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Ionization processes and photofragmentation via multiphoton excitation and state interactions Kristján Matthíasson Ionization processes and photofragmentation via multiphoton excitation and state interactions Kristján Matthíasson Dissertation submitted in partial fulfillment of a Philosophiae Doctor degree in Physical Chemistry Advisor Ágúst Kvaran PhD Committee Oddur Ingólfsson Ingvar Helgi Árnason Gísli Hólmar Jóhannesson Opponents Christof Maul Ragnar Jóhannsson Faculty of Physical Sciences School of Engineering and Natural Sciences University of Iceland Reykjavík, October 2011 Ionization processes and photofragmentation via multiphoton excitation and state interactions Dissertation submitted in partial fulfillment of a Philosophiae Doctor degree in Physical Chemistry Copyright © 2011 Kristján Matthíasson All rights reserved Faculty of Physical Sciences School of Engineering and Natural Sciences University of Iceland Dunhagi 3 107, Reykjavik Iceland Telephone: 525 4000 Bibliographic information: Kristján Matthíasson, 2011, Ionization processes and photofragmentation via multiphoton excitation and state interactions, PhD dissertation, Faculty of Physical Sciences, University of Iceland. ISBN 978-9979-9935-9-9 Printing: Háskólaprent ehf. Reykjavik, Iceland, October 2011 Abstract My Ph.D. work was centered on observing the relative formation of separate molecular and atomic fragments. This led to the development of a new method for measuring and analysing data entailing the simultaneous collection of mass and frequency data over a specific mass area and frequency range, resulting in a detailed 2D map of the measured area. From this map both a REMPI spectrum and a mass spectrum could be extracted as needed. Three separate molecules were studied, acetylene (C2H2), hydrogen chloride (HCl) and methyl bromide (CH3Br). By observing the relative formation of separate atoms and molecular fragments by photoexcitation as function of laser power and frequency it was possible to determine the dissociation mechanics for these molecules. For HCl, the relative intensity of Cl+/HCl+ ions that formed via photoexcitation proved to be a highly sensitive indicator of perturbation between Rydberg and ion-pair states. A mathematical model was developed to evaluate state interaction strengths from the relative intensity of Cl+/HCl+ ions and the interaction strengths of several states were calculated. The relative intensity of Cl+/HCl+ ions proved also to be a highly useful tool in spectrum assignment. iii Útdráttur Athugun á myndun sameinda- og atómbrota við ljósörvun var þungamiðja doktorsverkefnis míns. Það leiddi til þróunar á nýjum hugbúnaði og aðferðafræði við að safna og greina gögn með það‚ í huga að safna samtímis massa og tíðni gögnum yfir tiltekið mælisvið. Þessi aðferð myndar tvívíddar kort af mælisviðinu. Úr þessu korti má svo draga fram bæði massaróf fyrir tiltekna tíðni jafnt og tíðniróf fyrir tiltekin massa eftir þörfum. Þrjár mismunandi sameindir voru rannsakaðar, asetýlen (C2H2), saltsýra (HCl) og metýlbrómíð (CH3Br). Með því að bera saman hlutfallslega massamyndun þeirra atóma eða sameindabrota sem myndast við ljósörvun var hægt að ráða í niðurbrotsferla þessara sameinda. Hlutfallslegur styrkur Cl+/HCl+ jóna sem mynduðust við ljósörvun á HCl reyndist vera mjög nákvæmur vísir að víxlverkun milli Rydberg og jónparaástanda fyrir bæði H35Cl og H37Cl samsæturnar. Stærðfræðilíkan var þróað til að meta víxlverkunarstyrkinn út frá hlutföllum Cl +/HCl+ og víxlverkunarstyrkur reiknaður fyrir nokkur ástönd. Þetta hlutfall reyndist einnig vera nothæft tæki til að skilgreina litróf. iv Table of Contents List of Figures ........................................................................................ vii List of Tables ............................................................................................ x List of abbreviations ...............................................................................xi Acknowledgements............................................................................... xiii 1 Introduction ....................................................................................... 15 1.1 Acetylene (C2H2) ...................................................................... 16 1.2 Hydrogen Chloride (HCl) ......................................................... 17 1.3 Methyl bromide (CH3Br) .......................................................... 19 2 Experimental setup and analysis method ....................................... 21 2.1 Experimental apparatus ............................................................ 21 2.2 Analysis Method ....................................................................... 23 2.2.1 Simulations ..................................................................... 25 2.2.2 Time of flight analysis.................................................... 26 3 Theoretical considerations ............................................................... 27 3.1 Electronic spectroscopy of diatomic molecules72-74.................. 27 3.1.1 Electronic energy levels. ................................................ 27 3.1.2 Vibrational energy levels................................................ 29 3.1.3 Rotational energy levels ................................................. 31 3.2 The intensity of electronic excitation spectroscopy lines7274 ................................................................................................ 34 3.2.1 Transition probabilities................................................... 34 3.2.2 Boltzmann distribution ................................................... 35 3.2.3 Laser power dependence ................................................ 37 3.2.4 Multiphoton excitation intensities .................................. 38 3.3 Total angular momentum and Hund’s cases72 .......................... 39 3.3.1 Hund’s case a) ................................................................ 40 3.3.2 Hund’s case b) ................................................................ 42 3.3.3 Hund’s case c) ................................................................ 42 3.4 Symmetry properties72 .............................................................. 43 v 3.4.1 Parity of rotational levels ............................................... 44 3.4.2 Parity selection rules ...................................................... 44 3.5 Perturbations72.......................................................................... 45 3.5.1 Rotational perturbations ................................................ 45 3.5.2 Perturbation selection rules............................................ 46 3.6 Predissociation72....................................................................... 46 4 Published papers .............................................................................. 49 International Journals ......................................................................... 49 Icelandic Journals ............................................................................... 49 5 Ion formation through multiphoton processes for HCl35-39,77 ..... 113 5.1 Formation of HCl+ ................................................................. 113 5.1.1 Ionization via Rydberg states....................................... 113 5.1.2 Ionization via ion-pair state ......................................... 113 5.2 Formation of H+ ..................................................................... 115 5.2.1 Ionization via Rydberg states....................................... 115 5.2.2 Ionization via ion-pair state ......................................... 115 5.3 Formation of Cl+ .................................................................... 116 5.3.1 Ionization via Rydberg states....................................... 116 5.3.2 Ionization via ion-pair state ......................................... 116 6 The use of mass analysis to determine interaction constants ..... 119 7 Ionization of acetylene and methyl bromide compared to HCl................................................................................................... 123 8 Unpublished work .......................................................................... 125 8.1 C1-State ............................................................................... 125 8.2 E1-State ................................................................................ 126 References ............................................................................................ 129 Appendix A: Conference presentations ............................................. 135 Posters .............................................................................................. 135 Talks ............................................................................................... 136 vi List of Figures Figure 1. Schematic of the REMPI-TOF experimental equipment. ........ 22 Figure 2: HCl spectra in the range of 85320 – 85370 cm-1. Below is the 2D contour spectrum that shows clearly the different ions formed as a function of both atomic/molecular mass and wavenumbers. Above are REMPI spectra derived from the contour plot for each ion observed. Mass spectra for individual wavenumbers could also be derived in similar fashion. ...................................................... 24 Figure 3: Experimental data (above) for the excitation g3(1)+ X1+ (0,0) and the simulated spectrum (below) derived from spectroscopic constants. The experimental spectrum also contains a single peak due to the D1 ←← X1+ (0,0) excitation. Simulations can thus be of use for peak assignments in addition to accurately determining rotational constants. ............................................ 26 Figure 4: Energy diagram for molecular orbitals of HCl. a) Ionpair excitations. An electron is excited from the bonding orbital of the molecule to the antibonding orbital. b) Rydberg excitations. An electron is excited from the non-bonding orbital to a Rydberg orbital. .............................. 28 Figure 5: Rydberg potential vs. ion-pair potential. The figure illustrates the difference between an ion-pair state and a Rydberg state. The average bond length of the ion–pair state is longer than that of the Rydberg state due to the excitation of an electron to the antibonding orbital, giving the excited molecule semi-ionic properties. The vibrational levels are quantized and distributed according to the shape of the potentials. ................................. 30 Figure 6: For each molecular Rydberg state there are discrete vibrational levels. For each vibrational state there are also discrete rotational levels. The vibrational series depend on the shape of the potential and the rotational vii series depend on the energy and thus the mean bond length of the vibrational levels. ............................................... 32 Figure 7: Franck-Condon factors. The vibrational levels are positioned so that the probability function forms a standing wave. It is the overlap of these probability distributions that determines the Franck-Condon factors. Figure from http://www.chem.ucsb.edu/~kalju/chem126/public/elspe ct_theory.html ......................................................................... 36 Figure 8: When gas is jet-cooled the rotational energy of individual molecules shifts downwards, thus increasing the probability of excitation from the lower rotational levels compared to that from the higher ones. ................................. 