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Jaquet R. A nearly complete treatment of the effect of non-adiabaticity on rovibrational energies of H3+ (Part III). J Chem Phys 2024; 161:054109. [PMID: 39092944 DOI: 10.1063/5.0215051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2024] [Accepted: 07/16/2024] [Indexed: 08/04/2024] Open
Abstract
In this article, significant contributions of non-adiabaticity for the rovibrational bound states up to 25 000 cm-1 and total angular momentum J = 0-20 of H3+ are investigated. A coupled-perturbed full configuration interaction (CP-FCI) treatment is applied to calculate all couplings between electronic states caused by the nuclear motion. These derivative couplings were evaluated up to the second order by means of a perturbation treatment and include all nuclear Cartesian first and second derivatives of the electronic wavefunctions. In particular, the coupling of special derivatives with respect to r and R in the Jacobi coordinate representation is more significant than thought. The perturbation approach is especially optimal for the treatment of weak non-adiabaticity in case of rovibrational energies in H3+ and had not been available before for H3+ or other triatomics. Using exclusively Gaussian basis functions for CP-FCI appears to be sufficient, because explicit correlated wavefunctions are already used for all other potential energy contributions. Our work is an extension of earlier non-adiabatic investigations based on first derivative couplings of electronic states that led to the concept of geometry-dependent effective nuclear masses and which needs only a single potential energy surface for the dynamics. The implementation allows us to include all non-adiabatic effects up to the order of O(μ-2), μ being the reduced nuclear mass. Our treatment works for any isotopologue and for the whole potential energy curve or surface. By this treatment, a further reduction in deviations to experimental data for most rovibrational levels to less than 0.1 cm-1 is possible. For the related transition frequencies, 1366 of 1720 known rovibrational transitions in H3+ have deviations less than 0.1 cm-1 without using any empirically adjustable parameters or optimizing the nuclear mass for a specific transition. For many questionable assignments (deviations >0.3 cm-1) of observed transitions in H3+, a new labeling is proposed.
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Affiliation(s)
- Ralph Jaquet
- Theoretical Chemistry, Department of Chemistry and Biology, Siegen University, 57068 Siegen, Germany
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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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4
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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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Čurík R, Greene CH. Inelastic low-energy collisions of electrons with HeH+: Rovibrational excitation and dissociative recombination. J Chem Phys 2017; 147:054307. [DOI: 10.1063/1.4994921] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roman Čurík
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 182 23 Prague 8, Czech Republic
| | - Chris H. Greene
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
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Walton JR, Rivera−Rivera LA, Lucchese RR, Bevan JW. Canonical Approaches to Applications of the Virial Theorem. J Phys Chem A 2016; 120:817-23. [DOI: 10.1021/acs.jpca.5b11526] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jay R. Walton
- Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368, United States
| | - Luis A. Rivera−Rivera
- Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States
| | - Robert R. Lucchese
- Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States
| | - John W. Bevan
- Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States
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8
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Walton JR, Rivera-Rivera LA, Lucchese RR, Bevan JW. Canonical Potentials and Spectra within the Born–Oppenheimer Approximation. J Phys Chem A 2015; 119:6753-8. [DOI: 10.1021/acs.jpca.5b04008] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jay R. Walton
- Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368, United States
| | - Luis A. Rivera-Rivera
- Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States
| | - Robert R. Lucchese
- Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States
| | - John W. Bevan
- Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States
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9
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Jungen M, Jungen C. Rydberg states of the HeH+ion calculated byab initiomethods: potential energies and effective principal quantum numbers. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1040094] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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10
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Salam A. Quantum electrodynamics effects in atoms and molecules. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2014. [DOI: 10.1002/wcms.1211] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- A. Salam
- Department of Chemistry; Wake Forest University; Winston-Salem NC USA
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Perry AJ, Hodges JN, Markus CR, Kocheril GS, McCall BJ. Communication: High precision sub-Doppler infrared spectroscopy of the HeH+ ion. J Chem Phys 2014; 141:101101. [DOI: 10.1063/1.4895505] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adam J. Perry
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
| | - James N. Hodges
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
| | - Charles R. Markus
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
| | - G. Stephen Kocheril
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
| | - Benjamin J. McCall
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
- Departments of Astronomy and Physics, University of Illinois, Urbana, Illinois 61801, USA
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Stanke M, Adamowicz L. Molecular Relativistic Corrections Determined in the Framework Where the Born–Oppenheimer Approximation is Not Assumed. J Phys Chem A 2013; 117:10129-37. [DOI: 10.1021/jp4020492] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, ul. Grudzia̧dzka
5, Toruń, PL 87-100, Poland
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13
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Polyansky OL, Ovsyannikov RI, Kyuberis AA, Lodi L, Tennyson J, Zobov NF. Calculation of Rotation–Vibration Energy Levels of the Water Molecule with Near-Experimental Accuracy Based on an ab Initio Potential Energy Surface. J Phys Chem A 2013; 117:9633-43. [DOI: 10.1021/jp312343z] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Oleg L. Polyansky
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E
6BT, United Kingdom
- Institute
of Applied Physics, Russian Academy of Science, Ulyanov Street 46, Nizhny
Novgorod 603950, Russia
| | - Roman I. Ovsyannikov
- Institute
of Applied Physics, Russian Academy of Science, Ulyanov Street 46, Nizhny
Novgorod 603950, Russia
| | - Aleksandra A. Kyuberis
- Institute
of Applied Physics, Russian Academy of Science, Ulyanov Street 46, Nizhny
Novgorod 603950, Russia
| | - Lorenzo Lodi
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E
6BT, United Kingdom
| | - Jonathan Tennyson
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E
6BT, United Kingdom
| | - Nikolai F. Zobov
- Institute
of Applied Physics, Russian Academy of Science, Ulyanov Street 46, Nizhny
Novgorod 603950, Russia
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