cAb initio value not predicted. dNumber of transitions used in the fit. eRoot mean square deviation of the fit, (∑ [(obs − calc)2 ]/Nlines) fNumbers in square brackets indicate values held constant to those obtained for the parent. Figure 2. Theoretically determined ring-puckering potential function of C5F8. On the x-axis, Z is the puckering coordinate of the vibrational motion. Symmetric minima occur when the carbon ring assumes a puckered angle of ±22.9°. SPCAT22 programs in tandem with the AABS package.23 Table 1 presents a comparison of fits when the vibrational states are either fit individually or together. The comparison with the ab initio constants is very good, and deviations, to a large part, may be attributed to the calculation of equilibrium constants compared to the experimental determination of constants within the stated vibrational quanta. There is a small increase in RMS error when the states are fit together. This is perhaps an artifact of a small difference between the two states or because an increase in parameters causes a decrease in the statistical fit structure calculated at the MP2/cc-pVTZ level of theory using the GAUSSIAN09 Revision A.02 suite.15 Computation predicts that the carbon ring backbone assumes a puckered geometry with a puckering angle of ±22.9°. The barrier to ring inversion, which occurs when the puckering angle is 0°, was calculated to be 222 cm−1 at the same level of theory. Predicted vibrational frequencies for the molecule were computed using density functional theory (DFT) calculations at the B3LYP/cc-pVTZ 8687 80 DOI: 10.1021/acs.jpca.6b07554 J. Phys. Chem. A 2016, 120, 8686−8690 Article The Journal of Physical Chemistry A Table 2. Spectroscopic Parameters for Octafluorocyclopentene predicteda parent A0 (MHz) B0 (MHz) C0 (MHz) DJ,0 (kHz) dJ,0 (kHz) 965.0 889.0 623.1 − − 962.9590(1)b 885.1643(4) 616.9523(4) 0.0229(3) 0.0052(1) 960.2972(1) 884.465(1) 615.529(1) 0.026(1) 0.0079(5) 962.9430(1) 882.8039(2) 615.8092(1) 0.022(1) [0.0052]e 960.8169(1) 885.2221(7) 616.0695(8) 0.023(1) 0.0051(5) A1 (MHz) B1 (MHz) C1 (MHz) DJ,1 (kHz) dJ,1 (kHz) − − − − − 962.9590(1) 885.1643(4) 616.9528(4) 0.0223(3) 0.0050(1) 960.2977(1) 884.465(1) 615.530(1) 0.025(1) 0.0069(5) 962.9445(1) 885.8041(1) 615.8098(1) 0.022(1) [0.0050] 960.8151(1) 885.2231(9) 616.0703(8) 0.027(1) 0.0070(5) Fbc (MHz) ΔE01 (MHz) Nc RMSd (kHz) − − − − 12.508(5) 18.404(5) 176 4.1 12.58(1) 18.53(1) 38 1.0 [12.508] [18.404] 28 1.3 12.084(9) [18.404] 31 1.5 parameters a 13 C1,2 13 C3,5 13 C4 From MP2 level calculation. Results given are re values. bNumbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. cNumber of transitions used in the fit. dRoot mean square deviation of the fit, square brackets indicate values held constant to those obtained for the parent. (∑ [(obs − calc)2 ]/Nlines) eNumbers in Figure 3. Ring inversion accompanied by a c-dipole moment inversion. To fit the b- and c-type transitions, a rotation-vibration term, FaPApZ, was required, where Fa is the Coriolis parameter, PA is the angular momentum about the a-axis, and pZ is the linear momentum resulting from the inversion motion. As described by Pickett,24 a better fit of the vibration−rotation interaction results from using the equivalent operator Fbc, (PBPC+PCPB)pZ. Three rotational constants and two centrifugal distortion constants were fit spectroscopically for the v = 0 and v = 1 vibrational states. As seen in Figure 3, the ring-puckering motion resulted in the inversion of the c-dipole moment. As a direct result of this, c-type cross state transitions were observed. The J′ ← J″ transitions are shown in Figure 4. An additional parameter, ΔE01, was necessary to account for the inversion frequency of the ring-puckering motion. The experimental result is ΔE01 = 18.404(5) MHz. Figure 4. Roughly a 50 MHz portion of spectra obtained from 10 000 averages on the chirped FTMW. Intrastate b-type inversion pairs are shown in blue. Cross state c-type transitions are depicted in red. Labels ″ a k″c. for transitions are Jk′′ a k′c- Jk″ ■ DISCUSSION Ring-Puckering Potential Energy Function. As is wellknown,1−5 the ring-puckering potential energy functions for molecules such as cyclopentene and octafluorocyclopentene are determined by the competing forces of angle strain and torsional interactions. The former strives to maintain the planar rings, while the torsions prefer the rings to pucker. The barrier to planarity of cyclopentene is 232 cm−1, as determined from far-infrared spectra by Laane and Lord.8 The barrier for the error. The three 13C isotopologues were fit separately because the RMS error is better when the vibrational states are treated in this way. Spectroscopic constants for the parent species and three 13C isotopologues are presented in Table 2. The ab initio values agree to within 1% of the experimental rotational constants. Line listings for all of the fits performed are given in the supplementary data tables. 8688 81 DOI: 10.1021/acs.jpca.6b07554 J. Phys. Chem. A 2016, 120, 8686−8690 Article The Journal of Physical Chemistry A Table 3. Experimental r0 Structure for Octafluorocyclopentene a Carbons C1 and C5 are symmetrically equivalent, as well as C2 and C4. bNumbers in parentheses give standard Costain errors27 (1σ) in units of the least significant figure. the fluorine substitution also decreases the angle strain in the C5F8, leading to a similar barrier to planarity. A plausible rational for this observation in C5F8 may hinge on the electron withdrawing properties of the fluorines which, in turn, result in a reduced repulsion in the eclipsed torsion potential between the two C−C bonds in the ring when compared to the nonfluorinated C−C bonds in C5H8.26 Although the barriers are very similar for the two molecules, because of the much higher reduced mass for the C5H8, the ground state splitting for C5F8 is much smaller (18.404 MHz vs 27 GHz), and the 1 → 2 far-infrared transition is predicted to be 77 vs 127.1 cm−1 for cyclopentene.8 Structural Determination. The carbon skeleton was determined via isotopic substitution. All 13C isotopologues were