37 Figure 9: The precession of L about the internuclear axis. The precession forms a component along the internuclear axis..................39 Figure 10: Simple rotator. If S = 0 and L = 0 we only need to consider the angular momentum of nuclear rotation N. Therefore we have a simple rotator were N is equal to the total angular momentum J. .............................................. 41 Figure 11: Hund‘s case a). The orbital angular momentum and the electronic spin form the electronic angular momentum . The angular momentum of the rotation molecule N and the electronic angular momentum then form the total angular momentum J. .............................. 41 Figure 12: Hund‘s case b). and N form a resultant which is called K. The angular momenta K and S then form a resultant J. ................ 42 Figure 13: Hund‘s case c). L and S form a resultant Ja which is coupled to the internuclear axis with a component . and N then form a resultant J................................................. 43 Figure 14: Parity. The + and – suffixes in the term symbol indicate the parity of the rotational levels of the states. For multiplet states the parity depends on K instead of J. ............ 44 Figure 15: Perturbation. On the left we have an average ion ratio for the F1, ’=1 state. On the right we have the ratio for the perturbed F1, ’=1, J’=8 rotational level. As can be clearly seen, the perturbation to the ion-pair state causes considerable changes to the ratio of H+ and Cl+ vs. HCl+ ion formation for both the 35Cl and 37Cl isotopes................... 45 viii Figure 16: Predissociation of a diatomic molecule. a) Predissociation followed by a direct ionization. The molecule is initially excited to a bound state which interacts by a non-bound or a quasi-bound state. Some of the molecules in the bound state “leap” across to the predissociating state and are dissociated into its atomic components. The atoms formed can themselves absorb photon energy and ionize. b) Predissociation followed by a resonance-enhanced ionization. In this case the photon energy needed to excite the parent molecule corresponds to an excited state of the atom resulting in a resonance-enhanced excitation. ............................................. 47 Figure 17: Main ionization mechanisms of HCl. Figures a) and b) show possible ionization channels via Rydberg (HCl*) and ion-pair states (H+Cl-). The predissociation gateway mechanism forming H + Cl is included. Necessary amount of photons for ionization are shown. ...................... 114 Figure 18: (2+n) REMPI of C1 ←← X1+ (0,0) excitation. The figure shows a diffused spectrum of the H35Cl isotopologue. ....................................................................... 125 Figure 19: I(Cl+)/I(HCl+) ratio for the C1 state ’=0. The white columns represent the P-series, the black columns the R-series and the gray columns the S-series. An increased I(Cl+)/I(HCl+)ratio is observed for the J’=4 rotational level. A small increase in I I(Cl+)/I(HCl+) for the R-series at J’=4 is most likely due to an overlap with the J’=2 peak of the S-series. ............................................... 126 Figure 20: (2+n) REMPI of E1 ←← X1+ (1,0) and V1 ←← X1+ (14,0) excitations. The figure shows the HCl+/Cl+ ratio of individual rotational peaks. ..................................... 127 ix List of Tables Table 1: SHG crystals used for specific dyes and wavelengths of entering photons.................................................................. 21 Table 2: State interaction parameters. ................................................... 121 Table 3: E values for the rotational peaks of the E1 ←← X1+ (1,0) and V1 ←← X1+ (14,0) excitations. ......................... 127 x List of abbreviations a2 = probability distribution C = Speed of light Deq = Dissociation energy E = Energy FCF = Franck-Condon factors h = Planck constant I = Moment of inertial Irel = Relative intensity J = Rotational quantum number K = Total angular momentum apart from spin kb = Boltzmann constant L = Orbital angular momentum vector L = Orbital angular momentum quantum number m = Mass = Reduced mass Mw = Molecular weight N = Population of state P = Power r = Internuclear distance S = Spin vector S = Spin quantum number T = Temperature TOF = Time-of-Flight = Vibrational quantum number = Total angular momentum vector = Total angular momentum quantum number osc = Oscillation frequency e = Anharmonicity constant = wavefunction xi Acknowledgements I would like to thank my advisor Prof. Ágúst Kvaran for his guidance and patience during my Ph.D studies. I would also like to thank my many co-workers during this project, Victor Huasheng Wang, Erlendur Jónsson, Dr. Andras Bodi, and other members of the University of Iceland, Science Institute for their assistance, encouragement and support. The financial support of the University Research fund, University of Iceland and the Icelandic Science foundation is greatfully acknowledged. xiii 1 Introduction My Ph.D. work centered on observing the relative formation of separate molecular and atomic ion fragments via photoexcitation. It entailed gathering experimental data by utilising REMPI or Resonance-EnhancedMulti-Photon-Ionization and analysing the data both in terms of atomic mass and laser frequency. This led to the development of a new method for measuring and analysing data entailing the simultaneous collection of REMPI mass and frequency data over a certain mass area and frequency range into a single data matrix. This data matrix can be turned into a detailed 2D map of the measured area using commercial software such as Igor Pro and Labview which enables us to see important connections between formations of the various ions (in terms of relative intensities). Thus 2D data for HX show you how I(H+), I(X+) and I(HX+) vary with wavenumbers (hence quantum numbers J´) and states. From this 2D map both a REMPI spectrum of a specific atomic or molecular mass and a mass spectrum for a specific laser frequency could be extracted as needed. This method proved to be highly effective, both in accuracy and speed. Three separate molecules were studied in the following order, acetylene (C2H2), hydrogen chloride (HCl) and methyl bromide (CH3Br). By observing the relative formation of separate atoms and molecular fragments by photoexcitation as a function of laser power and frequency in conjucntion with theoretical ab initio calcualtions performed by my group members it was possible to determine the dissociation mechanics for these molecules. For HCl specifically, the relative intensity of Cl+/HCl+ ions that formed via photoexcitation proved to be a highly sensitive indicator of perturbation between Rydberg and ion-pair states for both H35Cl and H37Cl isotopologues surpassing those previously used, such as line shifts. A mathematical model was developed to evaluate state interaction strengths from the relative intensity of Cl+/HCl+ ions and the interaction strengths of several states were calculated using both this new method and older methods which relied on line shifts and relative intensities. The relative intensity of Cl+/HCl+ ions proved also to be a highly useful tool in spectrum assignment, notably in rotational line assignments. 15 1.1 Acetylene (C2H2) The UV spectroscopy, photochemistry and photophysics of acetylene (C2H2) have been widely studied over the recent years. This is partly due to its importance in interstellar space and cometary atmospheres, where it is a commonly observed molecule. There it has been considered to be a reservoir molecule for the production of carbon containing radicals which, in turn, are involved in the formation of larger organic compounds.1-3 Furthermore, being the simplest member of unsaturated hydrocarbons, acetylene is a fundamental unit in various organic photochemistry processes and synthesis work. Photodissociation of C2H2 has been the subject of numerous experimental investigations, among which are studies by single-1,2,4-8 , two-9,10 and three- 2,4 photon resonance excitations. Due to the strict u ↔ g selection for excitation per photon interaction, only ungerade Rydberg states are accessed by one- and three- (odd number) photon excitations from the 1 + g electronic ground state, whereas gerade Rydberg states are accessible by two-photon (even number) excitation. Considering this and the additional restriction on possible intersystem crossings based on the selection rules u↔u and g↔g, it is not surprising that the mechanism and outcome of photodissociation differs, depending on odd- or evennumber photon excitations. Fragmentation of C2H2 into C2H and H is found to be dominant following single and three-photon excitations.1,6,10 Thus, single-photon excitations of the Rydberg states below the first ionization potential reveal only the C2H product by emission spectra.6 Two distinct dissociation channels, following single-photon excitations, have been observed7,8, showing major differences with respect to internal energies and angular distributions of the fragments C2H and H. In both channels the observed decay dynamics is found to depend strongly on the excited state of the parent molecule, C2H2*. In the case of a predissociation of the C2H2 (H1u) Rydberg state it has been proposed that it occurs via the bent valence state A1Au.7 From less extensive two-photon excitation studies, on the other hand, both fragmentations into C2 + H2 and into C2H + H, are found to occur.9,11 Thus, H atoms, H2 molecules and C2 molecules in the X1g+, a3u , A1u and d3g states have been identified by time resolved photofragment and emission detection studies.9,11 Both the sequential bond-rupture mechanism and concerted two-bond fission processes have been proposed to explain the C2 16 and H2 fragment formations.11 Furthermore, long-lived bent isomers of C2H2 as well as C2H intermediates have been revealed experimentally. Tsuji et al. concluded, from detailed REMPI analysis9, that ion fragment formations are dominantly due to the ionization of neutral molecular fragments after predissociation. Because of the characteristic predissociation channels the ungerade and gerade Rydberg states of acetylene are found to be short lived; lifetimes range from 50 fs to more than 10 ps.4,9 More recently Matthíasson et al.12 were able to determine important thresholds for fragmentation processes by combining ion mass-analysis as a function of laser excitation frequencies and laser power with DFT/STQN calculations on C2H2 C2 + H2. 