1
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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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2
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Tao Z, Qiu T, Bhati M, Bian X, Duston T, Rawlinson J, Littlejohn RG, Subotnik JE. Practical phase-space electronic Hamiltonians for ab initio dynamics. J Chem Phys 2024; 160:124101. [PMID: 38526114 DOI: 10.1063/5.0192084] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 02/14/2024] [Indexed: 03/26/2024] Open
Abstract
Modern electronic structure theory is built around the Born-Oppenheimer approximation and the construction of an electronic Hamiltonian Ĥel(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ') and rotational (Γ″) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, ĤPS(X,P). While classical Born-Oppenheimer dynamics that run along the eigensurfaces of the operator Ĥel(X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of ĤPS(X,P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general.
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Affiliation(s)
- Zhen Tao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Tian Qiu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Mansi Bhati
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Titouan Duston
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Jonathan Rawlinson
- Department of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom
| | - Robert G Littlejohn
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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3
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Littlejohn R, Rawlinson J, Subotnik J. Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom. J Chem Phys 2024; 160:114103. [PMID: 38501907 DOI: 10.1063/5.0192465] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 02/19/2024] [Indexed: 03/20/2024] Open
Abstract
This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ2, where κ = (m/M)1/4 is the usual Born-Oppenheimer parameter. The lowest order term is the usual Born-Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born-Oppenheimer theory. We show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born-Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.
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Affiliation(s)
- Robert Littlejohn
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Jonathan Rawlinson
- School of Mathematics, University of Manchester, Manchester, United Kingdom
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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4
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Egorov O, Rey M, Viglaska D, Nikitin AV. Accurate ab initio potential energy surface, rovibrational energy levels and resonance interactions of triplet ( X ~ 3 B 1 ) methylene. J Comput Chem 2024; 45:83-100. [PMID: 37681560 DOI: 10.1002/jcc.27220] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Revised: 08/15/2023] [Accepted: 08/17/2023] [Indexed: 09/09/2023]
Abstract
In this work, we report rovibrational energy levels for four isotopologues of methylene (CH2 , CHD, CD2 , and 13 CH2 ) in their ground triplet electronic state (X ~ 3 B1 ) from variational calculation up to ~10,000 cm-1 and using a new accurate ab initio potential energy surface (PES). Triplet methylene exhibits a large-amplitude bending vibration and can reach a quasilinear configuration due to its low barrier (~2000 cm-1 ). To construct the ab initio PES, the Dunning's augmented correlation-consistent core-valence orbital basis sets were employed up to the sextuple-ζ quality [aug-cc-pCVXZ, X = T, Q, 5, and 6] combined with the single- and double-excitation unrestricted coupled cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. We have shown that the accuracy of the ab initio energies is further improved by including the corrections due to the scalar relativistic effects, DBOC and high-order electronic correlations. For the first time, all the available experimental rovibrational transitions were reproduced with errors less than 0.12 cm-1 , without any empirical corrections. Unlike more "traditional" nonlinear triatomic molecules, we have shown that even the energies of the ground vibrational state (000) with rather small rotational quantum numbers are strongly affected by the very pronounced rovibrational resonance interactions. Accordingly, the polyad structure of the vibrational levels of CH2 and CD2 was analyzed and discussed. The comparison between the energy levels obtained from the effective Watson A-reduced Hamiltonian, from the generating-function approach and from a variational calculation was given.