observed in natural abundance. A Schwendeman analysis28 was preformed to gather structural details for the molecule. Results from this analysis can be found in Table 3. Due to the Cs symmetry of the molecule, the carbons labeled 1 and 5 are equivalent, as are those labeled 2 and 4. The dihedral angle presented, 21.6°, refers to the puckering angle of the carbon ring in its minimum energy conformation. This value was calculated to be 22.9° from the MP2/cc-pVTZ structural optimization. These dihedral angles are all presented in Table 4. A Kraitchman analysis27,29 was also performed to confirm that the assigned carbon positions are correct. However, the Kraitchman errors are much larger than those from the Schwendeman fit. As a result, these values are not used for the structural determination of the molecule. The carbon ring is very close to planar, so the b- and c-coordinate values for carbons labeled 1, 2, 4, and 5 are very small. It then becomes rather difficult to determine the structure and at best these coordinates are found to be very small and nonzero. Kraitchman coordinates are presented in Table 5. Table 4. Dihedral Angle Determination dihedrala (deg) experimental, r0 MP2/cc-pVTZ C5H8 experimental,6 r0 a 21.6 22.9 22.3 Labeled as φ on the structure above. Table 5. Kraitchman Coordinates (Å) for Octafluorocyclopentene coordinates atoms |a| |b| |c| C1, C5 C2, C4 C3 0.6578(24)a 1.2334(12) 0.128(12)i 1.2105(13) 0.037(4) 1.0917(14) 0.073(21) 0.087(17) 0.144(11)i a Values in parentheses give absolute Costain errors27 of the least significant figure. Imaginary values are indicative that the coordinate is very close to zero. ■ analogous fluoro compound determined in the present work is 222 cm−1. This is somewhat surprising because the CF2−CF2 torsional interactions are expected to be greater than the CH2−CH2 interactions. The barrier to internal rotation of ethane is 1040 cm−1, while that of hexafluoroethane (C2F6) is 1564 cm−1.25 Thus, the C5F8 barrier would be higher than that for C5H8 based on the torsional interactions alone. Apparently, CONCLUSION Twelve unique spectroscopic constants were determined from the rotational spectra of C5F8 between 6 and 16 GHz. Isotopic substitution allowed for an experimentally derived carbon ring structure. The ring-puckering potential function was also fit, and both were explored in detail and compared to cyclopentene. 8689 82 DOI: 10.1021/acs.jpca.6b07554 J. Phys. Chem. A 2016, 120, 8686−8690 Article The Journal of Physical Chemistry A ■ Spectroscopy; Laane, J., Ed.; Elsevier: Amsterdam, The Netherlands, 2009; pp 25−32. (11) Caminati, W.; Danieli, R.; Fantoni, A. C.; Lopez, J. C. 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HighAccuracy Theoretical Thermochemistry of Fluoroethanes. J. Phys. Chem. A 2014, 118, 4824−4836. (26) Pringle, W. C.; Meinzer, A. L. Far Infrared Ring Puckering Vibration of 3,3-Difluoroxetane: Effect of Fluorine Substitution on the Ring Puckering Potential. J. Chem. Phys. 1974, 61, 2071−2076. (27) Costain, C. C. Determination of Molecular Structure from Ground State Rotational Constants. J. Chem. Phys. 1958, 29, 864−874. (28) Schwendeman, R. H. Structural Parameters from Rotational Spectra. In Critical Evaluation of Chemical and Physical Structural Information; Lide, D. R., Jr., Paul, M. A., Ed.; National Academy of Science, 1974; pp 94−115. (29) Kraitchman, J. Determination of Molecular Structure from Microwave Spectroscopic Data. Am. J. Phys. 1953, 21, 17−24. ASSOCIATED CONTENT S Supporting Information * The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b07554. ■ Formatted output of SPFIT file for data fits (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected], Phone: 914-251-6675. Present Addresses § B.E.L.: Department of Chemistry, Trinity University, San Antonio, Texas 78212-7200, United States. ⊥ D.A.O.: Institut fur Physikalische Chemie and Elektrochemie, Callinstr. 3A, 30167 Hannover, Germany. Notes The authors declare no competing financial interest. ■ ACKNOWLEDGMENTS The authors thank Stew Novick for many useful discussions. An internal grant from SUNY Purchase funded the chemicals used in these experiments. The cluster at Wesleyan University is supported by the NSF under Grant CNS-0619508. J.L. wishes to thank the Robert A. Welch Foundation for financial support under Grant A-0396. S.A.C. acknowledges financial support from the Petroleum Research Foundation administered by the American Chemical Society, Award 53451-UR6. Computations were carried out on the Texas A&M University Department of Chemistry Medusa computer system funded by the National Science Foundation, Grant No. CHE-0541587. ■ REFERENCES (1) Caminati, W.; Grabow, J.-U. Microwave Spectroscopy: Molecular Systems. In Frontiers of Molecular Spectroscopy; Laane, J., Ed.; Elsevier: Amsterdam, The Netherlands, 2009; pp 455−552, and references therein. (2) Caminati, W.; Grabow, J.-U. Microwave Spectroscopy: Molecular Systems. In Frontiers of Molecular Spectroscopy; Laane, J., Ed.; Elsevier: Amsterdam, The Netherlands, 2009; pp 383−454, and references therein. (3) Laane, J. Vibrational Potential Energy Surfaces in Electronic Excited States. In Frontiers of Molecular Spectroscopy; Laane, J., Ed.; Elsevier: Amsterdam: The Netherlands, 2009; pp 63−132, and references therein. (4) Laane, J. Experimental Determination of Vibrational Potential Energy Surfaces and Molecular Structures in Electronic Excited States. J. Phys. Chem. A 2000, 104, 7715−7733. and references therein. (5) Laane, J. Spectroscopic Determination of Ground and Excited State Vibrational Potential Energy Surfaces. Int. Rev. Phys. Chem. 1999, 18, 301−341. and references therein. (6) Rathjens, G. W., Jr. Microwave Investigation of Cyclopentene. J. Chem. Phys. 1962, 36, 2401−2406. (7) Butcher, S. S.; Costain, C. C. Vibration-Rotation Interaction in the Microwave Spectrum of Cyclopentene. J. Mol. Spectrosc. 1965, 15, 40−50. (8) Laane, J.; Lord, R. C. Far-Infrared Spectra of Ring Compounds. II. The Spectrum and Ring-Puckering Potential Function of Cyclopentene. J. Chem. Phys. 1967, 47, 4941−4945. (9) Harris, W. C.; Longshore, C. T. Interpretation of the Infrared and Laser-Raman Spectra of Cyclopentene and Perfluorocyclopentene. J. Mol. Struct. 