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Chang X, Dobrolyubov EO, Krasnoshchekov SV. Vibrational resonance analysis of linear molecules using resummation of divergent Rayleigh-Schrödinger perturbation theory series. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2023; 288:122071. [PMID: 36455465 DOI: 10.1016/j.saa.2022.122071] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Revised: 10/10/2022] [Accepted: 10/30/2022] [Indexed: 06/17/2023]
Abstract
The large order Rayleigh-Schrödinger perturbation theory (RSPT) was applied for calculating vibrational states of linear molecules. Two molecules (CO2 and C2H2) were used as test cases with using of isomorphic Watson Hamiltonian and quartic force fields. For CO2 the Sayvetz condition can remove all degeneracies for purely vibrational states and the non-degenerate perturbation theory can be applied. However, an existence of two degenerate modes in C2H2 requires using the upgraded degenerate version of RSPT that was employed in this context for the first time. The dominating divergent behavior of such series requires the resummation technique that mimics the multivalued nature of the underlying solutions, and the applied quartic Padé-Hermite approximants (QPHA) provided full solution of the problem. Moreover, some mathematical properties of QPHA proved to be an efficient tool for studying resonance effects through the Katz theorem that controls the singular points of the eigenvalues on the complex plane. In the case of C2H2, not only all earlier observed classical resonances were confirmed and quantified, but also subtle interpolyad resonances (K2/55,K3/4555), proposed recently by Herman (2011) were described as well. Following the analysis, we found several novel resonances, of which we proposed one independent interpolyad resonance K2/4444. The complete analysis of such critical points provided the full resonance picture of all studied molecules.
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Affiliation(s)
- Xuanhao Chang
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119899, Russian Federation
| | - Egor O Dobrolyubov
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119899, Russian Federation; Emanuel Institute of Biochemical Physics of the Russian Academy of Sciences, Kosygina ul., 4, Moscow, 119334, Russian Federation
| | - Sergey V Krasnoshchekov
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119899, Russian Federation.
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Tyuterev V, Tashkun S, Rey M, Nikitin A. High-order contact transformations of molecular Hamiltonians: general approach, fast computational algorithm and convergence of ro-vibrational polyad models. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2096140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Vladimir Tyuterev
- Groupe de Spectrométrie Moléculaire et Atmosphérique, Université de Reims, Reims, France
- Laboratory of Molecular Quantum Mechanics and Radiative Transfer, Tomsk State University, Tomsk, Russia
| | - Sergey Tashkun
- Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, Tomsk, Russia
| | - Michael Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, Université de Reims, Reims, France
| | - Andrei Nikitin
- Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, Tomsk, Russia
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Rey M. Novel methodology for systematically constructing global effective models from ab initio-based surfaces: A new insight into high-resolution molecular spectra analysis. J Chem Phys 2022; 156:224103. [PMID: 35705402 DOI: 10.1063/5.0089097] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, a novel methodology is presented for the construction of ab initio effective rotation-vibration spectroscopic models from potential energy and dipole moment surfaces. Non-empirical effective Hamiltonians are obtained via the block-diagonalization of selected variationally computed eigenvector matrices. For the first time, the derivation of an effective dipole moment is carried out in a systematic way. This general approach can be implemented quite easily in most of the variational computer codes and turns out to be a clear alternative to the rather involved Van Vleck perturbation method. Symmetry is exploited at all stages to translate first-principles calculations into a set of spectroscopic parameters to be further refined on experiment. We demonstrate on H2CO, PH3, CH4, C2H4, and SF6 that the proposed effective model can provide crucial information to spectroscopists within a very short time compared to empirical spectroscopic models. This approach brings a new insight into high-resolution spectrum analysis of polyatomic molecules and will be also of great help in the modeling of hot atmospheres where completeness is important.