1.2 Hydrogen Chloride (HCl) Since the original work by Price on hydrogen halides13, a wealth of spectroscopic data on HCl has been derived from absorption spectroscopy14-17, fluorescence studies17 as well as from REMPI experiments.18-32 Relatively intense single- and multiphoton absorption in conjunction with electron excitations as well as rich band-structured spectra make the molecule ideal for fundamental studies. A large number of Rydberg states, both several low lying repulsive states as well as the V(1+) ion-pair state have been identified. A number of spinforbidden transitions are observed, indicating that spin-orbit coupling is important in excited states of the molecule. Perturbations due to state mixing are widely seen both in absorption15-17 and REMPI spectra.19,20,22,24,25,27,28,32 The perturbations appear either as line shifts16,19,20,22,25,27,28,32 or as intensity and/or bandwidth alterations.16,19,20,22,24,25,27,28,32 Pronounced ion-pair to Rydberg state mixings are both observed experimentally15,16,20,22,25,27,28,32,33 and predicted from theory.33,34 Interactions between the V(1+) ion-pair state and the E(1+) state are found to be particularly strong and to exhibit nontrivial rotational, vibrational and electron spectroscopy. Perturbations due to Rydberg-Rydberg mixings have also been predicted and identified.16,24 Both homogeneous (= 0)27,28,33,34 and heterogeneous (> 0)28,32,33 couplings have been reported. Such quantitative data on molecule-photon interactions are of interest in understanding stratospheric photochemistry as well as being relevant to the photochemistry of planetary atmospheres and the interstellar medium.17 The excitation and subsequent ion formation mechanism of the HCl molecule have generally been considered a two-step process, i.e. the 17 excitation of the molecule to an energetically higher Rydberg or ion-pair state followed by its ionization. There is however evidence that a far more complex mechanism controls the ionization of HCl molecules and its atomic fragments. Photofragmentation studies of HCl have revealed a large variety of photodissociation and photoionization processes. In a detailed twophoton resonance-enhanced multiphoton ionization study, Green et al. report HCl+, Cl+ and H+ ion formations for excitations via a large number of = 0 Rydberg states as well as via the V1+ ( = 0) ion-pair state, whereas excitations via other Rydberg states are mostly found to yield HCl+ ions.19 More detailed investigations of excitations via various Rydberg states and the V1+ ion-pair state by use of photofragment imaging and/or mass-resolved REMPI techniques have revealed several ionization channels depending on the nature of the resonance excited state.35-39 Results are largely based on an analysis of excitations via the E1+ Rydberg state and the V1+ ion-pair state, which couple strongly to produce the mixed (adiabatic) B1+ state with two minima. Recently, analyses of excitations via the F1 (´=1) Rydberg state and the V1+(´=14) state have shown characteristic effects of near-resonance interactions on photoionization channels.39 Those studies introduced the possibility of a model that used the I(Cl+)/I(HCl+) rate to determine the max interaction strength ( W12 ) of a near resonance interaction. A more detailed analysis of excitations via low-energy triplet states has revealed similar fragmentations due to coupling with the ion-pair state and has introduced a model to determine the interaction strength of a nearresonance interaction.40 Those studies revealed characteristic ionization channels which have been summarized in terms of excitations via 1) resonance noncoupled (diabatic) Rydberg state excitations, 2) resonance noncoupled (diabatic) ion-pair excitations and 3) dissociation of resonance-excited Rydberg states to form H + Cl and/or H + Cl* via predissociation of some gateway states followed by ionization.39-41 This model is supported by Kauczok et al.42 as they used velocity mapping to determine the origins of H+ ions formed via the near-resonating lines of F1 ←←X1+, (0,0), J´= 8 and f32 ←←X1+, (0,0), J´= 5 reported by Kvaran et al. Their findings show that a major portion of H+ formed by these two excitations are via the ion-pair state and it is reasonable to assume that Cl+ is also formed by the same or similar pathways. 18 1.3 Methyl bromide (CH3Br) The spectroscopy43-47 and photofragmentation48-54 of methyl bromide have received considerable interest over the last decades, both experimentally43-53 and theoretically54, for a number of reasons. Methyl bromide as well as the chlorine and iodine containing methyl halides play important roles both in the chemistry of the atmosphere 47,55-57 and in industry. Thus, although far less abundant than methyl chloride in the stratosphere, methyl bromide is found to be much more efficient in ozone depletion57 and its use is now being phased out under the Montreal Protocol. Furthermore, bromocarbons are known to have a high global warming potential.58 Additionally, the molecule is a simple prototype system of a halogen containing an organic molecule and is as such well suited for fundamental studies of photodissociation and photoionization processes.51,54,59 Little is known about the UV spectroscopy of methyl bromide despite its importance in various contexts. Since a pioneering work by Price 43 in 1936 some absorption studies have appeared dealing with i) a weak continuous spectrum (the A band) in the low energy region (> 180 nm; E < 55500 cm-1)44,47,55,56 due to transitions to repulsive states54 and ii) higher energy (< 180 nm; E > 55500 cm-1) Rydberg series and its vibrational analysis.44-46 There has been some controversy in the literature concerning the assignment of the higher energy band spectra. Locht et al. recently reported on the analysis and assignments of spectra46 which differ from earlier reports.43-45 More recently, multiphoton absorption (REMPI) studies59 and ab initio calculations of excited states60 have been published which help clarify the discrepancy. Photofragmentation studies of methyl bromide can be classified into two groups. One group focuses on the characterization of photofragments CH3 + Br(2P3/2)/Br*(2P1/2) resulting from photodissociation in the A band48-51,54 whereas the other group concerns the CH3+ +Br- ion-pair formation52,53,59 in the energy region between the ion-pair formation threshold (76695 cm-1) and the ionization energy (85031.2 cm-1 for CH3Br+(23/2); 87615.2 cm-1 for CH3Br+(21/2)).59 To our knowledge no other photofragmentation channels have been reported so far. Some disagreement concerning the ion-pair formation is to be found in the literature. Thus Xu et al.53 and Shaw et al.52 conclude that direct excitation to the ion-pair state is the major step prior to ion-pair formation whereas more recently Ridley et al.59 give evidence for Rydberg doorway 19 states in the photoion-pair formation analogous to observations for some halogens containing diatomic molecules.61-65 The basic picture for the electron configuration of methyl halides is analogous to that for hydrogen halides, such that, in the first approximation, the symmetry notation C3v, which holds for methyl halides, can be replaced by Cv.60 Excited state potentials for methyl halides (CH3X; X = Cl, Br, I) as a function of the C - X bond closely resemble those for HX molecules showing i) a number of repulsive valence state potentials which correlate with the CH3 + Br(2P3/2)/Br*(2P 1/2) species, ii) series of Rydberg state potentials which closely resemble the neutral and first ionic ground state potentials and iii) an ion-pair 1 A1(C3v) (1(Cv)) state with a large average internuclear distance. Characteristic state interactions between the Rydberg and ion-pair states are found to affect the spectroscopy and excited state dynamics for hydrogen halides.19-21,27,28,32,39,40,66,67 It has been pointed out that analogous effects are to be found for methyl bromide.59,60 More recently Kvaran et al.68 have reported a two-dimensional (2+n) REMPI experiment analogous to those presented above for acetylene12 and HCl39,40,69, which helps elucidate the discrepancy concerning the VUV spectroscopy of methyl bromide, and which also yields evidence for new photodissociation channels via Rydberg states. 20 2 Experimental setup and analysis method 2.1 Experimental apparatus Tunable LASER radiation was acquired from a Coherent ScanMatePro dye laser, or in the case of acetylene a Lumonics Hyperdye 300 dye laser, pumped by a Lambda Physic COMPex 205 excimer LASER. The bandwidth of the tunable LASER radiation was about 0.095 cm-1. Depending on the frequency required, a SHG (second harmonic generator) unit could be placed in the LASER beam pathway to frequency double the LASER. For the second harmonic generation we used a Sirah frequency doubler equipped with interchangeable BBO-2 or KDP crystals, see Table 1 for details. The LASER was directed into a vacuum chamber containing electric platings designed to direct any ions formed down a TOF (time-of-flight) tube. These platings consist of a single repeller which is a highly charged positive plate and several extractors which having a lesser positive charge serve as focal and directional lenses for the ionic beam. The LASER was focused using either 20 cm or 30 cm focal length lenses. Table 1: SHG crystals used for specific dyes and wavelengths of entering photons. Wavenumber [cm-1] Wavelength [nm] Dye Crystal 22988-22124 435-452 C-440 BBO-2 22124-21186 452-472 C-460 BBO-2 21186-20408 472-490 C-480 BBO-2 20408-18622 490-537 C-503 BBO-2 18622-17637 537-567 R-540 BBO-2 17637-16750 567-597 R-590 KDP-R6G Diagonally to the LASER beam path, in line with the focus point, a nozzle sprayed gas into the vacuum chamber with regular intervals, thus creating a jet-cooled stream of molecular particles in the focal point of 21 the LASER. Ionization chamber was pumped by a diffusion pump backed by an Edwards mechanical pump whereas the TOF tube was pumped by a Pfeiffer turbo pump also backed by an Edwards mechanical pump. On top of the diffusion pump, located between the mechanical pump and the ionization chamber, were cooling rods filled with liquid nitrogen. An acetylene gas sample was acquired from Linde gas (AAS Acetylene 2.6). Pure acetylene or mixtures of C2H2 and argon (typically in ratios ranging from 1:1 to 1:4 = C2H2:Ar) were pumped through a 500 m pulsed nozzle from a typical total backing pressure of about 1.0 – 1.5 bar into the ionization chamber. The pressure in the ionization chamber was lower than 10-5 mbar during experiments. The distance between the nozzle and the center between the repeller and the extractor was about 6 cm. The nozzle was held open for about 200 s and the LASER beam was typically fired about 450 s after opening the nozzle. Figure 1. Schematic of the REMPI-TOF experimental equipment. HCl and CH3Br gas samples were acquired from Merck-Schuchardt, >99.5% purity both. They were pumped through a 500 m pulsed nozzle from a typical total backing pressure of about 1.0–1.5 bar into an ionization chamber. The pressure in the ionization chamber was lower than 10-6 mbar during experiments. The nozzle was held open for about 200 s and the LASER beam was typically fired about 500 s after opening the nozzle. 22 REMPI-TOF spectra for jet-cooled gas were acquired by detecting ions formed in the focal point that had been directed through a TOF tube, on a MCP (micro channel plate). LeCroy 9310A, 400 MHz storage oscilloscope was used to gather the data from the MCP in digital format. Typical repetition rates were 50-100 pulses for each frequency point. Figure 1 shows a schematic of the experimental setup. Information on the power dependence of the ion signals was generally acquired by systematically reducing the laser power by directing the laser through different numbers of quartz windows which reflected a part of the laser beam. Each data point was acquired by averaging over 1000 pulses. The reflection precentage of each quartz window was calibrated at about 8.4%. During a single measurement run one window was added in the path of the laser beam after each 1000 pulses up to a maximum of six windows at which point they where removed again one at a time every 1000 pulses. The laser power was measured before and after every measurement run and should optimally remain unchanged. To insure accuracy at least three measurement runs were preformed for each ion signal measured. Information on the power dependence of the ion signals was generally acquired by averaging over approximately 1000 pulses. 