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Affiliation(s)
- Oleg Egorov
- Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics SB RAS, Tomsk, Russia
- Faculty of Physics, Tomsk State University, Tomsk, Russia
| | - Michaël Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, UFR Sciences, Reims, France
| | - Dominika Viglaska
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, UFR Sciences, Reims, France
| | - Andrei V Nikitin
- Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics SB RAS, Tomsk, Russia
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5
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Franke PR, Stanton JF. Influence of fourth-order vibrational corrections on semi-experimental (reSE) structures of linear molecules. J Chem Phys 2024; 160:014102. [PMID: 38174791 DOI: 10.1063/5.0177694] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2023] [Accepted: 12/11/2023] [Indexed: 01/05/2024] Open
Abstract
Semi-experimental structures (reSE) are derived from experimental ground state rotational constants combined with theoretical vibrational corrections. They permit a meaningful comparison with equilibrium structures based on high-level ab initio calculations. Typically, the vibrational corrections are evaluated with second-order vibrational perturbation theory (VPT2). The amount of error introduced by this approximation is generally thought to be small; however, it has not been thoroughly quantified. Herein, we assess the accuracy of theoretical vibrational corrections by extending the treatment to fourth order (VPT4) for a series of small linear molecules. Typical corrections to bond distances are on the order of 10-5 Å. Larger corrections, nearly 0.0002 Å, are obtained to the bond lengths of NCCN and CNCN. A borderline case is CCCO, which will likely require variational computations for a satisfactory answer. Treatment of vibrational effects beyond VPT2 will thus be important when one wishes to know bond distances confidently to four decimal places (10-4 Å). Certain molecules with shallow bending potentials, e.g., HOC+, are not amenable to a VPT2 description and are not improved by VPT4.
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Affiliation(s)
- Peter R Franke
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
| | - John F Stanton
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
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6
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Athavale V, Bian X, Tao Z, Wu Y, Qiu T, Rawlinson J, Littlejohn RG, Subotnik JE. Surface hopping, electron translation factors, electron rotation factors, momentum conservation, and size consistency. J Chem Phys 2023; 159:114120. [PMID: 37728203 DOI: 10.1063/5.0160965] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 08/11/2023] [Indexed: 09/21/2023] Open
Abstract
For a system without spin-orbit coupling, the (i) nuclear plus electronic linear momentum and (ii) nuclear plus orbital electronic angular momentum are good quantum numbers. Thus, when a molecular system undergoes a nonadiabatic transition, there should be no change in the total linear or angular momentum. Now, the standard surface hopping algorithm ignores the electronic momentum and indirectly equates the momentum of the nuclear degrees of freedom to the total momentum. However, even with this simplification, the algorithm still does not conserve either the nuclear linear or the nuclear angular momenta. Here, we show that one way to address these failures is to dress the derivative couplings (i.e., the hopping directions) in two ways: (i) we disallow changes in the nuclear linear momentum by working in a translating basis (which is well known and leads to electron translation factors) and (ii) we disallow changes in the nuclear angular momentum by working in a basis that rotates around the center of mass [which is not well-known and leads to a novel, rotationally removable component of the derivative coupling that we will call electron rotation factors below, cf. Eq. (96)]. The present findings should be helpful in the short term as far as interpreting surface hopping calculations for singlet systems (without spin) and then developing the new surface hopping algorithm in the long term for systems where one cannot ignore the electronic orbital and/or spin angular momentum.
