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Chen Z, Yang J. Nucleus-electron correlation revising molecular bonding fingerprints from the exact wavefunction factorization. J Chem Phys 2021; 155:104111. [PMID: 34525813 DOI: 10.1063/5.0056773] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
We present a novel theory and implementation for computing coupled electronic and quantal nuclear subsystems on a single potential energy surface, moving beyond the standard Born-Oppenheimer (BO) separation of nuclei and electrons. We formulate an exact self-consistent nucleus-electron embedding potential from the single product molecular wavefunction and demonstrate that the fundamental behavior of the correlated nucleus-electron can be computed for mean-field electrons that are responsive to a quantal anharmonic vibration of selected nuclei in a discrete variable representation. Geometric gauge choices are discussed and necessary for formulating energy invariant biorthogonal electronic equations. Our method is further applied to characterize vibrationally averaged molecular bonding properties of molecular energetics, bond lengths, and protonic and electron densities. Moreover, post-Hartree-Fock electron correlation can be conveniently computed on the basis of nucleus-electron coupled molecular orbitals, as demonstrated for correlated models of second-order Møllet-Plesset perturbation and full configuration interaction theories. Our approach not only accurately quantifies non-classical nucleus-electron couplings for revising molecular bonding properties but also provides an alternative time-independent approach for deploying non-BO molecular quantum chemistry.
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Affiliation(s)
- Ziyong Chen
- Department of Chemistry, The University of Hong Kong, Hong Kong, People's Republic of China
| | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Hong Kong, People's Republic of China
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Foster PW, Jonas DM. Nonadiabatic conical nodes are near but not at an elliptical conical intersection. Chem Phys 2019. [DOI: 10.1016/j.chemphys.2019.01.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Jonas DM. Vibrational and Nonadiabatic Coherence in 2D Electronic Spectroscopy, the Jahn–Teller Effect, and Energy Transfer. Annu Rev Phys Chem 2018; 69:327-352. [DOI: 10.1146/annurev-physchem-052516-050602] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- David M. Jonas
- Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, USA
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Peters WK, Tiwari V, Jonas DM. Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer. J Chem Phys 2017; 147:194306. [PMID: 29166106 DOI: 10.1063/1.5009762] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.
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Affiliation(s)
- William K Peters
- Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, USA
| | - Vivek Tiwari
- Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, USA
| | - David M Jonas
- Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, USA
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Foster PW, Jonas DM. Nonadiabatic Eigenfunctions Can Have Amplitude, Signed Conical Nodes, or Signed Higher Order Nodes at a Conical Intersection with Circular Symmetry. J Phys Chem A 2017; 121:7401-7413. [DOI: 10.1021/acs.jpca.7b07140] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Peter W. Foster
- Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, United States
| | - David M. Jonas
- Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, United States
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Schild A, Agostini F, Gross EKU. Electronic Flux Density beyond the Born–Oppenheimer Approximation. J Phys Chem A 2016; 120:3316-25. [DOI: 10.1021/acs.jpca.5b12657] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Axel Schild
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - Federica Agostini
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - E. K. U. Gross
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
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Lefebvre R. Factorized molecular wave functions: Analysis of the nuclear factor. J Chem Phys 2015; 142:214105. [DOI: 10.1063/1.4922207] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
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Lefebvre R. Perturbations in vibrational diatomic spectra: Factorization of the molecular wave function. J Chem Phys 2015; 142:074106. [DOI: 10.1063/1.4907919] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gidopoulos NI, Gross EKU. Electronic non-adiabatic states: towards a density functional theory beyond the Born-Oppenheimer approximation. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2014; 372:20130059. [PMID: 24516183 PMCID: PMC3928867 DOI: 10.1098/rsta.2013.0059] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
A novel treatment of non-adiabatic couplings is proposed. The derivation is based on a theorem by Hunter stating that the wave function of the complete system of electrons and nuclei can be written, without approximation, as a Born-Oppenheimer (BO)-type product of a nuclear wave function, X(R), and an electronic one, ΦR(r), which depends parametrically on the nuclear configuration R. From the variational principle, we deduce formally exact equations for ΦR(r) and X(R). The algebraic structure of the exact nuclear equation coincides with the corresponding one in the adiabatic approximation. The electronic equation, however, contains terms not appearing in the adiabatic case, which couple the electronic and the nuclear wave functions and account for the electron-nuclear correlation beyond the BO level. It is proposed that these terms can be incorporated using an optimized local effective potential.