2.2 Analysis Method Using the equipment described we were able to measure simultaneously the formation of all atomic and molecular ions within a certain mass range as a function of laser frequency and gather this data into a single data matrix. To do so we used Labview version 8.0. A program was created by Erlendur Jónsson70 that gathered the summed data from the oscilloscope into a text file that included the wavenumber of the excitation, the mass data reading for each wavenumber and an integration over a certain mass area for each wavenumber. Igor Pro version 5.071 was used to process this text file to create a 2D contour plot of the measured area. REMPI spectra for specific atomic or molecular mass could then be extracted from the 2D image, in addition to mass spectra for specific wavenumbers. Figure 2 shows a 2D contour plot and samples of the rotational spectra of HCl that were extracted from the 2D contour plot. 23 Figure 2: HCl spectra in the range of 85320 – 85370 cm-1. Below is the 2D contour spectrum that shows clearly the different ions formed as a function of both atomic/molecular mass and wavenumbers. Above are REMPI spectra derived from the contour plot for each ion observed. Mass spectra for individual wavenumbers could also be derived in similar fashion. 24 This analysis method enables us to see important connections between formations of the various ions via REMPI (in terms of relative intensities) as the 2D data for HCl show you how I(H+), I(35Cl+), I(H35Cl+), I(37Cl+) and I(H37Cl+) vary with wavenumbers (hence quantum numbers J´) and states. It proved to be quite accurate in observing mass peaks that previously went undetected due to overlap or that were otherwise obscured allowing for a more robost assignment of rotational spectra. It also allowed us to discern if 35/37Cl+ signals originated from the Rydberg state rotational line in question or if it was due to overlap from a nearby ion-pair state rotational line. This last proved highly valuable in our studies on photofragmentations. 2.2.1 Simulations Gathered REMPI spectra (such as those shown in figure 2) can be simulated by a quantum mechanical simulation using Igor Pro 5.0. A macro (small program or script that is run inside Igor Pro) was used to simulate rotational spectra by using spectroscopic parameters. The simulation determines relative rotational line positions from first- and second-order rotational constants (B and D) for the excited and ground state. It also determines the relative intensity of the rovibrational lines by taking account of the ground state population and degeneracy.27 The experimental spectrum was displayed on a screen with the simulated spectrum. Realistic rotational parameters were then put into the macro and the simulated spectrum was generated. Finally the rotational constants were changed until a reasonable fit to experimental data was reached. In some cases a least squares analysis could be used to assist with the simulation, as was done in the case of C2H2. However the final simulation was always done by a visual comparison of the spectra as in some cases the least square analysis gives an inferior result due to computational errors. These errors were typically due to the program having too much emphasis on the bandwidth and shape of the rotational peaks and too little emphasis on peak positions, resulting in the center of the simulated peaks being shifted away from the center of the measured peaks. Simulations like the one shown in figure 3, which is a simulation of the g3(1)+ ←← X1+ (0,0) excitation, could be used to accurately determine rotational constants of the simulated spectra. They could also be useful for line assignments. From the calculated spectra in figure 3 it can clearly be seen that the experimental spectra contain a rotational peak outside of the g3(1)+ ←← X1+ (0,0) excitation, which was later found to be a part of the D1 ←← X1+ (0,0) excitation. In addition, when searching for 25 line perturbations, simulations like these can also be of moderate use as subtle line shifts become more obvious. 1.4 Experimental 1 D ; R-line ; J'=1 1.2 1.0 3 J'=1 0.8 5 Calculated 0.6 7 0.4 82508 82512 82516 -1 2xh[cm ] 82520 Figure 3: Experimental data (above) for the excitation g3(1)+ X1+ (0,0) and the simulated spectrum (below) derived from spectroscopic constants. The experimental spectrum also contains a single peak due to the D1 ←← X1+ (0,0) excitation. Simulations can thus be of use for peak assignments in addition to accurately determining rotational constants. 2.2.2 Time of flight analysis When a molecule is ionized in an electric field it gains momentum in the direction of the field. The relationship between the atomic or molecular mass of the ion (Mw) and the time-of-flight (TOF) for our equipment is TOF = a M w b (1) The constants a and b are experimental constants that vary between experiments which must be evaluated for each measurement and M w is the molecular weight of the ions formed from the sample injected into the gas chamber. Using equation (1) it was easy to evaluate the atomic mass of ions formed by REMPI as there were generally some known peak formations due to impurities and/or background gas in the vacuum chamber, such as C+ and C2+, which could be used for calibration. 26 3 Theoretical considerations 3.1 Electronic spectroscopy of diatomic molecules72-74 The quantum energy levels of a molecule can be broken down into three distinct parts. The electronic energy levels, which arise from the energy of different electron configurations, the vibrational energy levels, which correspond to the allowed energy for vibrations of molecular bonds and the rotational energy levels, which correspond to the allowed rotational energy of the molecule in question. The approximate order of magnitude for excitations within these energy levels is: Eelec ≈ Evib *103 ≈ Erot *106 (2) They are also interconnected in the sense that each vibrational state has a series of rotational levels and each electronic state has a series of vibrational levels. Therefore, the total energy of an electronic excitation can be expressed as: totalEelecEvibErot 3.1.1 Electronic energy levels. Electronic excitation occurs when an electron is excited to an energetically higher molecular orbital from its ground state or energetically lower orbital. A molecular Rydberg state is composed of atom like orbitals with primary quantum numbers higher than those of the ground state. During Rydberg excitation the electron in the highest occupied molecular orbital (HOMO) is excited into some energetically higher Rydberg orbitals depending on the frequency used for excitation. 27 An ion-pair state is formed when an electron of the bonding electron pair is excited into the antibonding orbital (* ←← Figure 4 gives an example using HCl. 4s 4s 1s 1s 3p 3p 3s 3s a) b) Figure 4: Energy diagram for molecular orbitals of HCl. a) Ion-pair excitations. An electron is excited from the bonding orbital of the molecule to the antibonding orbital. b) Rydberg excitations. An electron is excited from the nonbonding orbital to a Rydberg orbital. As the antibonding orbitals are located away from the center of the molecule this weakens the molecular bond and in some cases may cause it to break. However for diatomic molecules with a difference in electronegativity the antibonding electron is attracted to the atom with the higher electronegativity. In the case of HCl this means that the antibonding electron is attracted to the Cl atom, causing the atoms to attain ion-like properties (H+ and Cl-) and remain bonded through electrostatic properties. Nevertheless, the ion-pair bond is both weaker and longer than a regular bond. For a single-photon excitation, the total electronic angular momentum of the electron must remain the same or change by only one integer, according to the electronic excitation selection rule 0, ±1 28 For multiphoton excitations, as each photon must fulfil the selection rule, this rule is applied for each photon used in the excitation, resulting in 0, ±1, ±2 ... ±n where n is the number of photons in the excitations. Thus multiphoton excitations open up several possible excitation paths otherwise undetectable. For example, the ground state of HCl is a X1 state, thus for single-photon excitations only and states are accessible in HCl. However, for two-photon excitations states become accessible in addition to the and states. 3.1.2 Vibrational energy levels We have discussed the excitation of electrons in a molecule. The next effect we need to consider is the vibration of the molecular bond. A molecular bond is formed from the positive overlap of two atomic wavefunctions. The length of the bond is dictated by the attracting properties of the electrons of one atom to the nucleus of the other and the mutual repulsive forces of the electrons and the nuclei of each atom. As such there must be an internuclear distance where the attractive and repulsive forces of the atoms reach equilibrium. This internuclear distance, called the bond length of the molecule, corresponds to the bottom of the potential well. Pushing or pulling the atoms away from that optimal bond length increases the potential energy of the molecule. Figure 5 illustrates the difference between Rydberg states and ion-pair states. The bond length of the Rydberg state is smaller than that of the ion-pair state, in addition the energy gap is generally higher between vibrational levels of the Rydberg state than for the ion-pair state as they are quantized and distributed according to the shape of the potential. A simple harmonic oscillator is a useful approximation for the vibrational energies. In the simple harmonic model they are defined as ½osc cm-1 where is the vibrational quantum number. In equation (6) the energy difference between adjacent vibrational levels is equal to the oscillation frequency osc and the vibrational energy cannot be zero. 29 Energy Ion-pair Potential Rydberg Potential Vibrational levels Internuclear distance Figure 5: Rydberg potential vs. ion-pair potential. The figure illustrates the difference between an ion-pair state and a Rydberg state. The average bond length of the ion–pair state is longer than that of the Rydberg state due to the excitation of an electron to the antibonding orbital, giving the excited molecule semi-ionic properties. The vibrational levels are quantized and distributed according to the shape of the potentials. However, real molecules do not follow a simple harmonic path. The repulsive forces between electrons build up faster than the attractive force between the electrons and the nucleus when the atoms are pressed together and similarly they diminish slower when they are pulled apart. Therefore if the atoms move too far apart, which can happen if the vibrational energy reaches a certain amount, the bond between them will break and the molecule will dissociate into atoms. So while the simple harmonic oscillator approximation is useful as a tool, the deviations from the simple oscillator need to be taken into account for real molecules. An expression that fits to a good approximation is the Morse function: U (r ) Deq 1 expareq r 30 2 where a is a constant for a particular molecule, req is the bond length at equilibrium, r is the bond length and Deq is the dissociation energy. By using this potential energy in the Schrödinger equation, the allowed vibrational bands are found to be v½e- + ½)2 ee Where e is the oscillation frequency and ee is the anhermonicity constant. 