1973, 16, 187−204. (10) Caminati, W.; Favero, L. B.; Maris, A.; Favero, P. G. Microwave Spectrum of the Axial Conformer and Potential Energy Function of the Ring Puckering Motion in Fluorocyclobutane. In Frontiers of Molecular 8690 83 DOI: 10.1021/acs.jpca.6b07554 J. Phys. Chem. A 2016, 120, 8686−8690 Chapter 6 Appendix A 84 28_DIS Thu Apr 13 13:05:00 2017 -------------------------------------------------------------------------------------========= obs o-c error blends Notes o-c wt / instead of : below denotes (o-c)>3*err -------------------------------------------------------------------------------------========= 1: 5 1 5 6 7 4 0 4 5 6 12704.5896 -0.0003 0.003 2: 5 1 5 6 6 4 0 4 5 5 12705.2715 -0.0003 0.003 3: 5 1 5 6 5 4 0 4 5 4 12707.0747 0.0000 0.003 4: 5 1 5 5 6 4 0 4 4 5 12707.3164 0.0002 0.003 5: 5 1 5 6 4 4 0 4 5 3 12713.9846 0.0000 0.003 6: 5 1 5 7 8 4 0 4 6 7 12719.4873 0.0003 0.003 7: 5 1 5 4 5 4 0 4 3 4 12720.8934 -0.0003 0.003 8: 5 1 5 7 7 4 0 4 6 6 12723.9957 0.0000 0.003 9: 5 1 5 4 3 4 0 4 3 3 12724.8016 0.0000 0.003 10: 5 1 5 5 5 4 0 4 4 4 12726.1536 -0.0004 0.003 11: 5 1 5 5 3 4 0 4 4 2 12731.6211 0.0002 0.003 12: 5 1 5 5 4 4 0 4 4 3 12737.9413 -0.0006 0.003 13: 5 1 5 3 3 4 0 4 2 2 12738.4275 -0.0002 0.003 14: 5 1 5 3 4 4 0 4 6 3 12740.6469 0.0000 0.003 15: 5 1 5 7 5 4 0 4 6 4 12741.7150 0.0000 0.003 16: 5 1 5 4 4 4 0 4 3 4 12744.4589 0.0000 0.003 17: 5 1 5 8 8 4 0 4 7 7 12747.0235 0.0000 0.003 18: 5 1 5 4 4 4 0 4 3 3 12748.1912 -0.0002 0.003 19: 5 1 5 7 9 4 0 4 6 8 12749.1477 0.0002 0.003 20: 5 1 5 6 8 4 0 4 5 7 12754.4892 0.0000 0.003 21: 5 1 5 8 7 4 0 4 7 6 12754.7795 -0.0001 0.003 22: 5 1 5 4 3 4 0 4 3 2 12756.2451 0.0000 0.003 23: 5 1 5 5 2 4 0 4 4 1 12758.7377 -0.0004 0.003 24: 5 1 5 5 7 4 0 4 4 6 12759.0230 -0.0002 0.003 25: 5 1 5 8 9 4 0 4 7 8 12767.8070 0.0004 0.003 26: 5 1 5 7 4 4 0 4 2 3 12769.6420 0.0003 0.003 27: 5 1 5 4 2 4 0 4 3 1 12772.6902 0.0001 0.003 28: 5 1 5 8 6 4 0 4 7 5 12777.8249 0.0000 0.003 29: 5 1 5 4 6 4 0 4 3 5 12779.9351 0.0000 0.003 30: 5 1 5 8 10 4 0 4 7 9 12793.6087 0.0004 0.003 31: 5 1 5 3 5 4 0 4 2 4 12808.0834 0.0003 0.003 32: 5 1 5 8 5 4 0 4 7 4 12808.2025 0.0002 0.003 33: 6 1 6 6 6 5 0 5 5 5 13551.5292 -0.0006 0.003 34: 6 1 6 7 7 5 0 5 6 6 13557.1766 -0.0004 0.003 35: 6 1 6 7 6 5 0 5 6 5 13564.8330 -0.0002 0.003 36: 6 1 6 8 7 5 0 5 7 6 13568.0551 -0.0001 0.003 37: 6 1 6 7 8 5 0 5 6 7 13568.8305 -0.0002 0.003 38: 6 1 6 6 5 5 0 5 6 4 13575.8812 -0.0006 0.003 39: 6 1 6 7 5 5 0 5 5 4 13579.2094 -0.0006 0.003 40: 6 1 6 5 5 5 0 5 4 4 13592.3185 -0.0004 0.003 41: 6 1 6 6 7 5 0 5 5 6 13593.3875 0.0000 0.003 42: 6 1 6 8 8 5 0 5 7 7 13597.9169 -0.0004 0.003 43: 6 1 6 6 4 5 0 5 5 3 13599.3301 -0.0007 0.003 44: 6 1 6 5 6 5 0 5 4 5 13605.9188 -0.0005 0.003 45: 6 1 6 8 6 5 0 5 7 5 13606.9210 -0.0009 0.003 46: 6 1 6 5 4 5 0 5 4 3 13609.1579 -0.0005 0.003 47: 6 1 6 8 9 5 0 5 7 8 13615.4132 -0.0004 0.003 48: 6 1 6 4 4 5 0 5 6 3 13619.3685 0.0004 0.003 49: 6 1 6 6 8 5 0 5 5 7 13621.2529 -0.0003 0.003 85 50: 6 1 6 6 3 5 0 5 5 2 51: 6 1 6 9 8 5 0 5 8 7 52: 6 1 6 9 9 5 0 5 8 8 53: 6 1 6 8 5 5 0 5 7 4 54: 6 1 6 5 7 5 2 3 8 6 55: 6 1 6 9 7 5 0 5 8 6 56: 6 1 6 9 10 5 0 5 8 9 57: 6 1 6 9 11 5 0 5 8 10 58: 6 1 6 9 6 5 0 5 8 5 59: 7 1 7 8 8 6 0 6 7 8 60: 7 1 7 8 8 6 0 6 7 7 61: 7 1 7 7 7 6 0 6 6 6 62: 7 1 7 8 7 6 0 6 7 6 63: 7 1 7 8 9 6 0 6 7 8 64: 7 1 7 7 6 6 0 6 6 5 65: 7 1 7 7 8 6 0 6 8 7 66: 7 1 7 6 6 6 0 6 5 5 67: 7 1 7 9 8 6 0 6 6 7 68: 7 1 7 9 9 6 0 6 8 8 69: 7 1 7 7 5 6 0 6 6 4 70: 7 1 7 9 10 6 0 6 8 9 71: 7 1 7 6 7 6 0 6 5 6 72: 7 1 7 6 5 6 0 6 5 4 73: 7 1 7 8 10 6 0 6 7 9 74: 7 1 7 9 7 6 0 6 8 6 75: 7 1 7 8 5 6 0 6 7 4 76: 7 1 7 7 9 6 0 6 6 8 77: 7 1 7 5 5 6 0 6 4 4 78: 7 1 7 10 9 6 0 6 9 8 79: 7 1 7 9 11 6 0 6 8 10 80: 7 1 7 10 10 6 0 6 9 9 81: 7 1 7 6 4 6 0 6 6 3 82: 7 1 7 7 4 6 0 6 5 3 83: 7 1 7 5 4 6 0 6 4 3 84: 7 1 7 5 6 6 0 6 4 5 85: 7 1 7 9 6 6 0 6 8 5 86: 7 1 7 10 11 6 0 6 9 10 87: 7 1 7 10 8 6 0 6 9 7 88: 7 1 7 10 12 6 0 6 9 11 89: 7 1 7 5 7 6 0 6 9 6 90: 8 1 8 9 9 7 0 7 8 8 91: 8 1 8 8 8 7 0 7 7 7 92: 8 1 8 9 8 7 0 7 8 7 93: 8 1 8 8 7 7 0 7 7 6 94: 8 1 8 9 10 7 0 7 8 9 95: 8 1 8 7 7 7 0 7 6 6 96: 8 1 8 8 9 7 0 7 9 8 97: 8 1 8 9 7 7 0 7 8 6 98: 8 1 8 10 9 7 0 7 7 8 99: 8 1 8 8 6 7 0 7 7 5 100: 8 1 8 10 10 7 0 7 9 9 101: 8 1 8 10 11 7 0 7 9 10 102: 8 1 8 7 6 7 0 7 6 5 103: 8 1 8 9 11 7 0 7 8 10 104: 8 1 8 7 8 7 0 7 6 7 105: 8 1 8 11 12 7 0 7 10 11 13635.1161 0.0002 0.003 13635.4831 -0.0005 0.003 13643.6325 0.0000 0.003 13648.2388 0.0000 0.003 13661.5410 -0.0001 0.003 13663.0146 -0.0003 0.003 13666.9546 -0.0003 0.003 13692.9489 0.0000 0.003 13704.4371 -0.0001 0.003 14454.2586 -0.0002 0.003 14456.8196 0.0005 0.003 14459.3828 0.0000 0.003 14462.6604 0.0004 0.003 14471.8247 -0.0012 0.003 14471.8769 0.0024 0.003 14481.4661 0.0000 0.003 14486.8386 0.0000 0.003 14490.9100 0.0001 0.003 14493.2014 0.0000 0.003 14495.1007 -0.0001 0.003 14501.2843 0.0002 0.003 14509.6251 0.0000 0.003 14510.5048 -0.0002 0.003 14511.0545 0.0000 0.003 14511.7693 0.0000 0.003 14516.1558 -0.0002 0.003 14522.8469 -0.0003 0.003 14524.2769 0.0000 0.003 14525.9489 -0.0002 0.003 14527.1325 -0.0002 0.003 14527.9855 -0.0005 0.003 14530.1194 -0.0007 0.003 14540.8674 -0.0001 0.003 14541.9434 -0.0005 0.003 14545.5793 -0.0002 0.003 14548.1477 -0.0001 0.003 14554.2957 -0.0003 0.003 14555.2383 -0.0003 0.003 14578.5793 -0.0008 0.003 14594.6305 0.0027 0.003 15332.6888 0.0003 0.003 15334.2860 0.0005 0.003 15337.1315 0.0009 0.003 15344.9894 0.0006 0.003 15349.6643 0.0004 0.003 15360.3589 0.0000 0.003 15362.3482 0.0006 0.003 15362.5560 0.0001 0.003 15368.4731 0.0003 0.003 15370.9553 0.0001 0.003 15372.8132 0.0008 0.003 15379.4299 0.0006 0.003 15385.2579 0.0000 0.003 15385.9926 -0.0002 0.003 15390.7478 0.0005 0.003 15432.8127 0.0001 0.003 86 106: 107: 108: 109: 110: 111: 112: 113: 114: 115: 116: 117: 118: 119: 120: 121: 122: 123: 124: 125: 126: 127: 128: 129: 130: 131: 132: 133: 134: 135: 136: 137: 138: 139: 140: 141: 142: 143: 144: 145: 146: 147: 148: 149: 150: 151: 152: 153: 154: 155: 156: 