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Mátyus E, Ferenc D. Vibronic mass computation for the EF– GK– H 1Σ g+ manifold of molecular hydrogen. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2074905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Budapest, Hungary
| | - Dávid Ferenc
- Institute of Chemistry, ELTE, Eötvös Loránd University, Budapest, Hungary
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2
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Ferenc D, Mátyus E. Non-adiabatic mass correction for excited states of molecular hydrogen: Improvement for the outer-well HH¯ 1Σ g + term values. J Chem Phys 2019; 151:094101. [PMID: 31492075 DOI: 10.1063/1.5109964] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The mass-correction function is evaluated for selected excited states of the hydrogen molecule within a single-state nonadiabatic treatment. Its qualitative features are studied at the avoided crossing of the EF with the GK state and also for the outer well of the HH¯ state. For the HH¯ state, a negative mass correction is obtained for the vibrational motion near the outer minimum, which accounts for most of the deviation between experiment and earlier theoretical work.
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Affiliation(s)
- Dávid Ferenc
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
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3
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Mátyus E, Teufel S. Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states. J Chem Phys 2019; 151:014113. [PMID: 31272174 DOI: 10.1063/1.5097899] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multidimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear configurations. The electron-nucleus Hamiltonian is block-diagonalized up to O(εn+1) through a unitary transformation of the electronic subspace, and the corresponding nth-order effective Hamiltonian is derived for the quantum nuclear motion. Explicit but general formulas are given for the second- and the third-order corrections. As a special case, the second-order Hamiltonian corresponding to an isolated electronic state is recovered which contains the coordinate-dependent mass-correction terms in the nuclear kinetic energy operator. For a multidimensional, explicitly coupled electronic band, the second-order Hamiltonian contains the usual Born-Oppenheimer terms and nonadiabatic corrections, but generalized mass-correction terms appear as well. These, earlier neglected terms, perturbatively account for the outlying (discrete and continuous) electronic states not included in the explicitly coupled electronic subspace.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Stefan Teufel
- Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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Mátyus E. Non-adiabatic mass-correction functions and rovibrational states of 4 He 2 + ( X 2 Σ u + ). J Chem Phys 2018; 149:194112. [PMID: 30466288 DOI: 10.1063/1.5050403] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The mass-correction functions in the second-order non-adiabatic Hamiltonian are computed for the 4 He 2 + molecular ion using the variational method, floating explicitly correlated Gaussian functions, and a general coordinate-transformation formalism. When non-adiabatic rovibrational energy levels are computed using these (coordinate-dependent) mass-correction functions and a highly accurate potential energy and diagonal Born-Oppenheimer correction curve, significantly improved theoretical results are obtained for the nine rotational and two rovibrational intervals known from high-resolution spectroscopy experiments.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
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Mátyus E. Non-adiabatic mass correction to the rovibrational states of molecules: Numerical application for the H 2 + molecular ion. J Chem Phys 2018; 149:194111. [PMID: 30466265 DOI: 10.1063/1.5050401] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
General transformation expressions of the second-order non-adiabatic Hamiltonian of the atomic nuclei, including the kinetic-energy correction terms, are derived upon the change from laboratory-fixed Cartesian coordinates to general curvilinear coordinate systems commonly used in rovibrational computations. The kinetic-energy or so-called "mass-correction" tensor elements are computed with the stochastic variational method and floating explicitly correlated Gaussian functions for the H 2 + molecular ion in its ground electronic state. {Further numerical applications for the 4 He 2 + molecular ion are presented in the forthcoming paper, Paper II [E. Mátyus, J. Chem. Phys. 149, 194112 (2018)]}. The general, curvilinear non-adiabatic kinetic energy operator expressions are used in the examples, and non-adiabatic rovibrational energies and corrections are determined by solving the rovibrational Schrödinger equation including the diagonal Born-Oppenheimer as well as the mass-tensor corrections.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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Jaquet R, Khoma MV. Investigation of non-adiabatic effects for the ro-vibrational spectrum of H3+: the use of a single potential energy surface with geometry-dependent nuclear masses. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1464225] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Ralph Jaquet
- Theoretische Chemie, Universität Siegen , Siegen, Germany
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Beyer M, Merkt F. Observation and Calculation of the Quasibound Rovibrational Levels of the Electronic Ground State of H2+. PHYSICAL REVIEW LETTERS 2016; 116:093001. [PMID: 26991172 DOI: 10.1103/physrevlett.116.093001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2015] [Indexed: 06/05/2023]
Abstract
Although the existence of quasibound rotational levels of the X^{+} ^{2}Σ_{g}^{+} ground state of H_{2}^{+} was predicted a long time ago, these states have never been observed. Calculated positions and widths of quasibound rotational levels located close to the top of the centrifugal barriers have not been reported either. Given the role that such states play in the recombination of H(1s) and H^{+} to form H_{2}^{+}, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels of H_{2}^{+} and compare the experimental results with the positions and widths we calculate using a potential model for the X^{+} state of H_{2}^{+} which includes adiabatic, nonadiabatic, relativistic, and radiative corrections to the Born-Oppenheimer approximation.