3.1.3 Rotational energy levels The rotational energy of a molecule is inversely proportional to its moment of inertia. By looking at a rigid diatomic molecule we can see that its moment of inertia can be expressed as: I m1 m2 2 r0 r02 m1 m2 where m1 and m2 are the mass of each atom, is the reduced mass of the system and r0 the internuclear distance between the atoms. By solving the Schrödinger equation for a diatomic system it can be shown that the allowed rotational energy levels for a rigid diatomic molecule can be expressed as: EJ h2 8 2 I J ( J 1) Joules m 2 kg where h is the Planck constant (6,63*10-34 ) and I is the moment of inertia. J is the rotational quantum number andscan only take integer values of zero and higher. This restriction to integer values comes directly from the Schrödinger equation and it is this restriction that introduces the discrete rotational levels observed in spectroscopy, see figure 6. 31 Energy Rydberg Potential Vibrational levels Rotational levels Internuclear distance Figure 6: For each molecular Rydberg state there are discrete vibrational levels. For each vibrational state there are also discrete rotational levels. The vibrational series depend on the shape of the potential and the rotational series depend on the energy and thus the mean bond length of the vibrational levels. In this work I use wavenumbers [cm-1] instead of Joules [J]. To compensate for this common practise in spectroscopy, equation (10) becomes: EJ h2 j J ( J 1) cm-1 hc 8 2 Ic where c is the speed of light in cm s-1. This equation is usually abbreviated to: j BJ ( J 1) cm-1 where B is the rotational constant that is given by: 32 h 8 I B c B 2 From equation (12) it can be seen that the energy of the rotational levels will gradually increase as J increases and that the energy difference between adjacent rotational levels will also increase by 2B for each level of J. At this point it should be stated that the above only holds for an ideal rigid rotor. In reality the molecules are not completely rigid. As J increases, the distance between the atoms increases to some degree. This is somewhat like spinning a ball fastened to a rubber string. As you spin the ball faster, the string lengthens. This causes the moment of inertia of the molecules to diminish and introduces an effect called centrifugal distortion. To correct for this the centrifugal distortion constant is introduced and equation (12) becomes J= BJ(J+1) – DJ2 (J+1)2 cm-1 where D is defined as: D h3 32 4 I 2 r 2 kc These two values (B and D) usually suffice for modern spectroscopy fitting, since higher order fitting parameters have negligible effect. For a single-photon excitation, the angular momentum of the molecule must change by one, according to the rotational selection rule Jif Jif≠ For a multiphoton excitation, as each photon must fulfil the selection rule, this rule is applied for each photon used in the excitation, resulting in For when n J when n etc 33 For≠ Jn where n is the number of photons used for the excitation. Thus, as excitation is possible between more rotational levels, multiphoton excitations introduce additional line series for each vibrational level within a state. 3.2 The intensity of electronic excitation spectroscopy lines72-74 The intensity of absorption spectroscopic lines results from a combination of several factors. Most notable are the electron transition probabilities, the Frank-Condon principle and the Boltzmann distribution. The first two are due to molecular wave functions. Using the Born-Oppenheimer approximation we can treat a molecular wave function as a combination of an electronic wave function and a nuclear wave function. The Boltzmann distribution is a property-of-state population and is therefore affected by the temperature of the measured sample. The power of the excitation source also affects the intensity of the spectroscopic lines. This effect is however separate from the intrinsic properties of molecules and is simply due to an increased excitation rate from the higher density of photons. 3.2.1 Transition probabilities The transition probabilities of electronic excitation is one of the main properties that influence the intensity of spectroscopic lines. Transition probabilities (a2) describe the probability of an excitation between electronic states and are defined as a 2 ( m n d e ) 2 where is dipole moment of the molecule, m and n are the molecular wavefunctions and de is the volume element. The wavefunction can be regarded as a combination of electron wavefunctions, vibrational wavefunctions, rotational wavefunctions and even translational wavefunctions. e v r t 34 For rovibrational excitations the rotational and translational wavefunctions as considered to be constants. A common approximation is also to consider the electronic wavefunction as a constant which depends on the characteristics of the ground and excited state. As such the transition probability of rovibrational excitations can be defined as a 2 ( v ' v '' dr ) 2 This gives rise to the Frank-Condon factors (FCF) which are transition probabilities proportional to the overlap of the vibrational wave functions in the upper and lower vibrational states. The FCF influence on intensity varies with vibrational levels depending on the wavefunction overlap and remains the same for all rotational excitations within the same vibrational excitation to a first approximation. In figure 4 we see vibrational levels of two fictional states, E0 and E1. As electronic excitations are not influenced by vibrational selection rules, excitation from E0 (’=0) to any vibrational level of E1 is allowed as long as there is a non-zero chance that the internuclear distance is the same for the E1 and E0 states. In this case excitation between the ground vibrational states of E0 and E1 is highly unlikely, whereas excitation between the ground vibrational state of E0 and ’=2-5 of E1 is highly likely. 3.2.2 Boltzmann distribution The second property that influences line intensities is the population of the ground state as the rotational population of the ground state influences the number of molecules that are available for a specific excitation. The Boltzmann distribution is defined as EJ NJ exp N0 k bT (19) where N0 is the total number of particles in the ground state, NJ is the number of states having the energy EJ, kb is the Boltzmann constant (1.38 x 10-23 m2kgs-2K-1) and T is the temperature. 35 Figure 7: Franck-Condon factors. The vibrational levels are positioned so that the probability function forms a standing wave. It is the overlap of these probability distributions that determines the Franck-Condon factors. Figure from http://www.chem.ucsb.edu/~kalju/chem126/public/elspect_theory.html Therefore, as a sample is cooled down, more particles will occupy the lower rotational levels of the ground state, thus increasing the chance of excitation to the lower rotational levels of the excited state, while decreasing it for the higher rotational levels. In figure 8 we see an example of this using a fictional distribution. In the hot gas sample we would expect to see rotational peaks originating from the J’=0 to at least the J’=5 rotational level. For the cold sample however, only excitation 36 origination from the J’=0 to the J’=2 rotational levels would be expected. Thus cold samples show far fewer rotational lines than hot samples. This effect is very useful in spectroscopy as it allows for different degrees of spectrum complexity. Cold samples have few rotational lines and therefore do not offer the same amount of data, yet they are simpler and easier to assign. Hot samples have more rotational lines and more data, but are more complex to assign. Thus by varying the rotational temperature of a gas Rotational levels 5 4 3 2 1 0 Hot gas Cold gas sample and comparing, very useful information is gained. Figure 8: When gas is jet-cooled the rotational energy of individual molecules shifts downwards, thus increasing the probability of excitation from the lower rotational levels compared to that from the higher ones. 3.2.3 Laser power dependence Ion intensities (I(M+)) vary with the laser power (Plaser), the number of photons needed to ionize (n) and the transition probabilities as discussed above. The total ion intensity can be expressed as Plasern where is a proportionality constant depending on the transition probability. From equation (20) the following expression can be derived: 37 lognlog Plaser + C rel rel where Plaser is proportional to the laser power. From this equation it can be seen that the number of photons needed for excitation can be derived from a logI(M+) vs. logP plot. This permits an easy extraction of photon numbers and gives valuable information concerning excitation and ionization pathways. 3.2.4 Multiphoton excitation intensities These previously mentioned properties form a basis for the intensity of rovibrational lines. For a two-photon resonance excitation followed by ionization, the intensities are proportional to the products of the cross sections of two major steps, a) the resonance excitation and b) photoionization. According to Kvaran et al.25, the resonance excitation is proportional to a function S´´´(J, , ||, ±) which depends on the difference of the angular momentum quantum numbers J and as well as the parallel (||) and perpendicular (±) transition dipole moments between the two states, where || equals J←J transitions and ± equals J ±1 ← J transitions. The transition strengths for one-, two- and threephoton excitations have been formulated in terms of Hönl-London type approximations for diatomic molecules.72,75,76 The resonance excitation is also proportional to a function C(v’,v’’). In the case of a Boltzmann distribution, C(v’,v’’) can be expressed as C(v’,v’’) = KF(v’,v’’)Pn2(v´) where K is a parameter depending on the electronic structure of the molecule, geometrical factors and sample concentrations, F(v´,v´´) is the Franck-Condon factor for the transition v´←v´´, P is the laser power and n is the number of photons necessary to complete the ionization and 2(v´) is the ionization cross section which is a slowly varying function with laser energy. Thus by taking the degeneracy (g(J´´)) of the ground state rotational energy levels (E(J´´)) into account, the relative line intensity is defined as I rel C(v´, v´´)g(J´´)Sv´v´´ e 38 E ( J ´´) kT 3.3 Total angular momentum and Hund’s cases72 The total electronic angular momentum is composed of the electron spin angular momentum and the orbital angular momentum. An electron moving in its orbital is said to possess orbital angular momentum. For a diatomic molecule this momentum is quantized and expressed as L and has the magnitude |L| L( L 1) Unless L = 0 the orbital angular momentum vector L precesses about the internuclear axis of the molecule as figure 9 shows. L Figure 9: The precession of L about the internuclear axis. The precession forms a component along the internuclear axis. The angular momentum vector is the component of the orbital angular momentum along the internuclear axis with a magnitude of. ħ For each given value of the quantum number L the quantum number can take the values = 0, 1, 2, ... , L. (26) So for each value of L there are L+1 distinct states with different energy. The molecular state designations , , and represent values of 0, 1, 2 and 3 respectively. 