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Affiliation(s)
- Vishikh Athavale
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zhen Tao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Tian Qiu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Jonathan Rawlinson
- Department of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom
| | - Robert G Littlejohn
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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7
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High-level ab initio study of disulfur monoxide: ground state potential energy surface and band origins for six isotopic species. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2022.140216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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8
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Lai KF, Salumbides EJ, Beyer M, Ubachs W. Precision measurement of quasi-bound resonances in H2 and the H + H scattering length. Mol Phys 2021. [DOI: 10.1080/00268976.2021.2018063] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- K.-F. Lai
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit, Amsterdam, Netherlands
| | - E. J. Salumbides
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit, Amsterdam, Netherlands
| | - M. Beyer
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit, Amsterdam, Netherlands
| | - W. Ubachs
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit, Amsterdam, Netherlands
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9
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Lai KF, Salumbides EJ, Ubachs W, Beyer M. Shape Resonances in H_{2} as Photolysis Reaction Intermediates. PHYSICAL REVIEW LETTERS 2021; 127:183001. [PMID: 34767422 DOI: 10.1103/physrevlett.127.183001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2021] [Revised: 09/02/2021] [Accepted: 09/27/2021] [Indexed: 06/13/2023]
Abstract
Shape resonances in H_{2}, produced as reaction intermediates in the photolysis of H_{2}S precursor molecules, are measured in a half-collision approach. Before disintegrating into two ground state H atoms, the reaction is quenched by two-photon Doppler-free excitation to the F electronically excited state of H_{2}. For J=13, 15, 17, 19, and 21, resonances with lifetimes in the range of nano- to milliseconds were observed with an accuracy of 30 MHz (1.4 mK). The experimental resonance positions are found to be in excellent agreement with theoretical predictions when nonadiabatic and quantum electrodynamical corrections are included. This is the first time such effects are observed in collisions between neutral atoms. From the potential energy curve of the H_{2} molecule, now tested at high accuracy over a wide range of internuclear separations, the s-wave scattering length for singlet H(1s)+H(1s) scattering is determined at a=0.2735_{31}^{39} a_{0}.
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Affiliation(s)
- K-F Lai
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - E J Salumbides
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - W Ubachs
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - M Beyer
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
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10
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Matsika S. Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections. Chem Rev 2021; 121:9407-9449. [PMID: 34156838 DOI: 10.1021/acs.chemrev.1c00074] [Citation(s) in RCA: 59] [Impact Index Per Article: 19.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.
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Affiliation(s)
- Spiridoula Matsika
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
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11
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Amaral PHR, Stanke M, Adamowicz L, Diniz LG, Mohallem JR, Alijah A. Non-adiabatic effects in the H 3+ spectrum. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20180411. [PMID: 31378173 PMCID: PMC6710893 DOI: 10.1098/rsta.2018.0411] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/03/2019] [Indexed: 06/10/2023]
Abstract
The effect of non-adiabatic coupling on the computed rovibrational energy levels amounts to about 2 cm-1 for H3+ and must be included in high-accuracy calculations. Different strategies to obtain the corresponding energy shifts are reviewed in the article. A promising way is to introduce effective vibrational reduced masses that depend on the nuclear configuration. A new empirical method that uses the stockholder atoms-in-molecules approach to this effect is presented and applied to H3+. Furthermore, a highly accurate potential energy surface for the D3+ isotopologue, which includes relativistic and leading quantum electrodynamic terms, is constructed and used to analyse the observed rovibrational frequencies for this molecule. Accurate band origins are obtained that improve existing data. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.
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Affiliation(s)
- Paulo H. R. Amaral
- Department of Physics, Federal University of Minas Gerais, PO Box 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil
| | - Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, ul. Grudzia̧dzka 5, Toruń 87-100, Poland
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, The University of Arizona, Tucson, AZ 85721, USA
| | | | - José R. Mohallem
- Department of Physics, Federal University of Minas Gerais, PO Box 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil
| | - Alexander Alijah
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, University of Reims Champagne-Ardenne, 51687 Reims Cedex 2, France
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12
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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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13
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Mladenović M, Lewerenz M. Comparison of spectroscopic strategies to determine molecular geometries and the impact of nuclear versus atomic masses: the example of HCO + and HOC +. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1464227] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Mirjana Mladenović
- Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 77454 Marne la Vallée, France
| | - Marius Lewerenz
- Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 77454 Marne la Vallée, France
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14
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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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15
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Khoma M, Jaquet R. The kinetic energy operator for distance-dependent effective nuclear masses: Derivation for a triatomic molecule. J Chem Phys 2018; 147:114106. [PMID: 28938805 DOI: 10.1063/1.5000267] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The kinetic energy operator for triatomic molecules with coordinate or distance-dependent nuclear masses has been derived. By combination of the chain rule method and the analysis of infinitesimal variations of molecular coordinates, a simple and general technique for the construction of the kinetic energy operator has been proposed. The asymptotic properties of the Hamiltonian have been investigated with respect to the ratio of the electron and proton mass. We have demonstrated that an ad hoc introduction of distance (and direction) dependent nuclear masses in Cartesian coordinates preserves the total rotational invariance of the problem. With the help of Wigner rotation functions, an effective Hamiltonian for nuclear motion can be derived. In the derivation, we have focused on the effective trinuclear Hamiltonian. All necessary matrix elements are given in closed analytical form. Preliminary results for the influence of non-adiabaticity on vibrational band origins are presented for H3+.
