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NEW LINE LISTS WITH INTENSITIES FOR THE ROVIBRATIONAL TRANSITIONS WITHIN THE NH X 3 Σ− AND OH X2Π GROUND STATES James S.A. Brookea*, Peter F. Bernathb, Colin M. Westernc, Iouli E. Gordond, Gang Lid, Marc C. van Hermerte & Gerrit C. Groenenboomf a: Department of Chemistry, University of York,York, UK. b: Department of Chemistry & Biochemistry, Old Dominion University, Norfolk,VA, USA. c: School of Chemistry, University of Bristol, Bristol, UK. d: HarvardSmithsonian Center for Astrophysics, Cambridge, MA, USA. e: Department of Chemistry, Gorlaeus Laboratories, Leiden University,The Netherlands. f: Theoretical Chemistry, Institute for Molecules and Materials (IMM), Radboud University Nijmegen, Nijmegen, The Netherlands. Funded by: Abundances Spectrum of the Sun from the ACE satelliteNH Line lists • Quantum number assignments, line positions and intensities • Positions – Recorded directly from laboratory spectra • Intensities – Obtained with a combination of experimental and theoretical methods – Require potential energy curve and dipole moment function Potential Energy Curves – Experimental Spectrum • Spectrum is obtained from lab observations Line assignment and fit • Lines are assigned and a fit of line positions provides molecular constants for each vibrational level. Molecular constants fit • Equilibrium constants are obtained from fitting to 𝐺(𝑣) and 𝐵𝑣 molecular constants: • 𝜔𝑒 𝑧𝑒 𝑣 + Equilibrium constants RKR1 Potential energy curve 𝐺 𝑣 = 𝜔𝑒 𝑣 + • 1 4 2 1 2 𝐵𝑣 = 𝐵𝑒 − 𝛼𝑒 𝑣 + − 𝜔𝑒 𝑥𝑒 𝑣 + 1 2 2 1 2 1 2 2 + 𝛾𝑒 𝑣 + + 𝜔𝑒 𝑦𝑒 𝑣 + + 𝛿𝑒 𝑣 + 1 3 2 1 3 2 • RKR procedure generates potential energy curve – Bob Le Roy’s RKR1 program + Dipole Moment Function (DMF) Theoretical • Line intensities cannot be accurately obtained from the experimental spectra that we use. • Obtained from ab initio methods Ab initio Electronic (transition) dipole moment function LEVEL and PGOPHER to Final Line List Case (b) vibrational wavefunctions and matrix elements LEVEL Potential energy curve + Dipole moment function Hund’s case (b) to (a) • • • • LEVEL does not include electron spin. MEs are v′Λ′𝑁′ μ(𝑟) vΛ𝑁 - (Hund’s case (b)) PGOPHER needs case (a) MEs - v′Ω′𝐽′ μ(𝑟) vΩ𝐽 . Transformation equation was derived: v ′ Ω′ 𝐽′ 𝑇𝑞𝑘 vΩ𝐽 = −1 × −1 𝐽′−Ω′ 𝑁−𝑁′ +𝑆 ′ +𝐽+𝑘+Λ 𝐽′ 𝑘 −Ω′ 𝑞 𝐽 Ω −1 2𝑁 + 1 2𝑁′ + 1 𝑁′,𝑁′′ × 𝑁′ 𝐽′ 𝐽 𝑁 𝑆 𝑘 𝑁′ 𝑘 −Λ′ 𝑞 𝑁 Λ 𝐽′ 𝑆 Ω′ −Σ 𝑁′ −Λ′ v′Λ′𝑁′ 𝑇𝑞𝑘 vΛ𝑁 – Derivation published in CN paper in ApJS [1] [1] Brooke JSA, Ram RS, Western CM, Li G, Schwenke DW, and Bernath PF. ApJS 210, 15 (2014) 𝐽 𝑆 Ω −Σ 𝑁 −Λ The Herman-Wallis Effect • Rotation - centrifugal force causes change in bond length • Results in a change in the vibrational wavefunctions • MEs are changed due to this and the DMF • Effect is greater in NH than C2 due to light H atom The Herman-Wallis Effect - NH • The noticeable effect of the Herman-Wallis effect for NH is an increase in the strength of the R branch and a decrease in the strength of the P branch • To the right is the calculated spectrum of the NH X 3 Σ− (1,0) band. LEVEL and PGOPHER to Final Line List Case (a) matrix elements case (b) to (a) PGOPHER Einstein As Line list with positions and intensities Case (b) vibrational wavefunctions and matrix elements LEVEL