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Brady RP, Drury C, Yurchenko SN, Tennyson J. Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules. J Chem Theory Comput 2024; 20:2127-2139. [PMID: 38171539 PMCID: PMC10938500 DOI: 10.1021/acs.jctc.3c01150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Revised: 12/19/2023] [Accepted: 12/20/2023] [Indexed: 01/05/2024]
Abstract
The (time-independent) Schrödinger equation for atomistic systems is solved by using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. In cases where interactions between electronic states become important, the associated nonadiabatic effects are taken into account via derivative couplings (DDRs), also known as nonadiabatic couplings (NACs). For diatomic molecules, the corresponding PECs in the adiabatic representation are characterized by avoided crossings. The alternative to the adiabatic approach is the diabatic representation obtained via a unitary transformation of the adiabatic states by minimizing the DDRs. For diatomics, the diabatic representation has zero DDR and nondiagonal diabatic couplings ensue. The two representations are fully equivalent and so should be the rovibronic energies and wave functions, which result from the solution of the corresponding Schrödinger equations. We demonstrate (for the first time) the numerical equivalence between the adiabatic and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride (CH) as examples of two-state systems, where YO is characterized by a strong NAC, while CH has a strong diabatic coupling. Rovibronic energies and wave functions are computed using a new diabatic module implemented in the variational rovibronic code Duo. We show that it is important to include both the diagonal Born-Oppenheimer correction and nondiagonal DDRs. We also show that the convergence of the vibronic energy calculations can strongly depend on the representation of nuclear motion used and that no one representation is best in all cases.
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Affiliation(s)
- Ryan P. Brady
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, U.K.
| | - Charlie Drury
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, U.K.
| | - Sergei N. Yurchenko
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, U.K.
| | - Jonathan Tennyson
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, U.K.
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2
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Liu D, Li R, Ren J, Cheng Y, Yan B, Wu Y, Wang JG, Zhang SB. Predissociation resonances and accurate ab initio calculations of dication HF2+. RSC Adv 2021; 11:9600-9607. [PMID: 35423438 PMCID: PMC8695458 DOI: 10.1039/d1ra00837d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2021] [Accepted: 02/25/2021] [Indexed: 11/25/2022] Open
Abstract
It is very interesting and challenging to investigate the electronic structures of diatomic dications, due to the nature of coulombic repulsive and bound attractive dissociation limits and their avoided diabatic interactions. Using the multi-reference configuration interaction approach, comprehensive ab initio calculations of the first 36 electronic states, corresponding to 15 dissociation limits, of dication HF2+ are reported. Good agreements for the vertical excitation energies and dissociation limits are achieved with the available references. Besides the common interesting quantities as adiabatic potential energy curves, dipole moments and spectral constants for the bound states, the nonadiabatic radial coupling matrix elements for the 1,3Π states are also presented. A showcase for the diabatic potentials of 3Π states are presented and discussed. Furthermore, predissociation states from the nonadiabatic couplings or avoided crossing of potential energy curves, known as shape resonances in collisions, are also investigated by using the WKB and scattering methods. Highly accurate adiabatic potential curves of the 36 electronic states of the HF2+ dication by MRCI calculations. Panels (a), (b) and (c) correspond to the 16 singlet, 15 triplet and 4 quintet states, respectively. The nine bound states are highlighted and given in panel (d).![]()
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Affiliation(s)
- Dong Liu
- School of Physics and Information Technology
- Shaanxi Normal University
- Xi'an 710119
- China
| | - Rui Li
- Department of Physics,College of Science
- Qiqihar University
- Qiqihar 161006
- China
| | - Juan Ren
- School of Physics and Information Technology
- Shaanxi Normal University
- Xi'an 710119
- China
- School of Science
| | - Yongjun Cheng
- School of Physics and Information Technology
- Shaanxi Normal University
- Xi'an 710119
- China
| | - Bing Yan
- Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy
- Institute of Atomic and Molecular Physics
- Jilin University
- Changchun 130012
- China
| | - Yong Wu
- Data Center for High Energy Density Physics
- Institute of Applied Physics and Computational Mathematics
- Beijing
- China
| | - Jian Guo Wang