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Affiliation(s)
- Mykhaylo Khoma
- Theoretical Chemistry, Siegen University, Siegen, Germany
| | - Ralph Jaquet
- Theoretical Chemistry, Siegen University, Siegen, Germany
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16
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Shamasundar KR. Diagonal Born–Oppenheimer correction for coupled-cluster wave-functions. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1448946] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- K. R. Shamasundar
- Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Mohali, India
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17
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Affiliation(s)
- Alexander Alijah
- GSMA, Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, Université de Reims Champagne-Ardenne, U.F.R. Sciences Exactes et Naturelles, Reims, France
| | - David Lapierre
- GSMA, Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, Université de Reims Champagne-Ardenne, U.F.R. Sciences Exactes et Naturelles, Reims, France
| | - Vladimir Tyuterev
- GSMA, Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, Université de Reims Champagne-Ardenne, U.F.R. Sciences Exactes et Naturelles, Reims, France
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18
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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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19
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Jaquet R, Khoma MV. Investigation of Nonadiabatic Effects for the Vibrational Spectrum of a Triatomic Molecule: The Use of a Single Potential Energy Surface with Distance-Dependent Masses for H 3. J Phys Chem A 2017; 121:7016-7030. [PMID: 28820589 DOI: 10.1021/acs.jpca.7b04703] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
On the basis of first-principles, the influence of nonadiabatic effects on the vibrational bound states of H3+ has been investigated using distance-dependent reduced masses and only one single potential energy surface. For these new vibrational calculations, potentials based on explicitly correlated wave functions are used where, in addition, adiabatic corrections and relativistic contributions are taken into account. For the first time, several different fully distance-dependent reduced mass surfaces in three dimensions have been incorporated in the vibrational calculations.
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Affiliation(s)
- Ralph Jaquet
- Theoretische Chemie, Universität Siegen , D-57068 Siegen, Germany
| | - Mykhaylo V Khoma
- Theoretische Chemie, Universität Siegen , D-57068 Siegen, Germany
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Amaral PHR, Mohallem JR. Core-valence stockholder AIM analysis and its connection to nonadiabatic effects in small molecules. J Chem Phys 2017; 146:194103. [PMID: 28527456 PMCID: PMC5435498 DOI: 10.1063/1.4983394] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Accepted: 05/01/2017] [Indexed: 01/13/2023] Open
Abstract
A previous theory of separation of motions of core and valence fractions of electrons in a molecule [J. R. Mohallem et al., Chem. Phys. Lett. 501, 575 (2011)] is invoked as basis for the useful concept of Atoms-in-Molecules (AIM) in the stockholder scheme. The output is a new tool for the analysis of the chemical bond that identifies core and valence electron density fractions (core-valence stockholder AIM (CVSAIM)). One-electron effective potentials for each atom are developed, which allow the identification of the parts of the AIM which move along with the nuclei (cores). This procedure results in a general method for obtaining effective masses that yields accurate non-adiabatic corrections to vibrational energies, necessary to attain cm-1 accuracy in molecular spectroscopy. The clear-cut determination of the core masses is exemplified for either homonuclear (H2+, H2) or heteronuclear (HeH+, LiH) molecules. The connection of CVSAIM with independent physically meaningful quantities can resume the question of whether they are observable or not.