Potential energy curve + Dipole moment function Line Strength Equations • PGOPHER diagonalises the Hamiltonian matrix, and combines the resulting eigenvectors with the case (a) MEs and line positions to calculate Einstein A values: 𝐴𝐽′ →𝐽′′ ′ Ω′ 𝐽′ 𝑇 𝑘 vΩ𝐽 |2 | v 𝑝 = 3.136 189 32 × 10−7 𝜈 3 (2𝐽′ + 1) • where v ′ Ω′ 𝐽′ 𝑇𝑝𝑘 vΩ𝐽 is the ME. • The Einstein A values are also converted to oscillator strengths (f-values): 𝑓𝐽′ ←𝐽′′ 1 (2𝐽′ + 1) = 1.499 193 78 27 2 𝐴𝐽′ →𝐽′′ ′′ ν (2𝐽 + 1) NH X 3 Σ− state rovibrational and pure rotational transitions • NH is present in cool stars, comets, diffuse interstellar clouds, the Sun, and probably the upper atmospheres of extrasolar planets. • Magnetic trapping, combustion • Vibrational transitions have been used to calculate the actual nitrogen abundance in cool stars and the Sun. • Boudjaadar et al. 1986 - The Δv=1 sequence up to v′=5 [2] • Ram et al. 1999 - more transitions in the same sequence in 1999 [3] • Ram and Bernath 2010 - (6,5) band [4] • Robinson et al. 2007 – rotational transitions in in v=1 and 2 [5] [2] Boudjaadar D, Brion J, Chollet P, Guelachvili G, and Vervloet M. JMS 119, 352 (1986) [3] Ram RS, Bernath PF, and Hinkle KH. JCP 110, 5557 (1999) [4] Ram RS and Bernath PF. JMS 260, 115 (2010) [5] Robinson A, Brown J, Flores-Mijangos J, Zink L, and Jackson M. Mol Phys 105, 639 (2007) NH X 3 Σ − state calculations • No new line position fit used Ram and Bernath 2010 [4] • Dipole moment function calculated by Gerrit Groenenboom – not published [6] [6] Campbell WC, Groenenboom GC, Lu HI, Tsikata E, and Doyle JM. PRL, 100, 083003 (2008) NH X 3 Σ − spectra Comparison to Observed Spectra Einstein Av′v′′ and Lifetimes Einstein Av′v′′ (s-1) Band Ours D [7] R&W [8] M&R [9] 1-0 27.19 51.7 34.9 31.9 2-1 57.91 92.3 69.18 3-2 90.14 144.4 108.12 4-3 121.40 144.49 5-4 148.70 173.94 6-5 168.92 191.70 v=1 Lifetimes (ms) Observed [] Calculated [] Ours 37.0 ± 0.5stat +2.0 −0.8 syst 36.99 36.77 [7] Dodd JA, Lipson SJ, Flanagan DJ, Blumberg WAM, Person JC and Green BD. JCP 94, 4301 (1991) [8] Rosmus P and Werner H-J. J. Mol. Struct 60, 405 (1980) [9] Meyer W and Rosmus P. JCP 63, 2356 (1975) NH Line list • All possible bands calculated between observed v levels (up to v=6), up to J between 25 and 44, depending on the band. • Rotational transitions included v' 0 0 0 0 0 0 0 0 v'' J' 0 2.0 0 3.0 0 4.0 0 5.0 0 6.0 0 7.0 0 8.0 0 9.0 J'' 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 F' 1 1 1 1 1 1 1 1 F'' 1 1 1 1 1 1 1 1 p' p'' e e e e e e e e e e e e e e e e N' N'' Observed 1 0 32.50499 2 1 65.21272 3 2 97.79301 4 3 130.23878 5 4 162.51736 6 5 ... 7 6 ... 8 7 ... Calculated 32.504992 65.212716 97.793016 130.238779 162.517360 194.591348 226.422257 257.971567 Residual E'' A f -0.00000 -0.0077 8.361500E-3 1.977382E-5 0.00000 32.4973 8.082840E-2 3.989194E-5 -0.00001 97.7100 2.917113E-1 5.879492E-5 0.00000 195.5030 7.137733E-1 7.710589E-5 0.00000 325.7418 1.416599E+0 9.502893E-5 ... 488.2592 2.465530E+0 1.126338E-4 ... 682.8505 3.920697E+0 1.299393E-4 ... 