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Affiliation(s)
- Maximilian Beyer
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - Frédéric Merkt
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
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Tyuterev V, Tashkun S, Rey M, Kochanov R, Nikitin A, Delahaye T. Accurate Spectroscopic Models for Methane Polyads Derived from a Potential Energy Surface Using High-Order Contact Transformations. J Phys Chem A 2013; 117:13779-805. [DOI: 10.1021/jp408116j] [Citation(s) in RCA: 107] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Vladimir Tyuterev
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
| | - Sergei Tashkun
- LTS, V.E. Zuev Institute of Atmospheric Optics, Academician Zuev square 1, 634021, Tomsk, Russia
| | - Michael Rey
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
| | - Roman Kochanov
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
- LTS, V.E. Zuev Institute of Atmospheric Optics, Academician Zuev square 1, 634021, Tomsk, Russia
| | - Andrei Nikitin
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
- LTS, V.E. Zuev Institute of Atmospheric Optics, Academician Zuev square 1, 634021, Tomsk, Russia
| | - Thibault Delahaye
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
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De Fazio D, de Castro-Vitores M, Aguado A, Aquilanti V, Cavalli S. The He + H2+ → HeH+ + H reaction: ab initio studies of the potential energy surface, benchmark time-independent quantum dynamics in an extended energy range and comparison with experiments. J Chem Phys 2013; 137:244306. [PMID: 23277935 DOI: 10.1063/1.4772651] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work we critically revise several aspects of previous ab initio quantum chemistry studies [P. Palmieri et al., Mol. Phys. 98, 1835 (2000); C. N. Ramachandran et al., Chem. Phys. Lett. 469, 26 (2009)] of the HeH(2)(+) system. New diatomic curves for the H(2)(+) and HeH(+) molecular ions, which provide vibrational frequencies at a near spectroscopic level of accuracy, have been generated to test the quality of the diatomic terms employed in the previous analytical fittings. The reliability of the global potential energy surfaces has also been tested performing benchmark quantum scattering calculations within the time-independent approach in an extended interval of energies. In particular, the total integral cross sections have been calculated in the total collision energy range 0.955-2.400 eV for the scattering of the He atom by the ortho- and para-hydrogen molecular ion. The energy profiles of the total integral cross sections for selected vibro-rotational states of H(2)(+) (v = 0,...,5 and j = 1,...,7) show a strong rotational enhancement for the lower vibrational states which becomes weaker as the vibrational quantum number increases. Comparison with several available experimental data is presented and discussed.
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Affiliation(s)
- Dario De Fazio
- Istituto di Metodologie Inorganiche e dei Plasmi - C.N.R., 00016 Roma, Italy.
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Diniz LG, Alijah A, Mohallem JR. Core-mass nonadiabatic corrections to molecules: H2, H2+, and isotopologues. J Chem Phys 2013; 137:164316. [PMID: 23126719 DOI: 10.1063/1.4762442] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
For high-precision calculations of rovibrational states of light molecules, it is essential to include non-adiabatic corrections. In the absence of crossings of potential energy surfaces, they can be incorporated in a single surface picture through coordinate-dependent vibrational and rotational reduced masses. We present a compact method for their evaluation and relate in particular the vibrational mass to a well defined nuclear core mass derived from a Mulliken analysis of the electronic density. For the rotational mass we propose a simple, but very effective parametrization. The use of these masses in the nuclear Schrödinger equation yields numerical data for the corrections of a much higher quality than can be obtained with optimized constant masses, typically better than 0.1 cm(-1). We demonstrate the method for H(2), H(2)(+), and singly deuterated isotopologues. Isotopic asymmetry does not present any particular difficulty. Generalization to polyatomic molecules is straightforward.