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Affiliation(s)
- Michael Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, BP 1039, F-51687 Reims Cedex 2, France
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Chang X, Dobrolyubov EO, Krasnoshchekov SV. Fundamental studies of vibrational resonance phenomena by multivalued resummation of the divergent Rayleigh-Schrödinger perturbation theory series: deciphering polyad structures of three H 216O isotopologues. Phys Chem Chem Phys 2022; 24:6655-6675. [PMID: 35234755 DOI: 10.1039/d1cp04279c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
A fundamental quantitative study of the vibrational resonances of three H216O H,D-isotopologues with a quartic Watson Hamiltonian was carried out using the resummation of the high-order (∼λn, n ≤ 203) divergent Rayleigh-Schrödinger perturbation theory (RSPT) series by quartic Padé-Hermite multivalued diagonal approximants PH[m,m,m,m,m], m ≤ 40. The resonance condition between a pair of states is formulated as the existence of a common complex energy solution branch point inside the unit circle: |E(λj)|, Re(λj)2 + Im(λj)2 ≤ 1. For the matrix formulation of the vibrational problem (VCI), the existence of common branch points is governed by the Katz theorem and they can be found as roots of discriminant polynomials. The main branches of the Padé-Hermite approximants typically reproduce VCI energies with high accuracy while alternative branches often fit nearby resonant states. The resummation of the RSPT series for H2O and D2O (up to the tenth polyad) revealed not only Fermi and Darling-Dennison resonances, but also unusual (0,2,-5) and (5,-2,0) resonance effects matching the (5,2,5) polyad structure, while the (3,2,1) structure was rigorously confirmed for HDO. It is demonstrated that the (5,2,5) polyad structure ensures good organization of high-energy resonating states and breaks down the classic (2,1,2) structure. The advocated methodology of quantitative description of resonance phenomena and revealing polyad structures is suitable for larger molecules and can be adapted to linear molecules and symmetric tops. Its application ensures rigorous classification of vibrational states and can be used in quantitative vibration-rotation spectroscopy.
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Affiliation(s)
- Xuanhao Chang
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119899, Russian Federation.
| | - Egor O Dobrolyubov
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119899, Russian Federation.
| | - Sergey V Krasnoshchekov
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119899, Russian Federation.
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Jaliparthi V, Balla MR. Vibrational Hamiltonian of tetrachloro-, tetrafluoro-, and mono- silanes using U(2) Lie algebras. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2022; 264:120289. [PMID: 34455377 DOI: 10.1016/j.saa.2021.120289] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2021] [Revised: 07/02/2021] [Accepted: 08/14/2021] [Indexed: 06/13/2023]
Abstract
In this paper, we have applied the symmetry adapted one-dimensional framework of the U(2) Lie algebras to estimate the vibrational frequencies of tetrachloro-, tetrafluoro-, and mono- silanes in the gas phase having the spectroscopic interest of terrestrial volcanic plumes and other planetary atmospheres. A vibrational Hamiltonian that preserves the Td point group symmetry of each of these silane molecules is devised using ten interacting Morse oscillator bound state spectra. The calculated vibron numbers and locality parameters indicate that the vibrational motion is highly anharmonic in SiH4 (nearest to local mode), moderately anharmonic in SiF4 (mixed mode) and the least anharmonic in SiCl4 (near to local mode). RMS deviations of the derived vibrational frequencies [0.41 cm-1 (SiH4), 0.83 cm-1 (SiCl4), and 0.63 cm-1 (SiF4)], with reference to their experimental counterparts, assert that the U(2) Lie algebraic Hamiltonian is successful in deriving all the fundamental vibrations, their higher overtones and combination bands up to the fifth excitation, of each of the three silane molecules at the sub-cm-1 level of accuracy, possibly at a much lower computational cost as compared to other theoretical methods.