157: 158: 159: 160: 161: 4 4 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 4 4 5 4 5 6 4 4 4 4 6 7 4 5 6 8 10 8 8 9 6 8 8 10 8 11 10 8 10 12 8 11 11 8 6 6 8 7 5 8 6 5 8 6 7 8 10 7 8 7 9 8 11 9 8 6 4 8 7 4 8 6 8 8 6 3 4 3 4 4 5 5 4 5 4 4 6 5 4 5 3 4 6 6 4 6 4 4 4 3 4 4 2 4 7 7 4 5 7 4 7 6 4 4 6 4 6 8 4 3 3 4 7 8 4 3 5 4 7 9 4 4 5 4 3 4 4 4 4 2 2 4 4 2 4 2 3 1 2 3 0 2 4 2 2 3 4 2 4 1 2 3 3 2 3 2 2 4 6 1 4 2 1 2 2 1 4 2 3 0 3 3 4 3 0 3 4 5 3 0 3 3 3 3 0 3 5 6 3 0 3 5 6 7 0 7 9 7 7 0 7 8 5 7 0 7 7 9 7 0 7 10 9 7 0 7 9 11 7 0 7 10 10 7 0 7 5 5 7 0 7 6 4 7 0 7 7 4 7 0 7 5 6 7 0 7 9 6 7 2 5 10 8 7 0 7 10 8 7 0 7 5 3 7 0 7 6 3 7 0 7 10 7 7 0 7 5 2 3 0 3 2 3 3 0 3 5 4 3 0 3 4 3 3 0 3 4 4 3 0 3 4 2 3 0 3 5 5 3 0 3 5 3 3 0 3 3 2 3 0 3 4 1 3 0 3 6 6 3 0 3 4 6 3 0 3 6 5 3 0 3 3 5 3 0 3 5 7 3 0 3 2 2 3 0 3 6 7 3 0 3 6 4 3 0 3 6 8 3 0 3 4 5 3 0 3 3 4 3 0 3 5 4 3 2 1 1 3 3 0 3 1 3 1 0 1 4 1 1 0 1 2 1 1 0 1 4 2 1 0 1 2 4 1 0 1 2 1 1 0 1 2 3 1 0 1 2 2 1 0 1 4 6 0 0 0 3 3 0 0 0 3 2 0 0 0 3 1 11775.1200 0.0001 0.003 11781.3631 0.0002 0.003 11810.9765 0.0001 0.003 11811.0709 0.0002 0.003 11811.3036 0.0000 0.003 15392.2770 0.0001 0.003 15392.5908 -0.0006 0.003 15396.8794 0.0001 0.003 15398.8240 -0.0006 0.003 15399.3088 0.0001 0.003 15401.3983 -0.0001 0.003 15401.8726 -0.0001 0.003 15410.5467 0.0003 0.003 15418.9800 -0.0001 0.003 15427.3614 0.0004 0.003 15428.6473 0.0003 0.003 15431.0549 -0.0005 0.003 15431.2205 -0.0012 0.003 15458.3585 -0.0003 0.003 15458.8431 0.0003 0.003 15472.9416 -0.0012 0.003 15504.9780 -0.0001 0.003 11771.2023 0.0001 0.003 11796.2285 0.0000 0.003 11797.2635 0.0000 0.003 11803.8890 0.0001 0.003 11806.4168 0.0003 0.003 11812.6965 0.0001 0.003 11817.3375 0.0001 0.003 11822.8055 0.0005 0.003 11825.0506 0.0003 0.003 11835.7762 0.0005 0.003 11837.9801 0.0000 0.003 11839.4114 0.0000 0.003 11840.9462 0.0002 0.003 11844.7830 0.0003 0.003 11850.2713 0.0006 0.003 11853.6346 0.0005 0.003 11861.0686 0.0004 0.003 11878.0633 0.0006 0.003 11879.4192 0.0004 0.003 11880.4051 0.0003 0.003 11880.7757 0.0010 0.003 11888.4430 0.0007 0.003 11889.7283 0.0006 0.003 9770.9903 0.0008 0.003 9768.3847 0.0008 0.003 9808.8755 0.0000 0.003 9810.3398 -0.0002 0.003 9830.2520 0.0004 0.003 9831.2957 -0.0003 0.003 9833.8900 -0.0001 0.003 9840.5910 -0.0003 0.003 9034.0270 -0.0006 0.003 9038.6840 -0.0002 0.003 9040.4394 -0.0003 0.003 87 162: 1 1 1 4 3 0 0 0 3 4 9048.8638 0.0000 0.003 163: 1 1 1 4 3 0 0 0 3 2 9052.4708 0.0000 0.003 164: 1 1 1 2 3 0 0 0 3 3 9053.2430 -0.0005 0.003 165: 1 1 1 3 3 0 0 0 3 4 9062.3068 -0.0004 0.003 166: 1 1 1 3 4 0 0 0 3 4 9065.6225 -0.0003 0.003 167: 1 1 1 3 3 0 0 0 3 2 9065.9144 0.0001 0.003 168: 1 1 1 3 5 0 0 0 3 5 9070.3216 -0.0002 0.003 169: 1 1 1 3 2 0 0 0 3 3 9071.4422 0.0000 0.003 170: 1 1 1 4 6 0 0 0 3 5 9040.6087 -0.0001 0.003 171: 1 1 1 2 4 0 0 0 3 5 9031.8653 -0.0004 0.003 172: 1 1 1 4 5 0 0 0 3 4 9061.6310 -0.0002 0.003 173: 1 1 1 4 4 0 0 0 3 3 9063.9686 -0.0001 0.003 174: 2 1 2 4 5 1 0 1 4 6 9807.3710 -0.0001 0.003 175: 2 1 2 3 2 1 0 1 4 1 9859.4540 -0.0006 0.003 176: 2 1 2 5 5 1 0 1 2 4 9868.8689 0.0001 0.003 177: 2 1 2 2 1 1 0 1 2 2 9874.8862 0.0010 0.003 178: 2 1 2 4 3 1 0 1 4 3 9882.4455 -0.0003 0.003 179: 2 1 2 4 1 1 0 1 4 2 9896.0758 0.0002 0.003 180: 2 1 2 2 4 1 0 1 2 4 9898.0457 0.0001 0.003 181: 2 1 2 3 3 1 0 1 4 2 9906.4258 -0.0004 0.003 182: 2 1 2 5 4 1 0 1 2 3 9909.2522 -0.0001 0.003 183: 2 1 2 4 5 1 0 1 4 4 9917.5864 -0.0008 0.003 184: 2 1 2 2 2 1 0 1 2 3 9927.1941 0.0006 0.003 185: 2 1 2 3 5 1 0 1 4 5 9948.9017 -0.0010 0.003 186: 2 1 2 2 3 1 0 1 2 2 9951.7173 0.0010 0.003 187: 2 1 2 3 4 1 0 1 4 3 9965.0600 0.0000 0.003 188: 2 1 2 3 2 1 0 1 4 3 9966.5606 -0.0005 0.003 189: 2 1 2 5 3 1 0 1 2 3 9968.2242 0.0002 0.003 -------------------------------------------------------------------------------PARAMETERS IN FIT (values truncated): 10000 A /MHz 8574.5226(11) 1 20000 B /MHz 496.1276(29) 2 30000 C /MHz 471.4278(19) 3 110010000 3/2Chi_aa /MHz -1040.6316(70) 4 -220010000 3 /MHz -1040.6316(70) = 1.00000 * 4 110040000 1/4(Chi_bb /MHz -155.0030(18) 5 -220040000 1 /MHz -155.0030(18) = 1.00000 * 5 110610000 Chi_ab /MHz -856.223(11) 6 -220610000 Chi_ab /MHz 856.223(11) = -1.00000 * 6 110011000 3/2Chi_aa_ /MHz 0.0301(61) 7 -220011000 3 /MHz 0.0301(61) = 1.00000 * 7 200 DJ /kHz 0.0358(62) 8 1100 DJK /kHz -3.9(10) 9 10010000 Caa /MHz 0.00459(51) 10 -20010000 Caa /MHz 0.00459(51) = 1.00000 * 10 10020000 Cbb /MHz 0.00056(17) 11 -20020000 Cbb /MHz 0.00056(17) = 1.00000 * 11 10030000 Ccc /MHz 0.00090(12) 12 -20030000 Ccc /MHz 0.00090(12) = 1.00000 * 12 MICROWAVE AVG = -0.000001 MHz, IR AVG = MICROWAVE RMS = 0.000510 MHz, IR RMS = END OF ITERATION 1 OLD, NEW RMS ERROR= 88 0.00000 0.00000 0.16988 0.16988 distinct frequency lines in fit: 189 distinct parameters of fit: 12 for standard parameter errors previous errors are multiplied by: 0.175544 MICROWAVE lines fitted lines lines RMS RMS ERROR J range Ka range freq. range total dv=0 dv.ne.0 UNFITTD e>900 v"= 1 2 0 2 0 0 0.000652 0.21731 3 4 0 3 11888 11890 v"= 2 17 4 13 0 0 0.000483 0.16088 1 5 0 1 9768 12808 v"= 3 27 6 21 0 0 0.000258 0.08607 0 5 0 1 9032 12780 v"= 4 31 8 23 0 0 0.000418 0.13938 1 7 0 1 9771 14546 v"= 5 26 2 24 0 0 0.000339 0.11304 3 8 0 1 11796 15505 v"= 6 26 2 24 0 0 0.000578 0.19282 3 8 0 1 11836 15459 v"= 7 23 0 23 0 0 0.000426 0.14193 4 8 0 1 12747 15419 v"= 8 19 0 19 0 0 0.000325 0.10842 5 8 0 2 13635 15393 v"= 9 12 0 12 0 0 0.000907 0.30231 6 8 0 1 14526 15429 v"=10 6 0 6 0 0 0.000765 0.25495 7 8 0 2 15399 15473 -------------------------------------------------------------------------------------------total: 189 22 167 0 0 0.000479 0.15951 PARAMETERS IN FIT WITH STANDARD ERRORS ON THOSE THAT ARE FITTED: (values rounded) 10000 A /MHz 8574.52262(20) 20000 B /MHz 496.12760(51) 30000 C /MHz 471.42783(34) 110010000 3/2Chi_aa /MHz -1040.6316(12) -220010000 3 /MHz -1040.6316(12) 110040000 1/4(Chi_bb /MHz -155.00309(33) -220040000 1 /MHz -155.00309(33) 110610000 Chi_ab /MHz -856.2237(19) -220610000 Chi_ab /MHz 856.2237(19) 110011000 3/2Chi_aa_ /MHz 0.0301(10) -220011000 3 /MHz 0.0301(10) = 200 DJ /kHz 0.0358(10) 1100 DJK /kHz -3.94(17) 10010000 Caa /MHz 0.004590(89) -20010000 Caa /MHz 0.004590(89) 10020000 Cbb /MHz 0.000568(30) -20020000 Cbb /MHz 0.000568(30) 10030000 Ccc /MHz 0.000909(21) -20030000 Ccc /MHz 0.000909(21) 1 2 3 4 = 1.00000 * 4 5 = 1.00000 * 5 6 = -1.00000 * 6 7 1.00000 * 7 8 9 10 = 1.00000 * 10 11 = 1.00000 * 11 12 = 1.00000 * 12 CORRELATION COEFFICIENTS, C.ij: A B C 3/2Chi_a 1/4(Chi_ Chi_ab 3/2Chi_a -DJ A 1.0000 B -0.5237 1.0000 C 0.2478 -0.8102 1.0000 3/2Chi_aa -0.0902 -0.3493 0.1826 1.0000 1/4(Chi_bb 0.2135 -0.3206 0.1644 0.3188 1.0000 Chi_ab 0.6316 -0.5194 0.4070 0.2203 0.2753 1.0000 3/2Chi_aa_ -0.1063 -0.0526 0.1544 -0.1351 -0.7918 -0.1436 1.0000 -DJ -0.3301 0.6452 -0.1193 -0.4222 -0.3018 -0.2301 0.0649 1.0000 89 -DJK Caa Cbb Ccc -0.3399 0.1055 0.0486 -0.0254 -DJK -DJK Caa Cbb Ccc 0.8562 0.0484 0.0817 -0.0236 Caa -0.9941 -0.1200 -0.0586 0.1364 Cbb -0.1926 0.0972 -0.0545 -0.0197 -0.1939 -0.4575 -0.1366 0.1785 0.1832 -0.0245 -0.1777 -0.0521 0.0870 -0.0050 -0.0548 0.1120 0.0431 -0.0087 0.0108 0.1563 Ccc 1.0000 0.1088 1.0000 0.0516 -0.1695 1.0000 -0.1298 -0.4883 0.8105 1.0000 Mean value of |C.ij|, i.ne.j = 0.2366 Mean value of C.ij, i.ne.j = -0.0353 No correlations with absolute value greater than 0.9950 Worst fitted lines (obs-calc/error): 89: 63: 186: 152: 43: 96: 101: 145: 159: 135: 164: 51: 30: 0.9 -0.4 0.3 0.3 -0.2 0.2 0.2 0.2 -0.2 0.2 -0.2 -0.2 0.1 64: 0.8 185: -0.3 45: -0.3 151: 0.3 149: 0.2 38: -0.2 150: 0.2 175: -0.2 142: 0.2 104: 0.2 44: -0.2 60: 0.2 62: 0.1 126: -0.4 148: 0.3 92: 0.3 88: -0.3 81: -0.2 184: 0.2 93: 0.2 114: -0.2 83: -0.2 122: -0.2 143: 0.2 46: -0.2 123: -0.4 177: 0.3 100: 0.3 183: -0.3 112: -0.2 33: -0.2 12: -0.2 39: -0.2 188: -0.2 91: 0.2 80: -0.2 137: 0.2 89: 7 1 7 5 7 64: 7 1 7 7 6 126: 8 1 8 6 8 123: 8 1 8 11 9 63: 7 1 7 8 9 185: 2 1 2 3 5 148: 4 1 4 4 4 177: 2 1 2 2 1 186: 2 1 2 2 3 45: 6 1 6 8 6 6 0 6 9 6 14594.6305 0.0027 0.003 6 0 6 6 5 14471.8769 0.0024 0.003 7 0 7 10 7 15472.9416 -0.0012 0.003 7 0 7 10 8 15431.2205 -0.0012 0.003 6 0 6 7 8 14471.8247 -0.0012 0.003 1 0 1 4 5 9948.9017 -0.0010 0.003 3 0 3 5 4 11880.7757 0.0010 0.003 1 0 1 2 2 9874.8862 0.0010 0.003 1 0 1 2 2 9951.7173 0.0010 0.003 5 0 5 7 5 13606.9210 -0.0009 0.003 _____________________________________ __________________________________________/ SPFIT output reformatted with PIFORM 90 29_DIS Thu Apr 13 13:05:42 2017 -------------------------------------------------------------------------------------========= obs o-c error blends Notes o-c wt / instead of : below denotes (o-c)>3*err -------------------------------------------------------------------------------------========= 1: 4 1 4 7 9 3 0 3 6 8 11662.6836 0.0003 0.003 2: 4 1 4 6 7 3 0 3 5 6 11595.9342 0.0000 0.003 3: 4 1 4 7 8 3 0 3 6 7 11638.6578 0.0005 0.003 4: 4 1 4 6 8 3 0 3 5 7 11629.3248 0.0008 0.003 5: 4 1 4 4 6 3 0 3 3 5 11625.8288 -0.0003 0.003 6: 4 1 4 7 6 3 0 3 6 5 11623.9751 0.0000 0.003 7: 4 1 4 5 7 3 0 3 4 6 11623.2856 0.0004 0.003 8: 4 1 4 7 7 3 0 3 6 6 11620.3362 0.0005 0.003 9: 6 1 6 9 9 5 0 5 8 8 13423.0841 0.0001 0.003 10: 6 1 6 8 10 5 0 5 7 9 13422.9386 -0.0003 0.003 11: 6 1 6 9 8 5 0 5 8 7 13417.1411 -0.0002 0.003 12: 5 1 5 8 9 4 0 4 7 8 12550.1064 0.0004 0.003 13: 5 1 5 8 10 4 0 4 7 9 12575.5439 0.0004 0.003 14: 4 1 4 6 6 3 0 3 5 5 11598.1310 0.0002 0.003 15: 4 1 4 5 3 3 0 3 4 2 11590.7710 0.0005 0.003 16: 4 1 4 6 5 3 0 3 4 4 11589.3765 0.0000 0.003 17: 4 1 4 5 4 3 0 3 4 3 11581.9113 0.0002 0.003 18: 4 1 4 5 5 3 0 3 5 4 11581.2855 0.0001 0.003 19: 4 1 4 5 6 3 0 3 4 5 11566.2432 -0.0002 0.003 20: 4 1 4 4 5 3 0 3 3 4 11559.5108 0.0000 0.003 21: 4 1 4 2 4 3 0 3 1 3 11674.1603 0.0003 0.003 22: 4 1 4 3 4 3 0 3 3 4 11664.7741 0.0015 0.003 23: 4 1 4 3 5 3 0 3 6 4 11645.7732 0.0002 0.003 24: 5 1 5 6 7 4 0 4 5 6 12488.6550 -0.0001 0.003 25: 5 1 5 6 6 4 0 4 5 5 12489.8694 -0.0002 0.003 26: 5 1 5 5 6 4 0 4 4 5 12490.2596 0.0001 0.003 27: 5 1 5 6 5 4 0 4 5 4 12491.1294 -0.0001 0.003 28: 5 1 5 6 4 4 0 4 5 3 12497.4417 -0.0004 0.003 29: 5 1 5 7 8 4 0 4 6 7 12501.8745 0.0002 0.003 30: 5 1 5 4 5 4 0 4 3 4 12504.5934 -0.0001 0.003 31: 5 1 5 7 7 4 0 4 6 6 12507.9342 0.0001 0.003 32: 5 1 5 5 5 4 0 4 4 4 12512.5888 -0.0006 0.003 33: 5 1 5 5 3 4 0 4 4 2 12514.7924 -0.0002 0.003 34: 5 1 5 7 6 4 0 4 6 5 12516.3838 -0.0001 0.003 35: 5 1 5 5 4 4 0 4 4 3 12523.5643 0.0006 0.003 36: 5 1 5 7 5 4 0 4 6 4 12525.7282 0.0006 0.003 37: 5 1 5 8 8 4 0 4 7 7 12529.0405 0.0003 0.003 38: 5 1 5 7 9 4 0 4 6 8 12531.0982 0.0003 0.003 39: 5 1 5 8 7 4 0 4 7 6 12537.7610 0.0000 0.003 40: 5 1 5 6 8 4 0 4 5 7 12538.7924 -0.0001 0.003 41: 5 1 5 5 7 4 0 4 4 6 12542.5832 -0.0001 0.003 42: 5 1 5 7 4 4 0 4 2 3 12552.9662 0.0007 0.003 43: 5 1 5 8 6 4 0 4 7 5 12560.6268 0.0000 0.003 44: 5 1 5 4 6 4 0 4 3 5 12563.1557 -0.0004 0.003 45: 5 1 5 3 5 4 0 4 2 4 12590.4004 0.0005 0.003 46: 5 1 5 8 5 4 0 4 7 4 12590.5270 -0.0006 0.003 47: 7 1 7 10 11 6 0 6 9 10 14331.6714 -0.0009 0.003 48: 7 1 7 9 11 6 0 6 8 10 14303.5701 -0.0001 0.003 49: 7 1 7 10 12 6 0 6 9 11 14354.9464 -0.0007 0.003 91 50: 7 1 7 7 6 51: 7 1 7 8 9 52: 3 1 3 6 8 53: 3 1 3 6 7 54: 3 1 3 4 5 55: 3 1 3 5 6 56: 3 1 3 5 6 57: 3 1 3 5 4 58: 3 1 3 5 5 59: 3 1 3 4 4 60: 3 1 3 3 5 61: 3 1 3 4 3 62: 3 1 3 6 6 63: 3 1 3 6 5 64: 3 1 3 4 6 65: 3 1 3 4 5 66: 3 1 3 2 4 67: 3 1 3 5 7 68: 3 1 3 6 3 69: 3 1 3 1 3 70: 3 1 3 1 2 71: 6 1 6 7 7 72: 6 1 6 7 6 73: 6 1 6 7 8 74: 6 1 6 8 7 75: 6 1 6 6 5 76: 6 1 6 7 5 77: 6 1 6 6 7 78: 6 1 6 5 5 79: 6 1 6 8 8 80: 6 1 6 6 4 81: 6 1 6 5 6 82: 6 1 6 7 9 83: 6 1 6 8 6 84: 6 1 6 8 9 85: 6 1 6 4 4 86: 6 1 6 6 8 87: 6 1 6 8 5 88: 6 1 6 9 7 89: 6 1 6 9 10 90: 6 1 6 9 11 91: 6 1 6 9 6 92: 7 1 7 8 8 93: 7 1 7 7 7 94: 7 1 7 8 7 95: 7 1 7 7 8 96: 7 1 7 8 6 97: 7 1 7 6 6 98: 7 1 7 9 8 99: 7 1 7 9 9 100: 7 1 7 7 5 101: 7 1 7 9 10 102: 7 1 7 6 7 103: 7 1 7 8 10 104: 7 1 7 9 7 105: 7 1 7 8 5 6 0 6 6 5 6 0 6 7 8 2 0 2 5 7 2 0 2 5 6 2 0 2 3 4 2 0 2 4 6 2 0 2 4 5 2 0 2 4 3 2 0 2 4 4 2 0 2 3 3 2 0 2 2 4 2 0 2 4 2 2 0 2 5 5 2 0 2 5 4 2 0 2 3 5 2 0 2 4 5 2 0 2 5 3 2 0 2 4 6 2 0 2 1 2 2 0 2 5 2 2 0 2 1 3 5 0 5 6 6 5 0 5 6 5 5 0 5 6 7 5 0 5 7 6 5 0 5 6 4 5 0 5 5 4 5 0 5 5 6 5 0 5 4 4 5 0 5 7 7 5 0 5 5 3 5 0 5 4 5 5 0 5 6 8 5 0 5 7 5 5 0 5 7 8 5 0 5 6 3 5 0 5 5 7 