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Affiliation(s)
- Paulo H R Amaral
- Laboratório de Átomos e Moléculas Especiais, Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, Belo Horizonte, Minas Gerais, Brazil
| | - José R Mohallem
- Laboratório de Átomos e Moléculas Especiais, Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, Belo Horizonte, Minas Gerais, Brazil
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21
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Cassam-Chenaï P, Suo B, Liu W. A quantum chemical definition of electron–nucleus correlation. Theor Chem Acc 2017. [DOI: 10.1007/s00214-017-2081-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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22
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Nikitin AV, Rey M, Tyuterev VG. First fullyab initiopotential energy surface of methane with a spectroscopic accuracy. J Chem Phys 2016. [DOI: 10.1063/1.4961973] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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23
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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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24
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Lingerfelt DB, Williams-Young DB, Petrone A, Li X. Direct ab Initio (Meta-)Surface-Hopping Dynamics. J Chem Theory Comput 2016; 12:935-45. [DOI: 10.1021/acs.jctc.5b00697] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- David B. Lingerfelt
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Alessio Petrone
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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25
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Diniz LG, Alijah A, Adamowicz L, Mohallem JR. Connecting a new non-adiabatic vibrational mass to the bonding mechanism of LiH: A quantum superposition of ionic and covalent states. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.04.062] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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26
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Mátyus E, Szidarovszky T, Császár AG. Modelling non-adiabatic effects in H₃⁺: solution of the rovibrational Schrödinger equation with motion-dependent masses and mass surfaces. J Chem Phys 2015; 141:154111. [PMID: 25338885 DOI: 10.1063/1.4897566] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H3(+), for which a global adiabatic potential energy surface accurate to better than 0.1 cm(-1) exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D(3h) point-group symmetry is employed. The vibrational mass of the proton in H3(+) is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m(opt,p)((v))=m(nuc,p)+0.31224m(e). This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518 Budapest 112, Hungary
| | - Tamás Szidarovszky
- MTA-ELTE Research Group on Complex Chemical Systems, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Attila G Császár
- Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518, Budapest 112, Hungary and MTA-ELTE Research Group on Complex Chemical Systems, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
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27
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Reimers JR, McKemmish LK, McKenzie RH, Hush NS. Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: the general importance of all three Born–Oppenheimer breakdown corrections. Phys Chem Chem Phys 2015. [DOI: 10.1039/c5cp02238j] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Analytical and numerical solutions describing Born–Oppenheimer breakdown in a simple, widely applicable, model depict shortcomings in modern computational methods.
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Affiliation(s)
- Jeffrey R. Reimers
- International Centre for Quantum and Molecular Structure
- College of Sciences, Shanghai University
- Shanghai 200444
- China
- School of Mathematical and Physical Sciences
| | - Laura K. McKemmish
- Department of Physics and Astronomy
- University College London
- London
- UK
- School of Chemistry
| | - Ross H. McKenzie
- School of Mathematics and Physics
- The University of Queensland
- Australia
| | - Noel S. Hush
- School of Chemistry
- The University of Sydney
- Sydney
- Australia
- School of Molecular Biosciences
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28
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Zhang X, Herbert JM. Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory. J Chem Phys 2014; 141:064104. [DOI: 10.1063/1.4891984] [Citation(s) in RCA: 72] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Xing Zhang
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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29
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Furtenbacher T, Szidarovszky T, Mátyus E, Fábri C, Császár AG. Analysis of the Rotational–Vibrational States of the Molecular Ion H3+. J Chem Theory Comput 2013; 9:5471-8. [DOI: 10.1021/ct4004355] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Tibor Furtenbacher
- Laboratory
of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, H-1117 Budapest, Pázmány
Péter sétány 1/A, Hungary
- MTA-ELTE
Research Group on Complex Chemical Systems, H-1518 Budapest 112, P.O.
