Vol. 36, issue 03, article # 1

Egorov O. V. Diabatic potential energy surfaces of the interacting triplet states 3A2 и 3B1 of the ozone molecule. // Optika Atmosfery i Okeana. 2023. V. 36. No. 03. P. 161–169. DOI: 10.15372/AOO20230301 [in Russian].
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Three-dimensional ab initio potential energy surfaces of the interacting triplet states 3A2 and 3B1 of the О3 molecule are constructed within the diabatization approach implemented in the MOLPRO package. These two states are responsible for the strongest singlet-triplet transitions in the Wulf band of O3. The molecular orbitals are optimized by the state-averaged CASSCF with the active space CAS(18, 12) involving three electronic states (X1A1, 3A2, and 3B1). The correlation energy is computed by icMRCI(Q). The impact of the basis set size on the accuracy of both the adiabatic excitation energy and origins of the vibronic transitions is analyzed.


ozone, ab initio, triplet state, potential energy surface, diabatization



1. Vasilchenko S., Barbe A., Starikova E., Kassi S., Mondelain D., Campargue A., Tyuterev V. Detection and assignment of ozone bands near 95% of the disso­ciation threshold: Ultrasensitive experiments for probing potential energy function and vibrational dynamics // Phys. Rev. A. 2020. V. 102, N 5. P. 052804. DOI: 10.1103/ PhysRevA.102.052804.
2. Vasilchenko S.S., Kassi S., Mondelain D., Campargue A. Lazernaya spektroskopiya vysokogo razresheniya molekuly ozona vblizi poroga dissociatsii // Optika atmosf. i okeana. 2021. V. 34, N 5. P. 315–322.
3. Rusic B. Unpublished results obtained from active thermochemical tables (ATcT) based on the Core (Argonne) Thermochemical Network version 1.110. 2010.
4. Barbe A., Mikhailenko S., Starikova E., Tyuterev V. High resolution infrared spectroscopy in support of ozone atmospheric monitoring and validation of the potential energy function // Mol. 2022. V. 27, N 3. P. 911. DOI: 10.3390/MOLECULES27030911.
5. Gordon I.E., Rothman L.S., Hargreaves R.J., Hashe­mi R., Karlovets E.V., Skinner F.M., Conway E.K., Hill C., Kochanov R.V., Tan Y., Wcisło P., Finen­ko A.A., Nelson K., Bernath P.F., Birk M., Boudon V., Campargue A., Chance K.V., Coustenis A., Drouin B.J., Flaud J.M., Gamache R.R., Hodges J.T., Jacquemart D., Mlawer E.J., Nikitin A.V., Pereva­lov V.I., Rotger M., Tennyson J., Toon G.C., Tran H., Tyuterev V.G., Adkins E.M., Baker A., Barbe A., Canè E., Császár A.G., Dudaryonok A., Egorov O., Fleisher A.J., Fleurbaey H., Foltynowicz A., Furtenbacher T., Harrison J.J., Hartmann J.M., Horneman V.M., Huang X., Karman T., Karns J., Kassi S., Kleiner I., Kofman V., Kwabia-Tchana F., Lavrentieva N.N., Lee T.J., Long D.A., Lukashevskaya A.A., Lyulin O.M., Makhnev V.Y., Matt W., Massie S.T., Melosso M., Mikhailenko S.N., Mondelain D., Mül­ler H.S.P., Naumenko O.V., Perrin A., Polyansky O.L., Raddaoui E., Raston P.L., Reed Z.D., Rey M., Richard C., Tóbiás R., Sadiek I., Schwenke D.W., Starikova E., Sung K., Tamassia F., Tashkun S.A., Vander Auwera J., Vasilenko I.A., Vigasin A.A., Villanu­eva G.L., Vispoel B., Wagner G., Yachmenev A., Yurchenko S.N. The HITRAN2020 molecular spectroscopic database // J. Quant. Spectrosc. Radiat. Transfer. 2022. V. 277. P. 107949. DOI: 10.1016/J.JQSRT.2021. 107949.
6. Delahaye T., Armante R., Scott N.A., Jacquinet-Hus­son N., Chédin A., Crépeau L., Crevoisier C., Douet V., Perrin A., Barbe A., Boudon V., Campargue A., Coudert L.H., Ebert V., Flaud J.M., Gamache R.R., Jacquemart D., Jolly A., Kwabia Tchana F., Kyuberis A., Li G., Lyulin O.M., Manceron L., Mikhailenko S., Moazzen-Ahmadi N., Müller H.S.P., Naumenko O.V., Nikitin A., Perevalov V.I., Richard C., Starikova E., Tashkun S.A., Tyuterev V.G., Vander Auwera J., Vispoel B., Yachmenev A., Yurchenko S. The 2020 edition of the GEISA spectroscopic database // J. Mol. Spectrosc. 2021. V. 380. P. 111510. DOI: 10.1016/J.JMS. 2021.111510.