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Bykov A. Resummation of the Rayleigh-Schrödinger perturbation series. Vibrational energy levels of the H2S molecule. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1886362] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- A.D. Bykov
- V.E. Zuev Institute of Atmospheric Optics, Tomsk, Russia
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Krasnoshchekov SV, Dobrolyubov EO, Syzgantseva MA, Palvelev RV. Rigorous vibrational Fermi resonance criterion revealed: two different approaches yield the same result. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1743887] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- S. V. Krasnoshchekov
- Department of Chemistry, Lomonosov Moscow State University, Moscow, Russian Federation
| | - E. O. Dobrolyubov
- Department of Chemistry, Lomonosov Moscow State University, Moscow, Russian Federation
| | - M. A. Syzgantseva
- Department of Chemistry, Lomonosov Moscow State University, Moscow, Russian Federation
| | - R. V. Palvelev
- Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russian Federation
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Karmakar S, Keshavamurthy S. Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective. Phys Chem Chem Phys 2020; 22:11139-11173. [DOI: 10.1039/d0cp01413c] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.
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Affiliation(s)
- Sourav Karmakar
- Department of Chemistry
- Indian Institute of Technology
- Kanpur
- India
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9
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Sibert EL. Modeling vibrational anharmonicity in infrared spectra of high frequency vibrations of polyatomic molecules. J Chem Phys 2019; 150:090901. [DOI: 10.1063/1.5079626] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Edwin L. Sibert
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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Gong JZ, Matthews DA, Changala PB, Stanton JF. Fourth-order vibrational perturbation theory with the Watson Hamiltonian: Report of working equations and preliminary results. J Chem Phys 2018; 149:114102. [DOI: 10.1063/1.5040360] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Justin Z. Gong
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Devin A. Matthews
- Institute for Computational Engineering and Sciences, The University of Texas, Austin, Texas 78712, USA
| | - P. Bryan Changala
- JILA, National Institute of Standards and Technology, University of Colorado, Boulder, Colorado 80309, USA and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - John F. Stanton
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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11
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Pietropolli Charmet A, Cornaton Y. Benchmarking fully analytic DFT force fields for vibrational spectroscopy: A study on halogenated compounds. J Mol Struct 2018. [DOI: 10.1016/j.molstruc.2018.01.089] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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12
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Krasnoshchekov SV, Craig NC, Koroleva LA, Stepanov NF. Anharmonic vibrational analysis of s-trans and s-cis conformers of acryloyl fluoride using numerical-analytic Van Vleck operator perturbation theory. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2018; 189:66-79. [PMID: 28800431 DOI: 10.1016/j.saa.2017.07.062] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2017] [Revised: 07/22/2017] [Accepted: 07/30/2017] [Indexed: 06/07/2023]
Abstract
A new gas-phase infrared (IR) spectrum of acryloyl fluoride (ACRF, CH2CHCFO) with a resolution of 0.1cm-1 in the range 4000-450cm-1 was measured. Theoretical ab initio molecular structures, full quartic potential energy surfaces (PES), and cubic surfaces of dipole moments and polarizability tensor components (electro-optical properties, EOP) of the s-trans and s-cis conformers of the ACRF were calculated by the second-order Møller-Plesset electronic perturbation theory with a correlation consistent Dunning triple-ζ basis set. The numerical-analytic implementation of the second-order operator canonical Van Vleck perturbation theory was employed for predicting anharmonic IR and Raman scattering (RS) spectra of ACRF. To improve the anharmonic predictions, harmonic frequencies were replaced by their counterparts evaluated with the higher-level CCSD(T)/cc-pVTZ model, to form a "hybrid" PES. The original operator representation of the Hamiltonian is analytically reduced to a quasi-diagonal form, integrated in the harmonic oscillator basis and diagonalized to account for strong resonance couplings. Double canonical transformations of EOP expansions enabled prediction of integral intensities of both fundamental and multi-quanta transitions in IR/RS spectra. Enhanced band shape analysis reinforced the assignments. A thorough interpretation of the new IR experimental spectra and existing matrix-isolation literature data for the mixture of two conformers of ACRF was accomplished, and a number of assignments clarified.