909.2728 5.836083E+0 1.469401E-4 Desc Source rR1(1) K rR1(2) FL rR1(3) FL rR1(4) FL rR1(5) FL rR1(6) None rR1(7) None rR1(8) None • NH paper has been submitted to JCP [email protected] OH X2Π Ground State “Meinel” Transitions • Important in atmospheric chemistry – Oxidation of hydrocarbons – Airglow • Found in extra-terrestrial environments: – Stars, comets, interstellar medium, extraterrestrial atmospheres • Rotational and rovibrational transitions from – Bernath and Colin 2009 [10] – Martin-Drumel et al. 2011 [11] [10] Bernath PF, & Colin R. JMS 257, 20 (2009) [11] Martin-Drumel MA, Pirali O, Balcon D, Brechignac Ph, Roy P, & Vervloet M. Rev. Sci. Instr 82, 113106 (2011) Dipole Moments (μv), Calculated Using Various DMFs Our Einstein As compared to HITRAN Observed Not Observed OH Spectrum – (2,0) band Conclusions • New line list with positions and intensities produced for X 3 Σ− state vibration-rotation transitions, up to v=6. • Line lists also produced for OH up to v=13. • Transformation equation doesn’t work as expected for OH, but intensities are an improvement compared to what’s currently available in HITRAN. • The combination of experimental and theoretical results is very effective and will be used for more molecules in the future. Thanks for listening! Transition Dipole Moment Matrix Elements • It then overlaps them and multiplies the result by the electronic (transition) dipole moment function, which is then integrated to give the transition dipole moment matrix element (TDMME). R/P OH Intensities (2,0) with transformation Our DMF N only Our DMF with transformation HITRAN DMF N only HITRAN DMF v=0 Vibrationally Averaged Dipole Moments, μ0 Year 1974 1974 1975 1987 1992 2014 Authors Scarl and Dalby [] Das et al. [] Meyer and Rosmus [] Goldfield and Kirby [] Cantarella et al. [] This work aCalculated μ0 1.389±0.075 1.5155a 1.5546a 1.480 1.4827 1.5246 by Cantarella et al. using the reported data of Das et al. and Meyer and Rosmus [] Scarl EA and Dalby FW. Can. J. Phys. 52, 1429 (1974) [] Das G, Wahl AC, and Stevens WJ. JCP 61, 433 (1974) [] Goldfield EM and Kirby KP. JCP 87, 3986 (1987) [] Cantarella E, Colot F, and Liévin J. Phys. Scripta. 46, 489 (1992) Full Calculation Method Start Einstein As and f-values – line list with positions and intensities Spectrum PGOPHER Line assignment and fit Case (a) matrix elements Hund’s case (b) to (a) Molecular constants fit Equilibrium constants Case (b) vibrational wavefunctions and transition dipole moment matrix elements LEVEL Start Ab initio RKR1 Potential energy curve End + Electronic (transition) dipole moment function OH X2Π Ground State Transitions NH X 3 Σ− state rovibrational and pure rotational transitions • NH is present in cool stars, comets, diffuse interstellar clouds, the Sun, and probably the upper atmospheres of extrasolar planets. • Magnetic trapping, combustion • Vibrational transitions have been used to calculate the actual nitrogen abundance in cool stars and the Sun. • Boudjaadar et al. 1986 - The Δv=1 sequence up to v′=5 [] • Ram et al. 1999 - more transitions in the same sequence in 1999 [] • Ram and Bernath 2010 - (6,5) band [] • Robinson et al. 2007 – rotational transitions in in v=1 and 2 [] [] Boudjaadar D, Brion J, Chollet P, Guelachvili G, and Vervloet M. JMS 119, 352 (1986) [] Ram RS, Bernath PF, and Hinkle KH. JCP 110, 5557 (1999) [] Ram RS and Bernath PF. JMS 260, 115 (2010) [] Robinson A, Brown J, Flores-Mijangos J, Zink L, and Jackson M. Mol Phys 105, 639 (2007)