7. Barbe A., Mikhailenko S., Starikova E., Tyuterev V. Infrared spectra of 16O3 in the 900–5600 cm-1 range revisited: Empirical corrections to the S&MPO and HITRAN2020 line lists // J. Quant. Spectrosc. Radiat. Transfer. 2021. V. 276. P. 107936. DOI: 10.1016/ J.JQSRT.2021.107936.
8. Albert D., Antony B.K.K., Ba Y.A., Babikov Y.L., Bollard P., Boudon V., Delahaye F., Del Zanna G., Dimitrijević M.S., Drouin B.J., Dubernet M.-L.L., Duensing F., Emoto M., Endres C.P.P., Fazliev A.Z., Glorian J.-M.M., Gordon I.E., Gratier P., Hill C., Jevremović D., Joblin C., Kwon D.-H.H., Kocha­nov R.V., Krishnakumar E., Leto G., Loboda P.A., Lukashevskaya A.A., Lyulin O.M., Marinković B.P., Markwick A., Marquart T., Mason N.J., Mendoza C., Millar T.J., Moreau N., Morozov S.V., Möller T., Müller H.S.P.P., Mulas G., Murakami I., Pakhomov Y., Palmeri P., Penguen J., Perevalov V.I., Piskunov N., Postler J., Privezentsev A.I., Quinet P., Ralchenko Y., Rhee Y.-J.J., Richard C., Rixon G., Rothman L.S., Roueff E., Ryabchikova T., Sahal-Bréchot S., Scheier P., Schilke P., Schlemmer S., Smith K.W., Schmitt B., Skobelev I.Y., Srecković V.A., Stempels E., Tashkun S.A., Tennyson J., Tyuterev V.G., Vastel C., Vujčić V., Wakelam V., Walton N.A., Zeippen C., Zwölf C.M. A decade with VAMDC: Results and ambitions // Atoms. 2020. V. 8, N 4. P. 76. DOI: 10.3390/atoms8040076.
9. Vasilchenko S., Mondelain D., Kassi S., Campargue A. Predissociation and pressure dependence in the low frequency far wing of the Wulf absorption band of ozone near 1.2 mm // J. Quant. Spectrosc. Radiat. Transfer. 2021. P. 107678. DOI: 10.1016/j.jqsrt.2021. 107678.
10. Grebenshchikov S.Yu., Qu Z.-W., Zhu H., Schinke R. Spin-orbit mechanism of predissociation in the Wulf band of ozone // J. Chem. Phys. 2006. V. 125. P. 021102. DOI: 10.1063/1.2219444.
11. Mondelain D., Jost R., Kassi S., Judge R.H., Tyute­rev V., Campargue A. Predissociation and spectroscopy of the 3A2(000) state of 18O3 from CRDS spectra of the 3A2(000) X1A1(110) hot band near 7900 cm-1 // J. Quant. Spectrosc. Radiat. Transfer. 2012. V. 113, N 11. P. 840–849. DOI: 10.1016/j.jqsrt.2012.01.015.
12. Abel B., Charvát A., Deppe S.F. Lifetimes of the lowest triplet state of ozone by intracavity laser absorption spectroscopy // Chem. Phys. Lett. 1997. V. 277, N 4. P. 347–355. DOI: 10.1016/S0009-2614(97)00893-2.
13. Inard D., Bouvier A.J., Bacis R., Churassy S., Bohr F., Brion J., Malicet J., Jacon M. Absorption cross-sections and lifetime of the 3A2 “metastable” state of ozone // Chem. Phys. Lett. 1998. V. 287. P. 515–524. DOI: 10.1016/S0009-2614(98)00200-0.
14. Xie D., Guo H., Peterson K.A. Ab initio characterization of low-lying triplet state potential-energy surfaces and vibrational frequencies in the Wulf band of ozone // J. Chem. Phys. 2001. V. 115. P. 10404. DOI: 10.1063/ 1.1417502.
15. Wachsmuth U., Abel B. Linewidths and line intensity measurements in the weak 3A2(000) X1A1(000) band of ozone by pulsed cavity ringdown spectroscopy // J. Geophys. Res. 2003. V. 108, N D15. P. 4473. DOI: 10.1029/2002JD003126.
16. Wulf O.R., Deming L.S. The effect of visible solar radiation on the calculated distribution of atmospheric ozone // Terr. Magn. Atmos. Electr. 1936. V. 41, N 4. P. 375–378. DOI: 10.1029/TE041I004P00375.