Box 32, Hungary
| | - Tamás Szidarovszky
- Laboratory
of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, H-1117 Budapest, Pázmány
Péter sétány 1/A, Hungary
- MTA-ELTE
Research Group on Complex Chemical Systems, H-1518 Budapest 112, P.O.
Box 32, Hungary
| | - Edit Mátyus
- Laboratory
of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, H-1117 Budapest, Pázmány
Péter sétány 1/A, Hungary
| | - Csaba Fábri
- Laboratory
of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, H-1117 Budapest, Pázmány
Péter sétány 1/A, Hungary
| | - Attila G. Császár
- Laboratory
of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, H-1117 Budapest, Pázmány
Péter sétány 1/A, Hungary
- MTA-ELTE
Research Group on Complex Chemical Systems, H-1518 Budapest 112, P.O.
Box 32, Hungary
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30
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Jaquet R. Investigation of the highest bound ro-vibrational states of H+3, DH+2, HD+2, D+3, and T+3: use of a non-direct product basis to compute the highest allowedJ> 0 states. Mol Phys 2013. [DOI: 10.1080/00268976.2013.818727] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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31
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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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32
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Marquardt R. Theoretical methods for ultrafast spectroscopy. Chemphyschem 2013; 14:1350-61. [PMID: 23606322 DOI: 10.1002/cphc.201201096] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2012] [Indexed: 11/07/2022]
Abstract
Time-resolved spectroscopy in the femtosecond and attosecond time domain is a tool to unravel the dynamics of nuclear and electronic motion in molecular systems. Theoretical insight into the underlying physical processes is ideally gained by solving the time-dependent Schrödinger equation. In this work, methods currently used to solve this equation are reviewed in a compact presentation. These methods involve numerical representations of wavefunctions and operators, the calculation of time evolution operators, the setting up of the Hamiltonian operators and the types of coordinates to be used hereto. The advantages and disadvantages of some methods are discussed.
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Affiliation(s)
- Roberto Marquardt
- Laboratoire de Chimie Quantique, Institut de Chimie, UMR 7177 CNRS/UdS, Université de Strasbourg, 4, rue Blaise Pascal-CS90032, 67081 Strasbourg-Cedex, France.
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33
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Jaquet R, Carrington T. Using a Nondirect Product Basis to Compute J > 0 Rovibrational States of H3+. J Phys Chem A 2013; 117:9493-500. [DOI: 10.1021/jp312027s] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ralph Jaquet
- Theoretische Chemie, Universität Siegen, D-57068 Siegen, Germany
| | - Tucker Carrington
- Chemistry Department, Queens’s University, Kingston, Ontario, K7L
3N6, Canada
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34
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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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35
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Polyansky OL, Alijah A, Zobov NF, Mizus II, Ovsyannikov RI, Tennyson J, Lodi L, Szidarovszky T, Császár AG. Spectroscopy of H3+ based on a new high-accuracy global potential energy surface. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:5014-5027. [PMID: 23028150 DOI: 10.1098/rsta.2012.0014] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The molecular ion H(3)(+) is the simplest polyatomic and poly-electronic molecular system, and its spectrum constitutes an important benchmark for which precise answers can be obtained ab initio from the equations of quantum mechanics. Significant progress in the computation of the ro-vibrational spectrum of H(3)(+) is discussed. A new, global potential energy surface (PES) based on ab initio points computed with an average accuracy of 0.01 cm(-1) relative to the non-relativistic limit has recently been constructed. An analytical representation of these points is provided, exhibiting a standard deviation of 0.097 cm(-1). Problems with earlier fits are discussed. The new PES is used for the computation of transition frequencies. Recently measured lines at visible wavelengths combined with previously determined infrared ro-vibrational data show that an accuracy of the order of 0.1 cm(-1) is achieved by these computations. In order to achieve this degree of accuracy, relativistic, adiabatic and non-adiabatic effects must be properly accounted for. The accuracy of these calculations facilitates the reassignment of some measured lines, further reducing the standard deviation between experiment and theory.