39 The electron which orbits around the molecule is also spinning about an axis forming a spin orbit vector S which has the magnitude |S| S (S 1) Here the corresponding quantum number S can take integer or half integer values depending on whether there is an odd or even number of electrons. S then precesses about the internuclear axis (much in the same way as L) with a constant component with amagnitude ħ Where can take the values = S, S-1, S-3, ... -S As such can take 2S+1 different values and can also take negative values. These two elements of electron motion added together form the total angular momentum of the electrons: The molecule’s angular momenta, electron spin, electronic orbital angular momentum and the angular momentum of nuclear rotation form together a resultant J which is the total angular momentum of the molecule. For 1 states the spin and angular momenta are zero. Therefore the total angular momentum is the same as the angular momentum of nuclear rotation and we have a simple rotator as shown in figure 10. For states where and are nonzero we have special cases which are called Hund’s cases. 3.3.1 Hund’s case a) For Hund’s case a), the interaction of the nuclear rotation with the electronic motion is considered to be weak (both spin and orbital). However, the coupling of the electronic motion with the line joining the nuclei is considered to be strong. The electronic angular momentum is therefore well defined even in rotating molecules. 40 N J Figure 10: Simple rotator. If S = 0 and L = 0 we only need to consider the angular momentum of nuclear rotation N. Therefore we have a simple rotator were N is equal to the total angular momentum J. The angular momentum of the rotating molecule N and the electronic angular momentum then form the total angular momentum J as shown in Figure 11. J N Figure 11: Hund‘s case a). The orbital angular momentum and the electronic spin form the electronic angular momentum . The angular momentum of the rotation molecule N and the electronic angular momentum then form the total angular momentum J. Since it is obvious that J cannot be smaller than we get J and thus, levels with J < do not occur. 41 3.3.2 Hund’s case b) When L = 0 and S ≠ 0, a weak or zero coupling of the internuclear axis with the spin vector S occurs which is characteristic of Hund’s case b). In this case and N form a resultant which is called K which is the total angular momentum apart from spin. The corresponding quantum number K can take the values K = , +1, +2 .... (32) The angular momenta K and S then form a resultant J which is the total angular momentum, see Figure 12. S J K N Figure 12: Hund‘s case b). and N form a resultant which is called K. The angular momenta K and S then form a resultant J. The possible values of J are therefore J = (K+S), (K+S-1), ... , (K-S) Thus in general, every level with a given K has 2S+1 components. This appears as peak splitting in rotational spectra. Note that for singlet states the distinction between cases a) and b) are pointless, as S=0, = and therefore K=J. 3.3.3 Hund’s case c) In some cases the interaction of L and S may be stronger than the coupling with the internuclear axis. In these cases and are not defined. Instead L and S form a resultant Ja which is coupled to the internuclear axis by a component . and N then form a resultant J, see Figure 13. 42 J N L Ja S Figure 13: Hund‘s case c). L and S form a resultant Ja which is coupled to the internuclear axis with a component . and N then form a resultant J. Hund’s cases a), b) and c) are the most common Hund’s cases. There are two more, d) and e); however, they are of lesser importance for the scope of this dissertation. 3.4 Symmetry properties72 The symmetry properties of rotational levels are important for spectroscopic work. The rigorous selection rule which states that excitations can only occur between levels of the same symmetry can be of great help in assigning spectroscopic lines. The symmetry of rotational levels is a property of their eigenfunctions. If the eigenfunction of a rigid rotor remains unchanged when reflected at its origin by replacing by + and by - it is considered to be in a positive electronic state. Here is the azimuth of the line connecting the mass point to the origin and is the angle between this line and the z axis. Should the eigenfunction change sign it is considered to be in a negative electronic state. Rotator functions remain unchanged for even values of J but change sign for odd values of J. This characteristic is called parity and rotational levels can be assigned a + or – parity depending on the symmetry properties. 43 3.4.1 Parity of rotational levels For states that have = 0 and S = 0 the parity of the rotational levels switches between being positive or negative depending on whether J is even or odd. For 1+ states the first level has a positive parity. For 1states the reverse is true and the first level has a negative parity. The same holds for states were = 0 and S ≠ 0, however here the parity depends on K rather than J. For states were ≠ 0 the rotational levels have both a positive and negative parity, for which there is a small energy difference. See Figure 14 for further clarification. K 1+ 2+ 3+ 0 1 2 3 - + - 4 5 + - + 0 1 2 3 + 4 5 K 0 1 2 3 4 5 1- - + - + - + 0 1 2 3 4 5 - + + - - J 2- - - + + - - + + - - ½ ½ 3/2 3/2 5/2 5/2 7/2 7/2 9/2 9/2 11/2 + - - - + + + - - - + + + - - - 1 012 123 234 345 456 J J 3- + + - - + + ½ 3/2 3/2 5/2 5/2 7/2 7/2 9/2 9/2 11/2 + + + - - - + + + - - - + + + 012 123 234 345 ½ - 1 J J 456 J Figure 14: Parity. The + and – suffixes in the term symbol indicate the parity of the rotational levels of the states. For multiplet states the parity depends on K instead of J. 3.4.2 Parity selection rules For single photons, excitation may only occur between rotational levels with opposite parity. but not or For two-photon excitation, this turns into andbut not and for three-photon excitation, it again turns to + - but not + + or - thus only excitations between rotational levels of the same parity is allowed for an even number of photons and excitation between rotational levels of opposite parity is allowed for an odd number of photons. 44 3.5 Perturbations72 Sometimes a rotational spectrum can show a deviation from an otherwise smooth course. This deviation is generally caused by a perturbation. A perturbation can occur when rotational levels with the same J’ for different electronic states are close to each other. It is characterized by a shift from the expected line position and/or a change in the line intensity of the perturbed lines. Perturbations where the vibrational level has been shifted have also been observed; those are known as vibrational perturbations and are outside the scope of this work. 3.5.1 Rotational perturbations When two rotational levels with the same J’ are energetically close to each other it is possible for them to be perturbed, causing them to separate in energy and receive spectroscopic characteristics from each other. 1.2 HCl+ F, v´=1 d) X, v´=0 1 I(M+)/I1(HiCl+) 0.8 0.6 H+ Cl+ 0.4 0.2 0 J´ 8 / i = 35 J´ 8 / i = 37 J´=8 / i = 35 J´=8 / i = 37 Fig.3d Figure 15: Perturbation. On the left we have an average ion ratio for the F 1, ’=1 state. On the right we have the ratio for the perturbed F1, ’=1, J’=8 rotational level. As can be clearly seen, the perturbation to the ion-pair state causes considerable changes to the ratio of H+ and Cl+ vs. HCl+ ion formation for both the 35Cl and 37Cl isotopes. 45 As an example, the F1, ’ = 1, J’ = 8 and the V1, ’ = 14, J’ = 8 rotational levels of the HCl molecule are very close energetically. Due to this, the corresponding Rydberg rotational peak (for the F1state) shows a mass spectrum that has ion-pair state (V1) characteristics and vice versa, see Figure 15. In addition, the energy difference between J’ = 7 and J’ = 8 and also between J’ = 8 and J’ = 9 for both states is different from what one would expect from a non-perturbed progression of rotational lines, whereas the difference is in accordance with a shift due to perturbation.39 This does not mean that any rotational level that is energetically close to another is perturbed. The perturbation can only occur between specific rotational levels as governed by the selection rules. 3.5.2 Perturbation selection rules 1) Both states must have the same total angular momentum J; J = 0 2) Both states must have the same multiplicity; S = 0 3) The value of the two states must only differ by 0 or ±1; = 0 , ±1 4) Both states must have the same parity, either both positive or both negative; + // 5) For molecules with identical nuclei, both states must have the same symmetry in the nuclei; s // a Rules 1, 4 and 5 are perfectly rigorous. The second rule holds only approximately as perturbations between states of different multiplicity increase in magnitude with increasing multiplet splitting similarly to transitions with radiation. The third rule holds only when is defined, Hund’s case a) and b). For Hund’s case c) the total angular momentum is used instead. 3.6 Predissociation72 Predissociation is a fragmentation of a molecule into its atoms or smaller molecular fragments. It can occur through an interaction of a bound state with an unbound or quasi-bound state. Fragmentation can also occur via direct excitation to an unbound or quasi-bound state in which case it is simply referred to as dissociation. Predissociation can be detected in a rotational spectrum by a sudden uncharacteristic broadening of lines. This corresponds to the shortening of the lifetime of the rotational levels due to the molecule predissociating into smaller atomic or molecular fragments. The predissociation of a molecule 46 can be followed by an excitation of the fragments, either through direct ionization or by a resonance-enhanced ionization, see Figure 16 a) and b). a) b) A+ B+ A+ B+ A# AB# AB# A+B AB A+B AB Figure 16: Predissociation of a diatomic molecule. a) Predissociation followed by a direct ionization. The molecule is initially excited to a bound state which interacts by a non-bound or a quasi-bound state. Some of the molecules in the bound state “leap” across to the predissociating state and are dissociated into its atomic components. The atoms formed can themselves absorb photon energy and ionize. b) Predissociation followed by a resonance-enhanced ionization. In this case the photon energy needed to excite the parent molecule corresponds to an excited state of the atom resulting in a resonance-enhanced excitation. 47 4 Published papers International Journals Kristján Matthíasson, Jingming Long, Victor Huasheng Wang, Ágúst Kvaran. Two-dimensional resonance enhanced multiphoton ionization of H(i)Cl; i=35, 37: State interactions, photofragmentations and energetics of high energy Rydberg states. Journal of Chemical Physics, 134, 164302, 2011. Ágúst Kvaran, Victor Huasheng Wang, Kristján Matthíasson, Andras Bodi. Two-Dimensional (2+n) REMPI of CH(3)Br: Photodissociation Channels via Rydberg States. Journal of Physical Chemistry A, 114, 9991, 2010. Ágúst Kvaran, Kristján Matthíasson, Huasheng Wang. Two dimensional (2+n) REMPI of HCl: State interactions and photorupture channels via low energy triplet Rydberg states. Journal of Chemical Physics, 131, 044324, 2009. Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, Two Dimensional (2+n) REMPI of HCl: Observation of a new electronic state, Journal of Molecular Spectroscopy, available online, 2009. Ágúst Kvaran, Huasheng Wang, Kristján Matthíasson, Andras Bodi, Erlendur Jónsson, Two dimensional (2+n) resonance enhanced multiphoton ionisation of HCl: Photorupture channels via the F-1 Delta(2) Rydberg state and ab initio spectra, Journal of Chemical Physics, 129(16), 164313, 2008. Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, (2+n) REMPI of acetylene: Gerade Rydberg states and photorupture channels, Chemical Physiscs Letters, 458 (1-2), 58 (2008). Icelandic Journals Kristján Matthíasson, Victor Huasheng Wang, Ágúst Kvaran. Massagreining í kjölfar ljósgleypni: Víxlverkanir milli örvaðra ástanda uppgötvaðar. "Tímarit um raunvísindi og stærðfræði", 2011. 