- Data Center for High Energy Density Physics
- Institute of Applied Physics and Computational Mathematics
- Beijing
- China
| | - Song Bin Zhang
- School of Physics and Information Technology
- Shaanxi Normal University
- Xi'an 710119
- China
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3
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Thermodynamic stability and spectroscopic properties of alkaline earth monobromides: The cases of MgBr2+ and BaBr2+. COMPUT THEOR CHEM 2020. [DOI: 10.1016/j.comptc.2020.112792] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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4
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de Melo GF, Ornellas FR. A high-level theoretical characterization of the electronic states and spectroscopic parameters of SrBr2+ and SrI2+, and thermodynamic stability in the family of strontium monohalides dications. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.03.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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5
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Thermodynamic stability of diatomic dications of the families of alkaline earth oxides and hydrides: The cases of BaO2+ and BaH2+. Chem Phys 2019. [DOI: 10.1016/j.chemphys.2018.12.014] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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6
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de Melo GF, Ornellas FR. The thermodynamic stability of strontium monohalides dications: A theoretical exploration of the electronic states and spectroscopic parameters of SrF2+ and SrCl2+. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.09.055] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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7
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Fantuzzi F, Cardozo TM, Nascimento MAC. On the metastability of doubly charged homonuclear diatomics. Phys Chem Chem Phys 2018; 19:19352-19359. [PMID: 28703821 DOI: 10.1039/c7cp02792c] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Generalized valence bond (GVB) and spin-coupled (SC) calculations were used in conjunction with the generalized product function energy partitioning (GPF-EP) method to describe the origin of metastability in doubly charged homonuclear dications. A model to describe the formation of metastable potential wells based on interference and quasi-classical effects is presented. The GPF-EP picture of dications is the result of polarization-aided strong covalent bonding surpassing Coulomb electrostatic repulsion. Important differences in the quasi-classical density profiles of He22+ and Ne22+ reveal the underlying mechanism that could lead to bound or unbound states. Finally, the nature of the chemical bond of N22+, O22+, and F22+ is described. The results suggest that the ground states of the mentioned dications are bounded and that the depth of the potential wells of these exotic species is related to the interference effect, in the same way as in previously studied neutral molecules.
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Affiliation(s)
- Felipe Fantuzzi
- Instituto de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-909, Brazil.
| | - Thiago M Cardozo
- Instituto de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-909, Brazil.
| | - Marco A C Nascimento
- Instituto de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-909, Brazil.
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8
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Can substitution accomplish intact polycationic stability in polyatomic molecules? Illustration with acetylene molecule. J Mol Struct 2015. [DOI: 10.1016/j.molstruc.2015.05.059] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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9
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Sabzyan H, Keshavarz E, Noorisafa Z. Diatomic dications and dianions. JOURNAL OF THE IRANIAN CHEMICAL SOCIETY 2013. [DOI: 10.1007/s13738-013-0359-5] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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10
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de Oliveira-Filho AGS, Ornellas FR. The surprising metastability of TeH2+. J Chem Phys 2013; 138:224309. [DOI: 10.1063/1.4809566] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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11
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Brites V, Hammoutène D, Hochlaf M. Spectroscopy, Metastability, and Single and Double Ionization of AlCl. J Phys Chem A 2008; 112:13419-26. [DOI: 10.1021/jp805508f] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- V. Brites
- Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME FRE 3160 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France, and Laboratoire de Thermodynamique et Modélisation Moléculaire, Faculté de Chimie, USTHB, BP32 El Alia, 16111 Bab Ezzouar, Alger, Algeria
| | - D. Hammoutène
- Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME FRE 3160 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France, and Laboratoire de Thermodynamique et Modélisation Moléculaire, Faculté de Chimie, USTHB, BP32 El Alia, 16111 Bab Ezzouar, Alger, Algeria
| | - M. Hochlaf
- Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME FRE 3160 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France, and Laboratoire de Thermodynamique et Modélisation Moléculaire, Faculté de Chimie, USTHB, BP32 El Alia, 16111 Bab Ezzouar, Alger, Algeria
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12
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Palacios A, Corral I, Mó O, Martín F, Yáñez M. On the existence and lifetimes of Cu2+ complexes with water, ammonia, and hydrogen cyanide. J Chem Phys 2005; 123:014315. [PMID: 16035843 DOI: 10.1063/1.1950607] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
High-level ab initio calculations have been carried out to evaluate the lifetimes of complexes formed by the association of Cu2+ to water, ammonia, and hydrogen cyanide. The corresponding binding energies were evaluated at the CCSD(T)6-311+G(3df,2pd) level of theory. The potential-energy curves corresponding to their dissociation into Cu+ + L+ (L=H2O, NH3, and HCN) were obtained at the CCSD(T)6-311+G(3df,2p) level on BHLYP6-311+G(d,p) optimized geometries. Lifetimes were calculated using the exterior complex scaling and the semiclassical WKB methods. Although all the complexes investigated are thermodynamically unstable with respect to their dissociation into Cu+ + L+ in a typical Coulomb explosion, the activation barrier is high enough to accommodate several vibrational resonances, with very large lifetimes. As a matter of fact, if the three complexes are produced in the lowest vibrational levels, they behave as totally bound (with almost infinite lifetime) species.
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Affiliation(s)
- Alicia Palacios
- Departamento de Química, Universidad Autónoma de Madrid, Cantoblanco, C-9 E-28049 Madrid, Spain
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13
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Khait YG, Azenkeng A, Wang H, Dudley TJ, Hoffmann MR. Multireference configuration interaction based electronic Floquet states for molecules in an intense radiation field: Theory and application to Li2+. J Chem Phys 2005; 122:094111. [PMID: 15836116 DOI: 10.1063/1.1856452] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
A multireference configuration interaction (CI) method which includes single and double excitations based description of adiabatic Floquet states for the electronic structure of a molecule in an intense laser field is introduced. Using a variant of a recently introduced configuration state function (CSF) based Table-CI methodology, it is shown that the multiple states of several irreducible representations required for a good description of low-lying Floquet states can be obtained using modifications of computational molecular electronic structure techniques. In particular, formulas for all components of the transition dipole moment matrix elements within the CSF-based Table-CI method are derived and presented. Moreover, the flexibility of the recently introduced macroconfiguration description of model and external configuration spaces is shown to lead to multiple potential energy surfaces of sufficiently uniform quality to allow construction of useful Floquet states. The formalism and computer programs developed are demonstrated on Li(2) (+) in a 0.9 x 10(12) W/cm(2) field. In analogy with Na(2) (+), the 1,2 (2)Sigma(g) (+), 1,2 (2)Sigma(u) (+), 1 (2)Pi(g), and 1 (2)Pi(u) states are of relevance, although the pattern of couplings is shown to be more complex. A hitherto unnoticed metastable state, which correlates asymptotically with 2 (2)Sigma(u) (+), is described.
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Affiliation(s)
- Yuriy G Khait
- Chemistry Department, University of North Dakota, Grand Forks, North Dakota 58202, USA
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14
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Palacios A, Martín F, Mó O, Yáñez M, Maksić ZB. Stable doubly charged positive molecular ions formed by direct attachment of alpha particles to HCN and HNC. PHYSICAL REVIEW LETTERS 2004; 92:133001. [PMID: 15089599 DOI: 10.1103/physrevlett.92.133001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2003] [Revised: 12/24/2003] [Indexed: 05/24/2023]
Abstract
The existence of [HeNCH](2+) and [HeCNH](2+) is examined by reliable high-level ab initio methods. It is shown that both species are metastable with respect to the proton loss process, but the activation barriers are high enough to accommodate several resonant states. Their estimated lifetimes are practically infinite for v<3, implying that the attachment of alpha particles to HNC and HCN yields kinetically stable dications. This could be an important factor in the cyanide chemistry in interstellar and comet environments.