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Affiliation(s)
- Oleg L Polyansky
- Institute of Applied Physics, Russian Academy of Sciences, Ulyanov Street 46, Nizhny Novgorod 603950, Russia.
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36
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Patchkovskii S. Electronic currents and Born-Oppenheimer molecular dynamics. J Chem Phys 2012; 137:084109. [DOI: 10.1063/1.4747540] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Cencek W, Przybytek M, Komasa J, Mehl JB, Jeziorski B, Szalewicz K. Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium. J Chem Phys 2012; 136:224303. [DOI: 10.1063/1.4712218] [Citation(s) in RCA: 209] [Impact Index Per Article: 17.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
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38
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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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39
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Jaquet R, Khoma MV. A systematic investigation of the ground state potential energy surface of H3+. J Chem Phys 2012; 136:154307. [PMID: 22519326 DOI: 10.1063/1.4704123] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on different ab initio electronic structure calculations (CI-R12 and Gaussian Geminals) of the Born-Oppenheimer electronic energy E(BO) of H(3)(+) from high to highest quality, we build up a potential energy surface which represents a highly reliable form of the topology of the whole potential region, locally and globally. We use the CI-R12 method in order to get within reasonable CPU-time a relatively dense grid of energy points. We demonstrate that CI-R12 is good enough to give an accurate surface, i.e., Gaussian Geminals are not absolutely necessary. For different types of potential energy surface fits, we performed variational calculations of all bound vibrational states, including resonances above the dissociation limit, for total angular momentum J = 0. We clarify the differences between different fits of the energy to various functional forms of the potential surface. Small rms-values (<1 cm(-1)) of the fit do not provide precise information about the interpolatory behaviour of the fit functions.
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Affiliation(s)
- Ralph Jaquet
- Theoretische Chemie, Universität Siegen, D-57068 Siegen, Germany.
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40
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41
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Fatehi S, Alguire E, Shao Y, Subotnik JE. Analytic derivative couplings between configuration-interaction-singles states with built-in electron-translation factors for translational invariance. J Chem Phys 2011; 135:234105. [DOI: 10.1063/1.3665031] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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42
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Tennyson J. Accurate variational calculations for line lists to model the vibration-rotation spectra of hot astrophysical atmospheres. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2011. [DOI: 10.1002/wcms.94] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
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43
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Komasa J, Piszczatowski K, Łach G, Przybytek M, Jeziorski B, Pachucki K. Quantum Electrodynamics Effects in Rovibrational Spectra of Molecular Hydrogen. J Chem Theory Comput 2011; 7:3105-15. [DOI: 10.1021/ct200438t] [Citation(s) in RCA: 153] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jacek Komasa
- Faculty of Chemistry, A. Mickiewicz University, Grunwaldzka 6, 60-780 Poznań, Poland
| | | | - Grzegorz Łach
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Przybytek
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Bogumił Jeziorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland
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44
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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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45
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46
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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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47
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Send R, Furche F. First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: Consistent formalism, implementation, and performance. J Chem Phys 2010; 132:044107. [DOI: 10.1063/1.3292571] [Citation(s) in RCA: 179] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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48
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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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49
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50
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Hirata S, Miller EB, Ohnishi YY, Yagi K. On the Validity of the Born−Oppenheimer Separation and the Accuracy of Diagonal Corrections in Anharmonic Molecular Vibrations. J Phys Chem A 2009; 113:12461-9. [DOI: 10.1021/jp903375d] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- So Hirata
- Quantum Theory Project and The Center for Macromolecular Science and Engineering, Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611-8435
| | - Edward B. Miller
- Quantum Theory Project and The Center for Macromolecular Science and Engineering, Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611-8435
| | - Yu-ya Ohnishi
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan
| | - Kiyoshi Yagi
- Department of Applied Chemistry, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
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