17. Wulf O.R., Deming L.S. The distribution of atmosp­heric ozone in equilibrium with solar radiation and the rate of maintenance of the distribution // Terr. Magn. Atmos. Electr. 1937. V. 42, N 2. P. 195–202. DOI: 10.1029/TE042I002P00195.
18. Bouvier A.J., Inard D., Veyret V., Bussery B., Bacis R., Churassy S., Brion J., Malicet J., Judge R.H. Contribution to the analysis of the 3A2 X1A2 “Wulf” transition of ozone by high-resolution Fourier transform spectrometry // J. Mol. Spectrosc. 1998. V. 190, N 2. P. 189–197. DOI: 10.1006/jmsp.1998.7578.
19. Deppe S.F., Wachsmuth U., Abel B., Bittererová M., Grebenshchikov S.Yu., Siebert R., Schinke R. Resonance spectrum and dissociation dynamics of ozone in the 3B2 electronically excited state: Experiment and theory // J. Chem. Phys. 2004. V. 121. P. 5191. DOI: 10.1063/1.1778381.
20. Anderson S.M., Mauersberger K. Ozone absorption spectroscopy in search of low-lying electronic states // J. Geophys. Res. 1995. V. 100, N D2. P. 3033. DOI: 10.1029/94JD03003.
21. Anderson S.M., Morton J., Mauersberger K. Near infrared absorption spectra of 16O3 and 18O3: Adiabatic energy of the 1A2 state? // J. Chem. Phys. 1990. V. 93. P. 3826. DOI: 10.1063/1.458767.
22. Anderson S.M., Hupalo P., Mauersberger K. Rotational structure in the near infrared absorption spectrum of ozone // J. Chem. Phys. 1993. V. 99. P. 737. DOI: 10.1063/1.465747.
23. Günther J., Anderson S.M., Hilpert G., Mauersberger K. Rotational structure in the absorption spectra of 18O3 and 16O3 near 1 μm: A comparative study of the 3A2 and 3B2 states // J. Chem. Phys. 1998. V. 108. P. 5449. DOI: 10.1063/1.475933.
24. Braunstein M., Martin R.L., Hay P.J. Investigation of the role of triplet states in the Wulf bands of ozone // J. Chem. Phys. 1995. V. 102. P. 3662. DOI: 10.1063/ 1.468595.
25. Bouvier A.J., Veyret V., Russier I., Inard D., Churas­sy S., Bacis R., Brion J., Malicet J., Judge R.H. A comparative rotational analysis of the  bands of the 3A2 1A1 Wulf transition for the isotopomers 16O3 and 18O3 of ozone by high resolution Fourier transform spectrometry // Spectrochim. Acta. 1999. V. 55, N 14. P. 2811–2821. DOI: 10.1016/S1386-1425(99)00096-7.
26. Bouvier A.J., Wannous G., Churassy S., Bacis R., Brion J., Malicet J., Judge R.H. Spectroscopy and predissociation of the 3A2 electronic state of ozone 16O3 and 18O3 by high resolution Fourier transform spectrometry // Spectrochim. Acta. Part A. 2001. V. 57, N 3. P. 561–579. DOI: 10.1016/S1386-1425(00)00409-1.
27. Mirahmadi M., Pérez-Ríos J., Egorov O., Tyute­rev V., Kokoouline V. Ozone formation in ternary collisions: Theory and experiment reconciled // Phys. Rev. Lett. 2022. V. 128, N 10. P. 108501. DOI: 10.1103/PhysRev Lett.128.108501.
28. Rosmus P., Palmieri P., Schinke R. The asymptotic region of the potential energy surfaces relevant for the O(3P) + O2 @ O3 reaction // J. Chem. Phys. 2002. V. 117. P. 4871. DOI: 10.1063/1.1491396.
29. Braunstein M., Pack R.T. Simple theory of diffuse structure in continuous ultraviolet spectra of polyatomic molecules. III. Application to the Wulf–Chappuis band system of ozone // J. Chem. Phys. 1992. V. 96. P. 6378. DOI: 10.1063/1.462632.
30. Minaev B., Ågren H. The interpretation of the Wulf absorption band of ozone // Chem. Phys. Lett. 1994. V. 217, N 5–6. P. 531–538. DOI: 10.1016/0009-2614(93)E1445-M.
31. Egorov O., Valiev R.R., Kurten T., Tyuterev V. Franck-Condon factors and vibronic patterns of singlet-triplet transitions of 16O3 molecule falling near the dissociation threshold and above // J. Quant. Spectrosc. Radiat. Transfer. 2021. V. 273. P. 107834. DOI: 10.1016/ j.jqsrt.2021.107834.