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Affiliation(s)
- Alicia Palacios
- Departamento de Química, C-9, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
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15
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Nenajdenko VG, Shevchenko NE, Balenkova ES, Alabugin IV. 1,2-Dications in organic main group systems. Chem Rev 2003; 103:229-82. [PMID: 12517185 DOI: 10.1021/cr0000628] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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16
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17
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Schröder D, Schwarz H. Generation, Stability, and Reactivity of Small, Multiply Charged Ions in the Gas Phase. J Phys Chem A 1999. [DOI: 10.1021/jp991332x] [Citation(s) in RCA: 271] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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18
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Schröder D, Diefenbach M, Klapötke TM, Schwarz H. UF3+ – ein thermochemisch stabiles binäres Trikation mit kovalenter Bindung. Angew Chem Int Ed Engl 1999. [DOI: 10.1002/(sici)1521-3757(19990115)111:1/2<206::aid-ange206>3.0.co;2-2] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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19
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Schröder D, Harvey JN, Schwarz H. Long-Lived, Multiply Charged Diatomic TiFn+ Ions (n = 1−3). J Phys Chem A 1998. [DOI: 10.1021/jp9807827] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Detlef Schröder
- Institut für Organische Chemie der Technischen Universität Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany
| | - Jeremy N. Harvey
- Institut für Organische Chemie der Technischen Universität Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany
| | - Helmut Schwarz
- Institut für Organische Chemie der Technischen Universität Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany
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20
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Petrie S. Is the Gaussian-2 technique reliable for determining the energetics of small molecular dications? J Chem Phys 1997. [DOI: 10.1063/1.474660] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Wright JS, Carpenter DJ, Alekseyev AB, Liebermann HP, Lingott R, Buenker RJ. Thermodynamically stable diatomic dications: potential curves and radiative lifetimes for CaCl2+ including relativistic effects. Chem Phys Lett 1997. [DOI: 10.1016/s0009-2614(97)00007-9] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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22
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Ab initio investigation of the CO4 and CO2N2 molecules as possible high-energy metastable species. ACTA ACUST UNITED AC 1996. [DOI: 10.1016/s0166-1280(96)04535-6] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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23
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Aquilanti V, Cappelletti D, Pirani F. Range and strength of interatomic forces: dispersion and induction contributions to the bonds of dications and of ionic molecules. Chem Phys 1996. [DOI: 10.1016/0301-0104(96)00163-2] [Citation(s) in RCA: 67] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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24
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25
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Finger K, Daniel C, Saalfrank P, Schmidt B. Nonadiabatic Effects in the Photodissociation and Electronic Spectroscopy of HMn(CO)3(dab): Quantum Wave Packet Dynamics Based on ab Initio Potentials. ACTA ACUST UNITED AC 1996. [DOI: 10.1021/jp952497i] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- K. Finger
- Institut für Physikalische und Theoretische Chemie, Freie Universität Berlin, Takustrasse 3, D-14195 Berlin, Germany, and Laboratoire de Chimie Quantique, UPR 139 du CNRS, Université Louis Pasteur, 67000 Strasbourg, France
| | - C. Daniel
- Institut für Physikalische und Theoretische Chemie, Freie Universität Berlin, Takustrasse 3, D-14195 Berlin, Germany, and Laboratoire de Chimie Quantique, UPR 139 du CNRS, Université Louis Pasteur, 67000 Strasbourg, France
| | - P. Saalfrank
- Institut für Physikalische und Theoretische Chemie, Freie Universität Berlin, Takustrasse 3, D-14195 Berlin, Germany, and Laboratoire de Chimie Quantique, UPR 139 du CNRS, Université Louis Pasteur, 67000 Strasbourg, France
| | - B. Schmidt
- Institut für Physikalische und Theoretische Chemie, Freie Universität Berlin, Takustrasse 3, D-14195 Berlin, Germany, and Laboratoire de Chimie Quantique, UPR 139 du CNRS, Université Louis Pasteur, 67000 Strasbourg, France
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