49 Ágúst Kvaran, Victor Huasheng Wang og Kristján Matthíasson, Tveggja ljóseinda gleypni acetylens, "Tímarit um raunvísindi og stærðfræði", 1. hefti, 2007, bls. 41-44. 50 Paper I Kristján Matthíasson, Jingming Long, Victor Huasheng Wang, Ágúst Kvaran. Two-dimensional resonance enhanced multiphoton ionization of H(i)Cl; i=35, 37: State interactions, photofragmentations and energetics of high energy Rydberg states. Journal of Chemical Physics, 134, 164302, 2011. 51 53 54 55 56 57 58 59 60 Paper II Ágúst Kvaran, Victor Huasheng Wang, Kristján Matthíasson, Andras Bodi. Two-Dimensional (2+n) REMPI of CH(3)Br: Photodissociation Channels via Rydberg States. Journal of Physical Chemistry A, 114, 9991, 2010. 61 63 64 65 66 67 68 69 70 Paper III Ágúst Kvaran, Kristján Matthíasson, Huasheng Wang. Two dimensional (2+n) REMPI of HCl: State interactions and photorupture channels via low energy triplet Rydberg states. Journal of Chemical Physics, 131, 044324, 2009. 71 73 74 75 76 77 78 79 80 81 82 Paper IV 4Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, Two Dimensional (2+n) REMPI of HCl: Observation of a new electronic state, Journal of Molecular Spectroscopy, available online, 2009. 83 85 86 87 88 89 90 Paper V Ágúst Kvaran, Huasheng Wang, Kristján Matthíasson, Andras Bodi, Erlendur Jónsson, Two dimensional (2+n) resonance enhanced multiphoton ionisation of HCl: Photorupture channels via the F-1 Delta(2) Rydberg state and ab initio spectra, Journal of Chemical Physics, 129(16), 164313, 2008. 91 93 94 95 96 97 98 99 100 101 102 103 Paper VI Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, (2+n) REMPI of acetylene: Gerade Rydberg states and photorupture channels, Chemical Physiscs Letters, 458 (1-2), 58 (2008). 105 107 108 109 110 111 112 5 Ion formation through multiphoton processes for HCl35-39,77 The photoionization of HCl is a complex multiprocess mechanism that entails perturbations, photodissociations and predissociations. In this chapter I will go over the ionization mechanism that are know or have been suggested. Figure 17 shows all the mechanics discussed collected into a single figure. 5.1 Formation of HCl+ HCl+ ions are generally only formed through ionization via a Rydberg state via mechanism (1) shown in figure 17 a). However, electrons excited to an ion-pair state are able to access Rydberg states by perturbation. 5.1.1 Ionization via Rydberg states The formation of HCl+ via a Rydberg state is the simplest of the ionization mechanisms. HCl+ is formed by a simple two-step process, i.e. the formation of excited HCl# followed by the direct ionization of the excited molecule, forming HCl+. 5.1.2 Ionization via ion-pair state HCl+ ions are probably never formed directly via ion-pair states, or at most only a small fraction. However, HCl+ in considerable quantity has been observed from ionizations via ion-pair states.19-21,39,40 The cause of this is found to be a perturbation of the ion-pair state. When two rotational levels with similar energy are perturbed, the wavefunctions are overlapped allowing the electron to move from one state to the other, thus being observed to have characteristics of both states. The electron can therefore be excited into the ion-pair state, be perturbed into a Rydberg state, and from there follow channel (i) and (ii) shown in figure 17 a) forming an ion. 113 a) (2+n) HCl+* (4) HCl+* H+ + Cl H+ + Cl (iv) (ii) (v) HCl** (T) HCl+ (3) H+ Cl+ HCl+ (vi) HCl** 1+ HCl**[A]1+ H* +Cl H+ Cl* H+Cl* (i) H+ + Cl(vii) (iii) (2) HCl* (Ry, v´,J´) H+Cl(V1+, v´,J´) W12 (2) (1) (2+n) (2+n) b) HCl+* H+ Cl+ (5) Cl+ H+ +Cl (4) HCl+ (3) (ii) (ix) (4) HCl** H+ Cl* (viii) HCl* (RyG, v´,J´) (3) (i) (SO) (2) HCl* (Ry, v´,J´) SO HCl* 3 + (3) H + Cl(J =1/2,3/2) (1) Figure 17: Main ionization mechanisms of HCl. Figures a) and b) show possible ionization channels via Rydberg (HCl*) and ion-pair states (H+Cl-). The predissociation gateway mechanism forming H + Cl is included. Necessary amount of photons for ionization are shown. 114 Since the rotational levels of the ion-pair state in HCl are generally always perturbed by the Rydberg states close in energy, HCl+ is observed, in different amounts though, for almost every observed rotational line of the ion-pair state. Due to this fact there is a possibility that HCl + is formed directly from the ion-pair state as has been suggested as shown for channel (iii) in figure 17 a).35-38 This should however be in small amounts compared to the HCl+ formed via perturbation, as most low level ion-pair rotational lines, which are perturbed the least, show only a very limited HCl+ formation and the v’=4 ion-pair vibrational level shows no discernable HCl+ at all. 5.2 Formation of H+ H+ ions are formed by several possible channels depending on whether the ionization is through a Rydberg or ion-pair state. 5.2.1 Ionization via Rydberg states For unperturbed rotational levels the formation of H+ is initially the same as for HCl+ followed by a single-photon process that forms the H+ ion. For perturbed rotational levels the electron is initially excited by a multiphoton process into an energetically excited Rydberg state. Due to the perturbation the rotational level gains ion-pair characteristics and the electron can follow the same ionization mechanism as outlined for ionpair states (in other words it is perturbed into the ion-pair state). However, one must bear in mind that the proportion of HCl # that is not perturbed can continue to form H+ as outlined above. 5.2.2 Ionization via ion-pair state The electron is initially excited to the ion-pair state by a multi-photon process. The unperturbed electron then undergoes a single-photon excitation to an unbound state, causing the molecule to dissociate into a Cl atom and energetically excited H# atom which is ionized as shown in figure 17 a) channel (vi). For an electron perturbed into a Rydberg state the ionization mechanism is the same as outlined for Rydberg states, i.e. excitation to HCl + followed by a single-photon excitation forming H+. Additionally it has been suggested that H+ can be formed directly from the ion-pair state by a photodissociation of H+Cl- into H+ and Cl- as outlined in figure 17 a) channel (vii). 115 5.3 Formation of Cl+ Cl+ ions are generally only formed through ionization via an ion-pair state. However, electrons excited to a Rydberg state are able to access ion-pair states by perturbation. 5.3.1 Ionization via Rydberg states Cl+ in considerable quantity has been observed from ionization via Rydberg states.19-21,39,40 The cause of this is found to be a perturbation between the Rydberg state and a neighbouring ion-pair state. The electron is perturbed into the ion-pair state followed with a single-photon excitation to an unbound state, causing the molecule to dissociate into an H atom and an energetically excited Cl# atom which is ionized as shown in figure 17 a) channel (v). Typically the rotational levels in the Rydberg states of HCl are perturbed by the ion-pair state only in few specific cases. Thus, Cl+ is only observed in considerable amount in cases where the energy difference of comparable rotational levels is small, with the exception of the 1 states, which show Cl+ formation for all observed rotational levels. This selective appearance of the Cl+ ion is found to be an excellent diagnostic tool when characterising new states.41,78 However there are observable Cl+ signals for rotational levels that should not be perturbed by the ion-pair state. These signals are most likely due to a predissociation of the HCl molecule, followed by the ionization of the Cl atom as shown for channel (viii) figure 17 b). It is know that Cl atoms are formed by predissociation in the HCl molecule, specifically through the C-state. Therefore it is quite possible that these minute amounts of Cl+ ions that are formed are indeed formed via predissociation. It has also been suggested that Cl+ can form directly via Rydberg states by photoexcitation to inner walls of bound superexcited states as shown for channel (ix) in figure 17 b), where the molecule is dissociated into H + Cl* followed by ionization of the chlorine. 5.3.2 Ionization via ion-pair state Like the formation of H+ via the Rydberg state, the formation of Cl+ via an ion-pair state is somewhat straightforward. The electron is excited to the ion-pair state by a multi-photon process. What follows is then a single-photon excitation to an unbound state, causing the molecule to 116 dissociate into an H atom and an energetically excited Cl # atom which is ionized ( channel (v)). 117 6 The use of mass analysis to determine interaction constants Based on this overall ionization scheme presented above, Cl+ ions are characteristic indicators for the ion-pair state contribution, H+ formation clearly is both indicative of the ion-pair and the Rydberg state contribution and HCl+ formation is the main ion formation channel via Rydberg state excitation under low power conditions. There are reasons to believe that the HCl+ contribution to ion formation, via excitation to the V1 state, is rather small.39 Therefore, it has been found to be useful to define and work with normalized ion intensities for Cl+ (IN(Cl+) and HCl+ (IN(HCl+)) as indicators for the separate (diabatic) Rydberg and ion-pair states respectively, where IN(Cl+) is the Cl+ ion signal intensity normalized to (divided by) the HCl+ ion signal intensity and vice versa, i.e.: IN(Cl+) = I(Cl+)/I(HCl+); Rydberg state indicator IN(HCl+) = I(HCl+)/I(Cl+); ion-pair state indicator In addition to the photofragmentation channels, mentioned above, further dissociation of resonance-excited Rydberg states to form H + Cl and/or H + Cl* via predissociation of some gateway states could be important, as predicted by Alexander et al.77 In such cases, further photoionization of the Cl, Cl* and H fragments could also occur. Whereas the interactions between the states involved could be of various kinds77, spin-orbit couplings most probably are dominant. Assuming a level-to-level interaction scheme to hold for the Rydberg-toion-pair states interactions, weight factors (fractions) for the state mixing can be expressed as E 4 W12 2 1 c 2 2 i 2 E 2 (34) for E = E1 - E2, where E1 and E2 are the resulting level energies of the perturbed states (1 and 2) and W12 is the matrix element of the 119 perturbation function / interaction strength.39,72 In the case of homogeneous ( = 0) interaction W12 is independent of the total angular momentum quantum number, J´, whereas for heterogeneous ( > 0) interactions W12 is expressed as28,39,79 W12 W12' ( J ´( J ´1))1 / 2 (35) ' for constant W12 . W12 is related to the resulting level energies and the 0 0 zero-order level energies for the unperturbed state ( E1 and E 2 ; E 0 E10 E20 ) by Ei 1/ 2 1 0 1 2 E1 E20 4 W12 (E 0 ) 2 (36) 2 2 Assuming the mechanism discussed above to hold, we make the following assumptions: Cl+ ion intensity observed (I(Cl+)) is proportional 2 to the fraction of HCl* in the ion-pair state (2; c 2 ) as well as its fraction 2 in the Rydberg state (1; c1 ), I (Cl ) 2c22 1c12 (37) Similarly the HCl+ intensity (I(HCl+)) is assumed to be proportional to the same fractions, I ( HCl ) 1c12 2 c22 (38) For 2 / 1 , 1 / 2 , 1 ( 2 / 1 ) and c1 1 c2 , the ratio of I(Cl+) over I(HCl+) now can be expresses as 2 c22 (1 ) I (Cl ) I ( HCl ) 1 c 22 2 (39) There is a reason to believe that the contribution to the HCl+ formation by excitation from the diabatic ion-pair state