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Affiliation(s)
| | - E. K. U. Gross
- Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle (Saale), Germany
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Chiang YC, Klaiman S, Otto F, Cederbaum LS. The exact wavefunction factorization of a vibronic coupling system. J Chem Phys 2014; 140:054104. [DOI: 10.1063/1.4863315] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Cederbaum LS. The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction. J Chem Phys 2013; 138:224110. [DOI: 10.1063/1.4807115] [Citation(s) in RCA: 67] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Abedi A, Maitra NT, Gross EKU. Correlated electron-nuclear dynamics: exact factorization of the molecular wavefunction. J Chem Phys 2013; 137:22A530. [PMID: 23249067 DOI: 10.1063/1.4745836] [Citation(s) in RCA: 126] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It was recently shown [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] that the complete wavefunction for a system of electrons and nuclei evolving in a time-dependent external potential can be exactly factorized into an electronic wavefunction and a nuclear wavefunction. The concepts of an exact time-dependent potential energy surface (TDPES) and exact time-dependent vector potential emerge naturally from the formalism. Here, we present a detailed description of the formalism, including a full derivation of the equations that the electronic and nuclear wavefunctions satisfy. We demonstrate the relationship of this exact factorization to the traditional Born-Oppenheimer expansion. A one-dimensional model of the H(2)(+) molecule in a laser field shows the usefulness of the exact TDPES in interpreting coupled electron-nuclear dynamics: we show how features of its structure indicate the mechanism of dissociation. We compare the exact TDPES with potential energy surfaces from the time-dependent Hartree-approach, and also compare traditional Ehrenfest dynamics with Ehrenfest dynamics on the exact TDPES.
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Affiliation(s)
- Ali Abedi
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
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Fábri C, Czakó G, Tasi G, Császár AG. Adiabatic Jacobi corrections on the vibrational energy levels of H2+ isotopologues. J Chem Phys 2009; 130:134314. [DOI: 10.1063/1.3097327] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Sutcliffe BT, Woolley RG. Molecular structure calculations without clamping the nuclei. Phys Chem Chem Phys 2005; 7:3664-76. [PMID: 16358012 DOI: 10.1039/b509723c] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A number of recent papers have considered ways in which molecular structure may be calculated when both the electrons and the nuclei are treated from the outset as quantum particles. This is in contrast to the conventional approach in which the nuclei initially have their positions fixed and so merely provide a potential for electronic motion. The usual approach is generally assumed to be justified by the 1927 work of Born and Oppenheimer. In this paper we discuss what precisely might be anticipated in the way of molecular structure from a mathematical consideration of the spectral properties of the full Coulomb Hamiltonian, to what extent the very idea of molecular structure might be dependent upon treating the nuclei simply as providing a potential and the extent to which the work of Born and Oppenheimer can be used to support this position.
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Affiliation(s)
- Brian T Sutcliffe
- Department of Theoretical Chemistry, Eötvös Loránd University, 112 PO Box 32, H-1518 Budapest, Hungary.
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Point group symmetries of the molecular orbitals of HD+ beyond the Born–Oppenheimer approximation. Chem Phys Lett 2003. [DOI: 10.1016/s0009-2614(02)01734-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Ponomarev LI, Vinitsky SI, Vukajlovic FR. Adiabatic representation in the three-body problem with the Coulomb interaction. II. The effective two-level approximation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0022-3700/13/5/011] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Avery J, Goodson DZ, Herschbach DR. Dimensional scaling and the quantum mechanical many-body problem. ACTA ACUST UNITED AC 1991. [DOI: 10.1007/bf01113374] [Citation(s) in RCA: 38] [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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Yin L, Goscinski O. Non-adiabaticity in terms of dynamic potentials. An analysis of linear e⊗ϵ vibronic states. Chem Phys 1989. [DOI: 10.1016/0301-0104(89)87093-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Mujica V, Li Y, Goscinski O. Dynamic coordinate separation and state-dependent potentials. An analysis of localization in helium. Chem Phys 1987. [DOI: 10.1016/0301-0104(87)80158-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Accurate One- and Two-Electron Diatomic Molecular Calculations. ADVANCES IN QUANTUM CHEMISTRY 1980. [DOI: 10.1016/s0065-3276(08)60312-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/13/2023]
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