5 0 5 7 4 5 0 5 8 6 5 0 5 8 9 5 0 5 8 10 5 0 5 8 5 6 0 6 7 7 6 0 6 6 6 6 0 6 7 6 6 0 6 8 7 6 0 6 7 5 6 0 6 5 5 6 0 6 6 7 6 0 6 8 8 6 0 6 6 4 6 0 6 8 9 6 0 6 5 6 6 0 6 7 9 6 0 6 8 6 6 0 6 7 4 14249.0812 0.0000 0.003 14249.2691 0.0004 0.003 10718.4819 0.0000 0.003 10693.1120 -0.0002 0.003 10608.2921 -0.0005 0.003 10634.8502 -0.0001 0.003 10659.9003 0.0001 0.003 10668.2589 -0.0001 0.003 10668.3911 -0.0004 0.003 10634.5456 -0.0006 0.003 10671.3921 0.0004 0.003 10673.0757 0.0000 0.003 10682.5186 0.0001 0.003 10684.4968 0.0003 0.003 10687.4269 0.0000 0.003 10695.4596 0.0005 0.003 10698.9806 0.0000 0.003 10716.7465 0.0001 0.003 10731.2659 0.0011 0.003 10739.3862 0.0002 0.003 10766.3669 0.0008 0.003 13341.9368 0.0004 0.003 13349.2527 -0.0001 0.003 13353.8280 -0.0001 0.003 13356.3144 -0.0006 0.003 13360.3384 -0.0008 0.003 13365.7052 -0.0004 0.003 13376.2430 0.0003 0.003 13376.8583 -0.0005 0.003 13381.1838 -0.0002 0.003 13383.5938 -0.0006 0.003 13389.0404 0.0001 0.003 13389.8491 -0.0006 0.003 13392.2110 -0.0003 0.003 13395.3809 0.0000 0.003 13405.2182 -0.0001 0.003 13406.8618 -0.0006 0.003 13431.4258 0.0004 0.003 13444.8749 -0.0002 0.003 13446.7580 0.0000 0.003 13472.2111 -0.0002 0.003 13484.8327 -0.0006 0.003 14234.3519 0.0000 0.003 14236.9420 0.0001 0.003 14239.9459 0.0004 0.003 14259.6920 0.0004 0.003 14262.9232 0.0000 0.003 14264.0292 -0.0002 0.003 14268.1403 0.0002 0.003 14271.3685 0.0004 0.003 14272.6532 0.0000 0.003 14278.8875 0.0004 0.003 14286.9954 -0.0002 0.003 14288.1449 0.0002 0.003 14289.5529 0.0001 0.003 14293.0038 0.0000 0.003 92 106: 7 1 7 7 9 6 0 6 6 8 14299.9232 -0.0006 0.003 107: 7 1 7 10 9 6 0 6 9 8 14302.7686 0.0000 0.003 108: 7 1 7 10 10 6 0 6 9 9 14304.7204 -0.0003 0.003 109: 7 1 7 5 6 6 0 6 4 5 14322.6835 0.0000 0.003 110: 7 1 7 9 6 6 0 6 8 5 14325.4943 -0.0003 0.003 111: 7 1 7 10 8 6 0 6 9 7 14332.5252 -0.0008 0.003 112: 7 1 7 6 4 6 0 6 6 3 14308.3424 -0.0004 0.003 113: 2 1 2 5 7 1 0 1 4 6 9813.5359 0.0000 0.003 114: 2 1 2 5 6 1 0 1 4 5 9817.8772 -0.0002 0.003 115: 2 1 2 4 6 1 0 1 4 6 9630.4840 -0.0005 0.003 116: 2 1 2 5 5 1 0 1 4 4 9860.4421 -0.0009 0.003 117: 2 1 2 4 6 1 0 1 3 5 9880.0099 -0.0007 0.003 118: 2 1 2 4 5 1 0 1 3 5 9846.7150 -0.0002 0.003 119: 2 1 2 1 3 1 0 1 2 4 9791.4551 0.0005 0.003 120: 2 1 2 2 3 1 0 1 2 2 9741.0436 -0.0001 0.003 121: 2 1 2 5 4 1 0 1 2 3 9698.7910 -0.0001 0.003 122: 2 1 2 4 4 1 0 1 3 3 9803.4204 -0.0008 0.003 123: 1 1 1 2 1 0 0 0 3 1 8815.3291 -0.0005 0.003 124: 1 1 1 4 1 0 0 0 3 0 8816.6627 0.0007 0.003 125: 1 1 1 2 4 0 0 0 3 5 8820.9370 -0.0010 0.003 126: 1 1 1 2 2 0 0 0 3 2 8827.9837 -0.0006 0.003 127: 1 1 1 4 2 0 0 0 3 1 8829.4056 0.0002 0.003 128: 1 1 1 4 6 0 0 0 3 5 8829.7363 0.0002 0.003 129: 1 1 1 4 3 0 0 0 3 4 8838.0505 -0.0001 0.003 130: 1 1 1 4 3 0 0 0 3 2 8841.5895 -0.0003 0.003 131: 1 1 1 2 3 0 0 0 3 3 8842.8264 0.0001 0.003 132: 1 1 1 4 5 0 0 0 3 4 8851.1109 -0.0004 0.003 133: 1 1 1 4 4 0 0 0 3 3 8853.4289 0.0002 0.003 134: 1 1 1 3 4 0 0 0 3 4 8855.2453 0.0006 0.003 135: 1 1 1 3 5 0 0 0 3 5 8859.4731 -0.0004 0.003 136: 1 1 1 3 2 0 0 0 3 3 8860.8221 0.0008 0.003 137: 1 1 1 3 0 0 0 0 3 1 8864.3228 -0.0001 0.003 138: 1 1 1 3 2 0 0 0 3 1 8867.1129 0.0000 0.003 139: 8 1 8 9 9 7 0 7 8 8 15107.2397 0.0004 0.003 140: 8 1 8 8 8 7 0 7 7 7 15108.2355 0.0000 0.003 141: 8 1 8 9 8 7 0 7 8 7 15111.4244 0.0006 0.003 142: 8 1 8 8 7 7 0 7 7 6 15119.2324 0.0004 0.003 143: 8 1 8 8 6 7 0 7 7 5 15146.2147 -0.0012 0.003 144: 8 1 8 9 11 7 0 7 8 10 15159.5241 -0.0002 0.003 145: 8 1 8 11 12 7 0 7 10 11 15208.5465 -0.0001 0.003 146: 8 1 8 10 10 7 0 7 9 9 15149.3807 0.0017 0.003 147: 8 1 8 9 10 7 0 7 8 9 15124.6138 0.0006 0.003 -------------------------------------------------------------------------------PARAMETERS IN FIT (values truncated): 10000 A /MHz 8363.9676(10) 20000 B /MHz 496.1410(40) 30000 C /MHz 470.7846(34) 200 DJ /kHz 0.0343(53) 1100 DJK /kHz -3.8(17) 110010000 3/2*Chi_aa /MHz -1040.664(11) -220010000 3 /MHz -1040.664(11) 110040000 1/4(Chi_bb /MHz -154.9992(22) -220040000 1 /MHz -154.9992(22) 110610000 Chi_ab /MHz -856.226(10) 93 1 2 3 4 5 6 = 1.00000 * 6 7 = 1.00000 * 7 8 -220610000 Chi_ab /MHz 110011000 3/2*Chi_aa /MHz -220011000 3 /MHz 10010000 Caa /MHz -20010000 Caa /MHz 10020000 Cbb /MHz -20020000 Cbb /MHz 10030000 Ccc /MHz -20030000 Ccc /MHz 856.226(10) 0.0294(67) 0.0294(67) 0.00437(51) 0.00437(51) 0.00043(25) 0.00043(25) 0.00084(17) 0.00084(17) = -1.00000 * 8 9 = 1.00000 * 9 10 = 1.00000 * 10 11 = 1.00000 * 11 12 = 1.00000 * 12 MICROWAVE AVG = -0.000001 MHz, IR AVG = MICROWAVE RMS = 0.000483 MHz, IR RMS = END OF ITERATION 1 OLD, NEW RMS ERROR= 0.00000 0.00000 0.16094 0.16094 distinct frequency lines in fit: 147 distinct parameters of fit: 12 for standard parameter errors previous errors are multiplied by: 0.167941 MICROWAVE lines fitted lines lines RMS RMS ERROR J range Ka range freq. range total dv=0 dv.ne.0 UNFITTD e>900 v"= 1 3 1 2 0 0 0.000804 0.26805 2 4 0 1 10731 11674 v"= 2 6 1 5 0 0 0.000442 0.14720 1 5 0 1 9699 12590 v"= 3 27 6 21 0 0 0.000543 0.18088 0 5 0 1 8815 12563 v"= 4 24 3 21 0 0 0.000358 0.11941 1 7 0 1 9630 14323 v"= 5 21 1 20 0 0 0.000320 0.10666 2 7 0 1 10683 14287 v"= 6 22 2 20 0 0 0.000363 0.12102 3 7 0 1 11620 14308 v"= 7 21 0 21 0 0 0.000406 0.13550 4 8 0 1 12529 15146 v"= 8 16 0 16 0 0 0.000354 0.11785 5 8 0 1 13417 15160 v"= 9 6 0 6 0 0 0.000906 0.30185 6 8 0 1 14303 15149 v"=10 1 0 1 0 0 0.000100 0.03333 7 8 0 1 15209 15209 -------------------------------------------------------------------------------------------total: 147 14 133 0 0 0.000449 0.14955 PARAMETERS IN FIT WITH STANDARD ERRORS ON THOSE THAT ARE FITTED: (values rounded) 10000 A /MHz 8363.96765(18) 20000 B /MHz 496.14100(67) 30000 C /MHz 470.78460(57) 200 DJ /kHz 0.03430(89) 1100 DJK /kHz -3.86(28) 110010000 3/2*Chi_aa /MHz -1040.6649(18) -220010000 3 /MHz -1040.6649(18) 110040000 1/4(Chi_bb /MHz -154.99926(37) -220040000 1 /MHz -154.99926(37) 110610000 Chi_ab /MHz -856.2266(17) -220610000 Chi_ab /MHz 856.2266(17) 110011000 3/2*Chi_aa /MHz 0.0294(11) -220011000 3 /MHz 0.0294(11) = 10010000 Caa /MHz 0.004370(85) -20010000 Caa /MHz 0.004370(85) 10020000 Cbb /MHz 0.000434(43) -20020000 