is small39, hence, that the ratio of its proportionality factor ( 2 ) to that for the HCl+ formation from the diabatic Rydberg state, 1 , (i.e. 2 / 1 ) is negligible and ~1. By combining equations (34), (35) and (39) and assuming =1 the following expression is derived: 120 2 E ( J ´) 4 W12´2 J ´( J ´1) 1 (1 ) 2 E ( J ´) 2 I (Cl ) 2 I ( HCl ) E ( J ´) 4 W12´2 J ´( J ´1) 1 1 2 2 E ( J ´) (40) for excitations via a Rydberg state. Here ( 1 / 2 ), is a measure of the rate of formation of Cl + via the diabatic Rydberg state (the “gateway channel”) to that of its formation from the diabatic ion-pair state, which is one of the major/characteristic ionization channels. Hence is a relative measure of the importance of the “gateway channel”. Comparably ( 2 / 1 ) measures the relative rate of the two major/characteristic ionization channels, i.e. for the Cl+ formation for excitation from the diabatic ion-pair state ( 2 ) to the HCl+ formation from the diabatic Rydberg state ( 1 ). Considering the general fact that Cl+ ion signals via excitations to the ion-pair states and HCl+ ion signals via excitations to the Rydberg states, signals are comparable or certainly of the same order of magnitude (See Figs. 2-3) it is concluded that should be somewhat close to unity and certainly in the range 10-1 < < 10. By multiplying and (*) we get a measure of the actual rate of formation of Cl+ via the diabatic Rydberg state (the “gateway channel”) to that of its formation from the diabatic ion-pair state This expression allows relative ion signal data to be fitted for known E ' values using the variables , and W12 as has been previously accomplished40,41 and are here gathered together in Table 2. Table 2: State interaction parameters. State max W '12 * f 32 0.4 0 4 0 3 1 0.7 0.002 0.5 0.001 g 3(1) 1.0 0.5 0.6 0.3 j 3(1) 2.7 0.004 3.5 0.014 - 0.031 2.1 0.065 f j 3 (0+) 121 It is interesting to note that the * values are considerably different between and states. There’s also a increase by an order of magnitude between the g 3(1) state and the j 3(0+) and j 3(1) states. This opens up the possibility that the values are characteristic for certain states and could be used to assist in state assigments. Further experiments are needed to determine this as no data exists for states. For instances of off-resonance interaction we can assume, to a first approximation, that the ion intensity ratio is a sum of contributions due to interactions from the ion-pair states to the Rydberg state. In such cases common and parameters for I(Cl+)/I(HCl+) can be expressed as 2 2 I (Cl ) c 2,n (1 ) c 2,m (1 ) 2 I ( HCl ) (1 c 22,m ) (1 c 2,n ) (41) where c22,n and c22,m are the fractional mixing contributions for the interacting ion-pair states respectively. 122 7 Ionization of acetylene and methyl bromide compared to HCl It is interesting to compare the ionization mechanics of HCl on one hand and of acetylene and methyl bromide on the other. As HCl has been well covered in the previous parts of this dissertation, let us look at the organic molecules a little closer. The acetylene ion is formed by an ionization process similar to the formation of HCl+, i.e. excitation of the acetylene molecule followed by ionization. The formation of fragment ions are somewhat more complex.12 However, they generally go through a rearrangement followed by a predissociation of the parent molecule and a subsequent ionization of the fragments, forming H+, C+, C2+, C2H+ and CH+. For methyl bromide a similar story unfolds. Again the methyl bromide ion is formed by an ionization process similar to the formation of acetylene and HCl+, i.e. excitation of the methyl bromide molecule followed by ionization. The formation of fragment ions is again much more complex than of the parent molecule. In this case two rather predominant predissociations occur forming CH3 and Br atoms on one hand and C, H2 and HBr on the other, followed by ionization. Further dissociation of the fragments can occur in addition to several other ionization pathways. To emphasise, for methyl bromide and acetylene this is a simplified account of the ionization processes of the molecules. What is noteworthy, however, is that in all these cases the formation of ion fragments goes through a predissociation process of some sort. This would suggest that predissociation plays a much more important role in spectroscopy than hitherto believed. For HCl, predissociation also plays a key part in the W12 model presented above. It is interesting to note that it may be possible to use the and values of uncharacterised states to assist in their assignment. 41 However, more research is needed to ascertain a correlation between the values of known states and their assignment. 123 8 Unpublished work 8.1 C1-State The C1 state of HCl is of interest due to its heavy predissociation. The spectrum shown in Figure 18 has a typical form suggesting short lifetimes due to predissociation. The mass spectrum analysis in Figure 19 confirms this theory as a much higher ratio of Cl+ is formed for all rotational levels than expected for a Rydberg state. Most likely the HCl molecule is predissociating into neutral H and Cl followed by a direct three-photon ionization of Cl to Cl+. 1 C ' = 0, R 300 2 200 4 1 6 1 C ' = 0, S C ' = 0, Q 1 2 C ' = 0, P 100 4 6 1 6 0 3 1 1 C ' = 0, O -100 3 1 77300 77400 -200 -300 -400 77500 77600 77700 -1 [cm ] Figure 18: (2+n) REMPI of C1 ←← X1+ (0,0) excitation. The figure shows a diffused spectrum of the H35Cl isotopologue. A mass spectrum also shows an interesting difference between mass peaks belonging to the R and P series on the one hand and those belonging to the S series on the other hand. The J’ = 4 peak of the S series diverges from the almost linear mass ratios of the other rotational peaks. This divergence is typically due to perturbation with an ion-pair state. 125 I(35Cl+)/I(H35Cl+) ratio 0.12 0.1 0.08 0.06 0.04 0.02 0 1 2 3 4 5 6 J' Figure 19: I(Cl+)/I(HCl+) ratio for the C1 state ’=0. The white columns represent the P-series, the black columns the R-series and the gray columns the S-series. An increased I(Cl+)/I(HCl+)ratio is observed for the J’=4 rotational level. A small increase in I I(Cl+)/I(HCl+) for the R-series at J’=4 is most likely due to an overlap with the J’=2 peak of the S-series. By using equation (40) it is possible to calculate the position of the J’=4 line of the ion-pair state. A comparison of this calculation with the ionpair states measured by Jacques and Barrow80 suggests however that this cannot be as the energy difference between the rotational lines would need to be much smaller. This perturbation effect may therefore be due to a previously undetected state, possibly a gateway state, as the increased ratio of I(Cl+)/I(HCl+)suggests. 8.2 E1-State The E1 state of HCl is of interest due to its extended perturbation via off resonance interaction. Figure 20 shows the I(Cl+)/I(HCl+)and I(H+)/I(HCl+)ratio of individual rotational peaks for the E1 ←← X1+ (1,0) excitation. 126 I(H+)/(HCl+) and I(Cl+)/(HCl+) 1,4 2,5 a) b) 1,2 2 1 Cl+ Cl+ H+ 1,5 0,8 H+ 0,6 1 0,4 0,5 0,2 0 0 0 1 2 J´ 3 4 5 0 1 2 3 J´ 4 5 5 6 7 Figure 20: (2+n) REMPI of E1 ←← X1+ (1,0) and V1 ←← X1+ (14,0) excitations. The figure shows the HCl+/Cl+ ratio of individual rotational peaks. Table 3 shows the E values for the rotational peaks shown in figure 20. Interestingly the mass ratio for E1 J’=0 and J’=1 appear to have reached a perturbation “saturation” point as one would expect to see an increased Cl+ formation for J’=0 compared with J’=1. Perturbation “saturation” refers to a 50% mixture of the perturbed states. Table 3: E values for the rotational peaks of the E 1 ←← X1+ (1,0) and V1 ←← X1+ (14,0) excitations. J’ E; [cm-1] E1 (v’=1) ↔ V1(v’=14) 0 246.00 1 247.70 2 251.30 3 260.40 4 280.20 5 319.80 By assuming a 50% state mixing equation (34) can be used directly to evaluate the W12 constant for this interaction. By doing so a value of W12=124±2 cm-1 is found. For further studies it would be interesting to use equation (41) to evaluate W12 using mass ratios and assuming a considerable off reasonance interaction. 127 References 1 S. Boye, A. Campos, S. Douin, C. Fellows, D. Gauyacq, N. Shafizadeh, P. Halvick, and M. Boggio-Pasqua, J Chem. Phys 116 (20), 8843 (2002). 2 A. Campos, S. Boye, S. Douin, C. Fellows, J. Fillion, N. Shafizadeh, and D. Gauyacq, J. Phys. Chem. 105, 9104 (2001). 3 N. Shafizadeh, J. H. Fillion, D. Gauyacq, and S. 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Two dimensional (2+n) REMPI of HCl; Photorupture Channels via the F1 2 Rydberg state and Ab Initio; The 20th International Conference on High Resolution Molecular Spectroscopy, Prague, Czech Republic, September 2-6, 2008, MATTHIASSON K., KVARAN A., WANG V.H. Two Dimensional (2+n) REMPI of HCl; Photorupture Channels via Various Rydberg States; The 20th International Conference on High Resolution Molecular Spectroscopy, Prague, Czech Republic, September 2-6, 2008, MATTHIASSON K., WANG H., KVARAN A. HCl Photorupture Studies, Raunvísindaþing 2008, 14. og 15. mars í Öskju, Náttúrufræðahúsi Háskóla Íslands, Kristján Matthíasson. HCl Photorupture Studies, 4. ráðstefna Efnafræðifélags Íslands á Hótel Loftleiðum, 2007; Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran. Rannsóknir á vetnistengdum sameindaþyrpingum: HF-þyrpingar. Raunvísindaþing 2006, 3. og 4. mars í Öskju, Kristján Matthíasson, Victor Huasheng Wang, Ómar F. Sigurbjörnsson og Ágúst Kvaran. Three photon absobtion of open shell structured molecules. Annual NordForsk Network Meeting 2005; Fundamental Quantum Processes in Atomic and Molecular Systems, Sandbjerg, Denmark, 18. Agust – 22. August, 2005, Kristján Matthíasson, Victor Huasheng Wang and Ágúst Kvaran. Multiphoton absorption: LASER ionization and mass analysis, 3. ráðstefna Efnafræðifélags Íslands á Nesjavöllum, 18. - 19. september, 2004; Victor Huasheng Wang, Kristján Matthíasson og Ágúst Kvaran. 135 Fjölljóseindagleypni niturmonoxíð-sameindarinnar, 3. ráðstefna Efnafræðifélags Íslands á Nesjavöllum, 18. - 19. september, 2004; Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran. Multiphoton absorption: LASER ionization and mass analysis, Raunvísindaþing 2004 í Öskju, Náttúrufræðahúsi Háskóla Íslands, 16. - 17. apríl 2004; Victor Huasheng Wang, Kristján Matthíasson og Ágúst Kvaran. Fjölljóseindagleypni niturmonoxíð-sameindarinnar, Raunvísindaþing 2004 í Öskju, Náttúrufræðahúsi Háskóla Íslands, 16. - 17. apríl 2004; Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran. Talks Resonance enhanced multiphoton ionization and time of flight mass analysis of C2H2, Annual NordForsk Network Meeting 2007; Fundamental quantum processes in atomic and molecular systems, Nesbúð, near Reykjavík, Iceland, 30. June – 2. July, 2007, Kristján Matthíasson, Victor Huasheng Wang and Ágúst Kvaran. Research on Hydrogen Bonded Molecular Clusters: HF-Clusters .Annual NordForsk Network Meeting 2006; Fundamental quantum processes in atomic and molecular systems, Petursburg, Russia.17-19 June 2006 Kristján Matthíasson, Victor Huasheng Wang and Ágúst Kvaran. Research on Hydrogen Bonded Molecular Clusters: HF-Clusters Raunvísindaþing 2006 í Öskju, Náttúrufræðahúsi Háskóla Íslands, 3. - 4. mars. 2006; Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran Resonance Enhanced Multiphoton Ionization and Time of Flight Mass Analysis of C2H2, Annual NordForsk Network Meeting 2005; Fundamental Quantum Processes in Atomic and Molecular Systems, Sandbjerg, Denmark, 18. Agust – 22. August, 2005, Kristján Matthíasson, Victor Huasheng Wang and Ágúst Kvaran. 136