32. Grebenshchikov S.Yu., Qu Z.-W., Zhuz H., Schinke R. New theoretical investigations of the photodissociation of ozone in the Hartley, Huggins, Chappuis, and Wulf bands // Phys. Chem. Chem. Phys. 2007. V. 9. P. 2044–2064. DOI: 10.1039/B701020F.
33. Vasilchenko S.S., Egorov O.V., Tyuterev V.G. Eksperiment po registratsii pogloshcheniya ozona pri perekhodakh v tripletnoe elektronnoe sostoyanie 3A2 vysokochuvstvitel'nym metodom lazernoi spektroskopii vnutrirezonatornogo zatukhaniya v intervale 9350–10000 cm–1 // Optika atmosf. i okeana. 2022. V. 35, N 12. P. 971–978.
34. Tyuterev V.G., Kochanov R.V., Tashkun S.A., Holka F., Szalay P.G. New analytical model for the ozone electronic ground state potential surface and accurate ab initio vibrational predictions at high energy range // J. Chem. Phys. 2013. V. 139. P. 134307. DOI: 10.1063/1.4821638.
35. Simah D., Hartke B., Werner H.-J. Photodissociation dynamics of H2S on new coupled ab initio potential energy surfaces // J. Chem. Phys. 1999. V. 111. P. 4523. DOI: 10.1063/1.479214.
36. Karman T., Besemer M., van der Avoird A., Groenenboom G.C. Diabatic states, nonadiabatic coupling, and the counterpoise procedure for weakly interacting openshell molecules // J. Chem. Phys. 2018. V. 148. P. 094105. DOI: 10.1063/1.5013091.
37. Mead C.A., Truhlar D.G. Conditions for the definition of a strictly diabatic electronic basis for molecular systems // J. Chem. Phys. 1982. V. 77. P. 6090. DOI: 10.1063/1.443853.
38. Werner H.-J., Meyer W. MCSCF study of the avoided curve crossing of the two lowest 1Σ+ states of LiF // J. Chem. Phys. 1981. V. 74. P. 5802. DOI: 10.1063/ 1.440893.
39. Varandas A.J.C. Accurate ab initio potential energy curves for the classic Li–F ionic-covalent interaction by extrapolation to the complete basis set limit and modeling of the radial nonadiabatic coupling // J. Chem. Phys. 2009. V. 131. P. 124128. DOI: 10.1063/1.3237028.
40. An H., Baeck K.K. A practical and efficient diabatization that combines Lorentz and Laplace functions to approximate nonadiabatic coupling terms // J. Chem. Phys. 2015. V. 143. P. 194102. DOI: 10.1063/1.4935607.
41. Brady R.P., Yurchenko S.N., Kim G.-S., Somogyi W., Tennyson J. An ab initio study of the rovibronic spectrum of sulphur monoxide (SO): Diabatic vs. adiabatic representation // Phys. Chem. Chem. Phys. 2022. V. 24. P. 24076–24088. DOI: 10.1039/D2CP03051A.
42. Werner H.-J., Knowles P.J., Manby F.R., Black J.A., Doll K., Heßelmann A., Kats D., Köhn A., Korona T., Kreplin D.A., Ma Q., Miller T.F., Mitrushchenkov A., Peterson K.A., Polyak I., Rauhut G., Sibaev M. The Molpro quantum chemistry package // J. Chem. Phys. 2020. V. 152. P. 144107. DOI: 10.1063/5.0005081.
43. Werner H.-J., Knowles P.J., Knizia G., Manby F.R., Schütz M. et al. MOLPRO, version 2019.2, a package of ab initio programs. URL: https://www.molpro.net (last access: 15.11.2022).
44. Partridge H., Schwenke D.W. The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data // J. Chem. Phys. 1997. V. 106. P. 4618. DOI: 10.1063/1.473987.
45. Ho T.-S., Rabitz H. A general method for constructing multidimensional molecular potential energy surfaces from ab initio calculations // J. Chem. Phys. 1996. V. 104. P. 2584. DOI: 10.1063/1.470984.
46. Tennyson J., Kostin M.A., Barletta P., Harris G.J., Polyansky O.L., Ramanlal J., Zobov N.F. DVR3D: A program suite for the calculation of rotation-vibration spectra of triatomic molecules // Comp. Phys. Comm. 2004. V. 163, N 2. P. 85–116. DOI: 10.1016/ j.cpc.2003.10.003.
47. Allan M., Mason N.J., Davies J.A. Study of electronically excited states of ozone by electron-energy-loss spectroscopy // J. Chem. Phys. 1996. V. 105. P. 5665. DOI: 10.1063/1.472412.