Cbb /MHz 0.000434(43) 10030000 Ccc /MHz 0.000845(29) 94 1 2 3 4 5 6 = 1.00000 * 6 7 = 1.00000 * 7 8 = -1.00000 * 8 9 1.00000 * 9 10 = 1.00000 * 10 11 = 1.00000 * 11 12 -20030000 Ccc /MHz 0.000845(29) = 1.00000 * 12 CORRELATION COEFFICIENTS, C.ij: A B C -DJ -DJK 3/2*Chi_ 1/4(Chi_ Chi_ab A 1.0000 B -0.5099 1.0000 C 0.2721 -0.9319 1.0000 -DJ -0.3980 0.2654 0.0625 1.0000 -DJK -0.3266 0.9474 -0.9981 -0.0372 1.0000 3/2*Chi_aa 0.1151 -0.1082 0.0663 -0.0843 -0.0750 1.0000 1/4(Chi_bb 0.2063 -0.1218 0.0482 -0.1500 -0.0620 0.7589 1.0000 Chi_ab 0.5393 -0.3475 0.1910 -0.3356 -0.2197 0.0489 0.1070 1.0000 3/2*Chi_aa -0.0914 -0.1408 0.1783 0.0060 -0.1687 -0.5815 -0.8157 0.0007 Caa 0.1766 -0.1067 0.0503 -0.1515 -0.0573 0.0222 0.1257 0.0774 Cbb 0.0604 -0.0222 -0.0063 0.0258 -0.0061 0.0359 -0.0035 0.0388 Ccc -0.0211 0.0509 -0.0626 0.0606 0.0537 0.1182 0.0466 -0.0034 3/2*Chi_ Caa Cbb Ccc 3/2*Chi_aa 1.0000 Caa -0.0925 1.0000 Cbb -0.0389 -0.2753 1.0000 Ccc -0.0424 -0.5428 0.8450 1.0000 Mean value of |C.ij|, i.ne.j = 0.2051 Mean value of C.ij, i.ne.j = -0.0354 Worst correlations, with absolute value greater than 0.9950: 1100 -DJK <-> 30000 C -0.998071 Worst fitted lines (obs-calc/error): 146: 125: 75: 4: 124: 35: 86: 36: 115: 8: 119: 142: 51: 0.6 -0.3 -0.3 0.3 0.2 0.2 -0.2 0.2 -0.2 0.2 0.2 0.1 0.1 22: 0.5 116: -0.3 111: -0.3 49: -0.2 147: 0.2 141: 0.2 106: -0.2 74: -0.2 45: 0.2 123: -0.2 3: 0.2 12: 0.1 135: -0.1 143: -0.4 47: -0.3 136: 0.3 42: 0.2 46: -0.2 126: -0.2 32: -0.2 82: -0.2 15: 0.2 54: -0.2 112: -0.1 139: 0.1 146: 8 1 8 10 10 7 0 7 9 9 22: 4 1 4 3 4 3 0 3 3 4 143: 8 1 8 8 6 7 0 7 7 5 68: 3 1 3 6 3 2 0 2 1 2 125: 1 1 1 2 4 0 0 0 3 5 68: 0.4 122: -0.3 70: 0.3 117: -0.2 80: -0.2 59: -0.2 134: 0.2 91: -0.2 78: -0.2 65: 0.2 94: 0.1 76: -0.1 15149.3807 0.0017 0.003 11664.7741 0.0015 0.003 15146.2147 -0.0012 0.003 10731.2659 0.0011 0.003 8820.9370 -0.0010 0.003 95 116: 2 1 2 5 5 1 0 1 4 4 9860.4421 -0.0009 0.003 47: 7 1 7 10 11 6 0 6 9 10 14331.6714 -0.0009 0.003 122: 2 1 2 4 4 1 0 1 3 3 9803.4204 -0.0008 0.003 75: 6 1 6 6 5 5 0 5 6 4 13360.3384 -0.0008 0.003 111: 7 1 7 10 8 6 0 6 9 7 14332.5252 -0.0008 0.003 _____________________________________ __________________________________________/ SPFIT output reformatted with PIFORM 96 30_DIS Thu Apr 13 13:06:27 2017 -------------------------------------------------------------------------------------========= obs o-c error blends Notes o-c wt / instead of : below denotes (o-c)>3*err -------------------------------------------------------------------------------------========= 1: 5 1 5 8 10 4 0 4 7 9 12369.4447 0.0010 0.003 2: 5 1 5 4 6 4 0 4 3 5 12358.7678 -0.0010 0.003 3: 5 1 5 8 9 4 0 4 7 8 12344.3718 -0.0001 0.003 4: 5 1 5 5 7 4 0 4 4 6 12338.5530 -0.0001 0.003 5: 5 1 5 6 8 4 0 4 5 7 12335.7161 0.0002 0.003 6: 5 1 5 6 7 4 0 4 5 6 12285.3090 -0.0004 0.003 7: 5 1 5 5 6 4 0 4 4 5 12285.4822 0.0001 0.003 8: 5 1 5 6 6 4 0 4 5 5 12287.2590 0.0000 0.003 9: 5 1 5 6 4 4 0 4 5 3 12293.4061 0.0007 0.003 10: 5 1 5 7 8 4 0 4 6 7 12296.2462 0.0002 0.003 11: 5 1 5 4 5 4 0 4 3 4 12300.9302 0.0004 0.003 12: 5 1 5 7 7 4 0 4 6 6 12304.3179 -0.0003 0.003 13: 5 1 5 5 3 4 0 4 4 2 12310.3467 -0.0005 0.003 14: 5 1 5 5 5 4 0 4 4 4 12312.5163 0.0005 0.003 15: 5 1 5 7 6 4 0 4 6 5 12315.6631 -0.0007 0.003 16: 5 1 5 3 4 4 0 4 2 3 12320.7392 -0.0003 0.003 17: 5 1 5 7 5 4 0 4 6 4 12322.2885 0.0008 0.003 18: 5 1 5 5 4 4 0 4 4 3 12322.4681 -0.0002 0.003 19: 5 1 5 8 8 4 0 4 7 7 12323.0305 -0.0002 0.003 20: 5 1 5 7 9 4 0 4 6 8 12325.0168 0.0002 0.003 21: 5 1 5 4 4 4 0 4 3 3 12328.8735 0.0002 0.003 22: 5 1 5 8 7 4 0 4 7 6 12333.1126 -0.0005 0.003 23: 4 1 4 7 8 3 0 3 6 7 11435.4934 -0.0009 0.003 24: 4 1 4 7 9 3 0 3 6 8 11459.1547 0.0009 0.003 25: 8 1 8 9 11 7 0 7 8 10 14945.1307 -0.0008 0.003 26: 8 1 8 10 10 7 0 7 9 9 14938.6617 0.0007 0.003 27: 8 1 8 9 8 7 0 7 8 7 14897.9638 0.0001 0.003 -------------------------------------------------------------------------------PARAMETERS IN FIT (values truncated): 10000 A /MHz 8165.331(22) 1 20000 B /MHz 496.1493(65) 2 30000 C /MHz 470.1462(35) 3 200 DJ /kHz [ 0.034273534] 4 1100 DJK /kHz [-3.863214938] 5 110010000 3/2*Chi_aa /MHz -1040.687(63) 6 -220010000 3 /MHz -1040.687(63) = 1.00000 * 6 110040000 1/4*(Chi_b /MHz -154.9940(43) 7 -220040000 1 /MHz -154.9940(43) = 1.00000 * 7 110610000 Chi_ab /MHz -856.237(55) 8 -220610000 Chi_ab /MHz 856.237(55) = -1.00000 * 8 110011000 3/2*Chi_aa /MHz [ 0.029390982] 9 -220011000 3 /MHz [ 0.029390982] = 1.00000 * 9 10010000 Caa /MHz [ 0.004374655873] 10 -20010000 Caa /MHz [ 0.004374655873] = 1.00000 * 10 10020000 Cbb /MHz [ 0.000434372859] 11 -20020000 Cbb /MHz [ 0.000434372859] = 1.00000 * 11 10030000 Ccc /MHz [ 0.000845412496] 12 97 -20030000 Ccc /MHz [ 0.000845412496] MICROWAVE AVG = 0.000000 MHz, IR AVG = MICROWAVE RMS = 0.000576 MHz, IR RMS = END OF ITERATION 1 OLD, NEW RMS ERROR= distinct frequency lines in fit: distinct parameters of fit: = 1.00000 * 12 0.00000 0.00000 0.19184 0.19184 27 6 for standard parameter errors previous errors are multiplied by: 0.217526 MICROWAVE lines fitted lines lines RMS RMS ERROR freq. range total dv=0 dv.ne.0 UNFITTD e>900 v"= 2 1 0 1 0 0 0.000300 0.10000 4 5 0 v"= 3 3 0 3 0 0 0.000632 0.21082 4 5 0 v"= 4 5 0 5 0 0 0.000335 0.11155 4 5 0 v"= 5 4 0 4 0 0 0.000415 0.13844 4 5 0 v"= 6 7 0 7 0 0 0.000646 0.21529 3 5 0 v"= 7 4 0 4 0 0 0.000570 0.19003 4 5 0 v"= 8 2 0 2 0 0 0.000570 0.19003 7 8 0 v"= 9 1 0 1 0 0 0.000700 0.23333 7 8 0 -------------------------------------------------------------------------------------------total: 27 0 27 0 0 0.000541 0.18031 J range Ka range 1 1 1 1 1 1 1 1 12321 12301 12285 12285 11435 12323 14898 14939 12321 12359 12339 12336 12325 12369 14945 14939 PARAMETERS IN FIT WITH STANDARD ERRORS ON THOSE THAT ARE FITTED: (values rounded) 10000 A /MHz 8165.3310(48) 1 20000 B /MHz 496.1493(14) 2 30000 C /MHz 470.14620(76) 3 200 DJ /kHz [ 0.034273534] 4 1100 DJK /kHz [-3.863214938] 5 110010000 3/2*Chi_aa /MHz -1040.687(13) 6 -220010000 3 /MHz -1040.687(13) = 1.00000 * 6 110040000 1/4*(Chi_b /MHz -154.99400(93) 7 -220040000 1 /MHz -154.99400(93) = 1.00000 * 7 110610000 Chi_ab /MHz -856.237(11) 8 -220610000 Chi_ab /MHz 856.237(11) = -1.00000 * 8 110011000 3/2*Chi_aa /MHz [ 0.029390982] 9 -220011000 3 /MHz [ 0.029390982] = 1.00000 * 9 10010000 Caa /MHz [ 0.004374655873] 10 -20010000 Caa /MHz [ 0.004374655873] = 1.00000 * 10 10020000 Cbb /MHz [ 0.000434372859] 11 -20020000 Cbb /MHz [ 0.000434372859] = 1.00000 * 11 10030000 Ccc /MHz [ 0.000845412496] 12 -20030000 Ccc /MHz [ 0.000845412496] = 1.00000 * 12 CORRELATION COEFFICIENTS, C.ij: A B C 3/2*Chi_ 1/4*(Chi Chi_ab A 1.0000 B -0.9949 1.0000 C -0.9979 0.9991 1.0000 3/2*Chi_aa 0.0851 -0.0701 -0.0757 1.0000 98 1/4*(Chi_b 0.1551 -0.1138 -0.1299 0.6499 1.0000 Chi_ab -0.8048 0.8369 0.8300 0.2019 0.2696 1.0000 Mean value of |C.ij|, i.ne.j = 0.4810 Mean value of C.ij, i.ne.j = 0.0560 Worst correlations, with absolute value greater than 0.9950: 30000 C 30000 C <-> <-> 10000 A 20000 B -0.997920 0.999121 Worst fitted lines (obs-calc/error): 1: 25: 15: 6: 5: 18: 7: 0.3 -0.3 -0.2 -0.1 0.1 -0.1 0.0 2: -0.3 17: 0.3 14: 0.2 11: 0.1 21: 0.1 10: 0.1 4: 0.0 23: -0.3 9: 0.2 22: -0.2 12: -0.1 20: 0.1 27: 0.0 8: 0.0 24: 26: 13: 16: 19: 3: 0.3 0.2 -0.2 -0.1 -0.1 0.0 1: 5 1 5 8 10 4 0 4 7 9 12369.4447 0.0010 0.003 2: 5 1 5 4 6 4 0 4 3 5 12358.7678 -0.0010 0.003 23: 4 1 4 7 8 3 0 3 6 7 11435.4934 -0.0009 0.003 24: 4 1 4 7 9 3 0 3 6 8 11459.1547 0.0009 0.003 25: 8 1 8 9 11 7 0 7 8 10 14945.1307 -0.0008 0.003 17: 5 1 5 7 5 4 0 4 6 4 12322.2885 0.0008 0.003 9: 5 1 5 6 4 4 0 4 5 3 12293.4061 0.0007 0.003 26: 8 1 8 10 10 7 0 7 9 9 14938.6617 0.0007 0.003 15: 5 1 5 7 6 4 0 4 6 5 12315.6631 -0.0007 0.003 14: 5 1 5 5 5 4 0 4 4 4 12312.5163 0.0005 0.003 _____________________________________ __________________________________________/ SPFIT output reformatted with PIFORM 99 List of Figures 2.1 The experimental rotational spectrum of 2-iodobutane is shown above the baseline and the simulated spectra of the various conformers are shown below. This portion of spectrum illustrates the heavy overlap of the hyperfine structure due to the iodine nucleus in each of the three conformers. The predicted gauche-, anti-, and gauche0 -2-iodobutane transitions are represented by purple, red, and green, respectively. Theoretical transition intensities have been scaled using the relative ab initio energies. . . . . . . . . . . . . . 2.2 14 Illustrations of the three ab initio structures. The C1 −C2 −C3 −C4 dihedral angles for the a-, g0 -, and g-conformers are 64◦ , -62◦ , and 171◦ , respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The Doppler doublet of the a-type S-branch transition, 404 3 2 14 ← 221 21 , of the parent conformer of g-2-iodobutane is shown, where the average of each peak is taken to be the transition frequency, 11011.621 MHz. Labels on the y-axis of the plot were omitted, since the intensity of the transition is arbitrary. The transition was measured on a Balle-Flygare type spectrometer with 100 averages, with a signal-to-noise ratio of 76. . . . . . . . . . . . . . . . . . . 100 18 3.1 Calculated structures of the anti-anti (aa)-, gauche-anti (ga)-, and gauche-gauche (gg)-conformers of 1-iodobutane from an ab initio optimization. The C−C−C−C and C−C−C−I dihedral angles for the aa-, ga-, and gg-species were calculated to be 180◦ , 180◦ ; 179◦ , 66◦ ; and -65◦ , -63◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 37 A small portion of the experimental spectrum of 1-iodobutane is shown in black, with the final simulated spectra for the aa-, ga-, and gg-conformers shown below in green, purple, and red, respectively. The quantum numbers associated with each rotational transition are also presented above the experimental spectrum, in the form 0 0 00 00 JK 0 0 F ← JK 00 K 00 F . . . . . . . . . . . . . . . . . . . . . . . . . . a Kc a c 3.3 38 A 100 MHz portion of three different predictions of the rotational spectrum of aa-1-iodobutane. The top orange spectrum is based on a hybrid tensor (discussed in Spectral Assignments) and ab initio rotational constants, the middle blue spectrum is the prediction using the experimental results belonging to the aa-conformer, and the bottom orange spectrum is based completely on ab initio results. 38 101 List of Tables 1.1 Classes of rigid rotors . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Ab initio results of 2-iodobutane at the MP2 level of theory . . . 15 2.2 Spectroscopic parameters of three conformations of 2-iodobutane . 20 2.3 Spectroscopic parameters for g-2-iodobutane . . . . . . . . . . . . 21 2.4 STRFIT r0 structural parameters of gauche-2-iodobutane . . . . . 23 2.5 Kraitchman versus ab initio coordinates for gauche-2-iodobutane . 24 2.6 Conformational comparison of the diagonalized NQC tensor of iodine in 2-iodobutane . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Comparison of the diagonalized NQC tensor of iodine 2-iodobutane with other iodoalkanes . . . . . . . . . . . . . . . . . . . . . . . . 2.8 25 27 Rotation of the diagonalized NQC tensor of iodine into the principal axis system of g-2-iodobutane . . . . . . . . . . . . . . . . . . 28 2.9 Changes in the ab initio NQC tensor due to isotopic substitution 29 3.1 Rotational constants and NQCCs for three conformers of 1-iodobutane as determined from ab initio optimization at the MP2 level of theory 37 3.2 Spectroscopic parameters of 1-iodobutane . . . . . . . . . . . . . . 3.3 Comparison of the two methods of prediction for the NQC tensors 39 in 1-iodobutane . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 Comparison of this work with the previous study of 1-iodobutane 43 3.5 NQC tensor of iodine in 1-iodobutane . . . . . . . . . . . . . . . . 44 3.6 NQC tensor of bromine in 1-bromobutane[37] . . . . . . . . . . . 45 3.7 A comparison of this work with similar haloalkanes . . . . . . . . 46 102 4.1 Results obtained from equation (4.1) . . . . . . . . . . . . . . . . 56 4.2 Spectroscopic parameters of three silicon isotopologues of diiodosilane 57 4.3 NQC tensor of iodine in diiodosilane . . . . . . . . . . . . . . . . 59 4.4 r0 structure versus GED of diiodosilane . . . . . . . . . . . . . . . 61

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