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Affiliation(s)
- Sergey V Krasnoshchekov
- Department of Chemistry, Lomonosov Moscow State University, Leninskiye Gory 1-3, 119991 Moscow, Russian Federation.
| | - Norman C Craig
- Department of Chemistry and Biochemistry, Oberlin College, Oberlin, Ohio 44074, USA
| | - Lidiya A Koroleva
- Department of Chemistry, Lomonosov Moscow State University, Leninskiye Gory 1-3, 119991 Moscow, Russian Federation
| | - Nikolay F Stepanov
- Department of Chemistry, Lomonosov Moscow State University, Leninskiye Gory 1-3, 119991 Moscow, Russian Federation
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13
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Johnson BA, Sibert EL. Assigning the low lying vibronic states of CH 3O and CD 3O. J Chem Phys 2017; 146:174112. [PMID: 28477600 DOI: 10.1063/1.4981795] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
The assignment of lines in vibrational spectra in strongly mixing systems is considered. Several low lying vibrational states of the ground electronic X∼2E state of the CH3O and CD3O radicals are assigned. Jahn-Teller, spin-orbit, and Fermi couplings mix the normal mode states. The mixing complicates the assignment of the infrared spectra using a zero-order normal mode representation. Alternative zero-order representations, which include specific Jahn-Teller couplings, are explored. These representations allow for definitive assignments. In many instances it is possible to plot the wavefunctions on which the assignments are based. The plots, which are shown in the adiabatic representation, allow one to visualize the effects of various higher order couplings. The plots also enable one to visualize the conical seam and its effect on the wavefunctions. The first and the second order Jahn-Teller couplings in the rocking motion dominate the spectral features in CH3O, while first order and modulated first order couplings dominate the spectral features in CD3O. The methods described here are general and can be applied to other Jahn-Teller systems.
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Affiliation(s)
- Britta A Johnson
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Edwin L Sibert
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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14
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Sibaev M, Crittenden DL. Balancing accuracy and efficiency in selecting vibrational configuration interaction basis states using vibrational perturbation theory. J Chem Phys 2016. [DOI: 10.1063/1.4960600] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Duchko AN, Bykov AD. Resummation of divergent perturbation series: Application to the vibrational states of H2CO molecule. J Chem Phys 2015; 143:154102. [PMID: 26493892 DOI: 10.1063/1.4933239] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Large-order Rayleigh-Schrödinger perturbation theory (RSPT) is applied to the calculation of anharmonic vibrational energy levels of H2CO molecule. We use the model of harmonic oscillators perturbed by anharmonic terms of potential energy. Since the perturbation series typically diverge due to strong couplings, we apply the algebraic approximation technique because of its effectiveness shown earlier by Goodson and Sergeev [J. Chem. Phys. 110, 8205 (1999); ibid. 124, 094111 (2006)] and in our previous articles [A. D. Bykov et al. Opt. Spectrosc. 114, 396 (2013); ibid. 116, 598 (2014)]. To facilitate the resummation of terms contributing to perturbed states, when resonance mixing between states is especially strong and perturbation series diverge very quick, we used repartition of the Hamiltonian by shifting the normal mode frequencies. Energy levels obtained by algebraic approximants were compared with the results of variational calculation. It was found that for low energy states (up to ∼5000 cm(-1)), algebraic approximants gave accurate values of energy levels, which were in excellent agreement with the variational method. For highly excited states, strong and multiple resonances complicate series resummation, but a suitable change of normal mode frequencies allows one to reduce the resonance mixing and to get accurate energy levels. The theoretical background of the problem of RSPT series divergence is discussed along with its numerical analysis. For these purposes, the vibrational energy is considered as a function of a complex perturbation parameter. Layout and classification of its singularities allow us to model the asymptotic behavior of the perturbation series and prove the robustness of the algorithm.