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Affiliation(s)
- Leonardo G Diniz
- Laboratório de Átomos e Moléculas Especiais, Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P. O. Box 702, 30123-970 Belo Horizonte, MG, Brazil.
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Jaquet R, Khoma MV. Nonadiabatic investigations of ro-vibrational frequencies within the systems , H2, and prospects for : use of distance-dependent effective masses. Mol Phys 2012. [DOI: 10.1080/00268976.2012.671969] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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12
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Schwenke DW, Tashkun SA, Lee TJ. An isotopic-independent highly accurate potential energy surface for CO2 isotopologues and an initial 12C16O2 infrared line list. J Chem Phys 2012; 136:124311. [DOI: 10.1063/1.3697540] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
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13
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Holka F, Szalay PG, Fremont J, Rey M, Peterson KA, Tyuterev VG. Accurate ab initio determination of the adiabatic potential energy function and the Born–Oppenheimer breakdown corrections for the electronic ground state of LiH isotopologues. J Chem Phys 2011; 134:094306. [DOI: 10.1063/1.3555758] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
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Huang X, Schwenke DW, Lee TJ. Rovibrational spectra of ammonia. I. Unprecedented accuracy of a potential energy surface used with nonadiabatic corrections. J Chem Phys 2011; 134:044320. [DOI: 10.1063/1.3541351] [Citation(s) in RCA: 91] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Szalay PG, Holka F, Fremont J, Rey M, Peterson KA, Tyuterev VG. Are ab initio quantum chemistry methods able to predict vibrational states up to the dissociation limit for multi-electron molecules close to spectroscopic accuracy? Phys Chem Chem Phys 2011; 13:3654-9. [DOI: 10.1039/c0cp01334j] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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16
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An empirical formula to estimate off-diagonal adiabatic corrections to rotation–vibrational energy levels. Theor Chem Acc 2009. [DOI: 10.1007/s00214-009-0710-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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17
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Fábri C, Czakó G, Tasi G, Császár AG. Adiabatic Jacobi corrections on the vibrational energy levels of H2+ isotopologues. J Chem Phys 2009; 130:134314. [DOI: 10.1063/1.3097327] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Császár AG, Czakó G, Furtenbacher T, Mátyus E. Chapter 9 An Active Database Approach to Complete Rotational–Vibrational Spectra of Small Molecules. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2007. [DOI: 10.1016/s1574-1400(07)03009-5] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Rey M, Tyuterev VG. Adiabatic and non-adiabatic corrections to rovibrational energies of diatomic molecules: variational calculations with experimental accuracy. Phys Chem Chem Phys 2007; 9:2538-48. [PMID: 17508086 DOI: 10.1039/b700044h] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Using the variational technique, eigensolutions of the radial Herman-Asgharian equation accounting for non-adiabatic terms are determined within the experimental accuracy of the high-resolution spectroscopy. This method, which is independent of the algebraic and numerical approaches currently used in the literature for a "direct-potential-fit" of diatomic rovibrational spectra, is shown to be useful for validation of available calculations and for resolving some controversial issues. Comparative discussions are reported in this paper for a dozen diatomic molecules.
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Affiliation(s)
- M Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, CNRS UMR 6089, BP 1039, F-51687 Reims Cedex 2, France.
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Tennyson J, Barletta P, Kostin MA, Polyansky OL, Zobov NF. Ab initio rotation-vibration energy levels of triatomics to spectroscopic accuracy. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2002; 58:663-72. [PMID: 11991489 DOI: 10.1016/s1386-1425(01)00663-1] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
The factors that need to be taken into account to achieve spectroscopic accuracy for triatomic molecules are considered focusing on H3+ and water as examples. The magnitude of the adiabatic and non-adiabatic corrections to the Born-Oppenheimer approximation is illustrated for both molecules, and methods of including them ab initio are discussed. Electronic relativistic effects are not important for H3+, but are for water for which the magnitude of the various effects is discussed. For H3+ inclusion of rotational non-adiabatic effects means that levels can be generated to an accuracy approaching 0.01 cm(-1); for water the error is still dominated by the error in the correlation energy in the electronic structure calculation. Prospects for improving this aspect of the calculation are discussed.
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TARCZAY GYÖRGY, CSÁSZÁR ATTILAG, KLOPPER WIM, QUINEY HARRYM. Anatomy of relativistic energy corrections in light molecular systems. Mol Phys 2001. [DOI: 10.1080/00268970110073907] [Citation(s) in RCA: 105] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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