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Affiliation(s)
- A N Duchko
- National Research Tomsk Polytechnic University, Tomsk, Russia
| | - A D Bykov
- V.E. Zuev Institute of Atmospheric Optics, Tomsk, Russia
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Krasnoshchekov SV, Craig NC, Boopalachandran P, Laane J, Stepanov NF. Anharmonic Vibrational Analysis of the Infrared and Raman Gas-Phase Spectra of s-trans- and s-gauche-1,3-Butadiene. J Phys Chem A 2015; 119:10706-23. [DOI: 10.1021/acs.jpca.5b07650] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Norman C. Craig
- Department of Chemistry and Biochemistry, Oberlin College, Oberlin, Ohio 44074, United States
| | | | - Jaan Laane
- Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States
| | - Nikolay F. Stepanov
- Lomonosov Moscow State University, Leninskiye Gory, 119991, Moscow, Russian Federation
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Cassam-Chenaï P, Rousseau G, Ilmane A, Bouret Y, Rey M. Application of quasi-degenerate perturbation theory to the calculation of rotational energy levels of methane vibrational polyads. J Chem Phys 2015. [DOI: 10.1063/1.4926471] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- P. Cassam-Chenaï
- University Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
| | - G. Rousseau
- University Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
| | - A. Ilmane
- University Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
| | - Y. Bouret
- University Nice Sophia Antipolis, CNRS, LPMC, UMR 7336, 06100 Nice, France
| | - M. Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, CNRS UMR 6089, BP 1039, F-51687 Reims Cedex 2, France
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Krasnoshchekov SV, Vogt N, Stepanov NF. Ab Initio Anharmonic Analysis of Vibrational Spectra of Uracil Using the Numerical-Analytic Implementation of Operator Van Vleck Perturbation Theory. J Phys Chem A 2015; 119:6723-37. [DOI: 10.1021/acs.jpca.5b03241] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sergey V. Krasnoshchekov
- Lomonosov Moscow State University, Leninskiye Gory, 119991, Moscow, Russian Federation
- Chemieinformationssysteme, Universität Ulm, Albert Einstein Allee 47, D-89069 Ulm, Germany
| | - Natalja Vogt
- Lomonosov Moscow State University, Leninskiye Gory, 119991, Moscow, Russian Federation
- Chemieinformationssysteme, Universität Ulm, Albert Einstein Allee 47, D-89069 Ulm, Germany
| | - Nikolay F. Stepanov
- Lomonosov Moscow State University, Leninskiye Gory, 119991, Moscow, Russian Federation
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Krasnoshchekov SV, Isayeva EV, Stepanov NF. Criteria for first- and second-order vibrational resonances and correct evaluation of the Darling-Dennison resonance coefficients using the canonical Van Vleck perturbation theory. J Chem Phys 2015; 141:234114. [PMID: 25527926 DOI: 10.1063/1.4903927] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The second-order vibrational Hamiltonian of a semi-rigid polyatomic molecule when resonances are present can be reduced to a quasi-diagonal form using second-order vibrational perturbation theory. Obtaining exact vibrational energy levels requires subsequent numerical diagonalization of the Hamiltonian matrix including the first- and second-order resonance coupling coefficients. While the first-order Fermi resonance constants can be easily calculated, the evaluation of the second-order Darling-Dennison constants requires more complicated algebra for seven individual cases with different numbers of creation-annihilation vibrational quanta. The difficulty in precise evaluation of the Darling-Dennison coefficients is associated with the previously unrecognized interference with simultaneously present Fermi resonances that affect the form of the canonically transformed Hamiltonian. For the first time, we have presented the correct form of the general expression for the evaluation of the Darling-Dennison constants that accounts for the underlying effect of Fermi resonances. The physically meaningful criteria for selecting both Fermi and Darling-Dennison resonances are discussed and illustrated using numerical examples.
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Affiliation(s)
| | - Elena V Isayeva
- Chemistry Department, Lomonosov Moscow State University, Moscow 119991, Russia
| | - Nikolay F Stepanov
- Chemistry Department, Lomonosov Moscow State University, Moscow 119991, Russia
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Lemus R, Sánchez-Castellanos M, Pérez-Bernal F, Fernández JM, Carvajal M. Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra. J Chem Phys 2014; 141:054306. [DOI: 10.1063/1.4889995] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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