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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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Tao Z, Bian X, Wu Y, Rawlinson J, Littlejohn RG, Subotnik JE. Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states. J Chem Phys 2024; 160:054104. [PMID: 38310474 DOI: 10.1063/5.0177778] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2023] [Accepted: 12/18/2023] [Indexed: 02/05/2024] Open
Abstract
We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, "Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions," J. Chem. Phys. 122, 084113 (2005) and V. Krishna, "Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit," J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree-Fock with spin-orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born-Oppenheimer approximation when using ab initio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results.
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Affiliation(s)
- Zhen Tao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Yanze Wu
- 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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Hanasaki K, Takatsuka K. Spin current in the early stage of radical reactions and its mechanisms. J Chem Phys 2023; 159:144111. [PMID: 37830453 DOI: 10.1063/5.0169281] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 09/25/2023] [Indexed: 10/14/2023] Open
Abstract
We study the electronic spin flux (atomic-scale flow of the spin density in molecules) by a perturbation analysis and ab initio nonadiabatic calculations. We derive a general perturbative expression of the charge and spin fluxes and identify the driving perturbation of the fluxes to be the time derivative of the electron-nucleus interaction term in the Hamiltonian. We then expand the expression in molecular orbitals so as to identify relevant components of the fluxes. Our perturbation theory describes the electronic fluxes in the early stage of reactions in an intuitively clear manner. The perturbation theory is then applied to an analysis of the spin flux obtained in ab initio calculations of the radical reaction of O2 and CH3· starting from three distinct spin configurations; (a) CH3· and triplet O2 with total spin of the system set Stot=1/2 (b) CH3· and singlet O2, Stot=1/2, and (c) CH3· and triplet O2, Stot=3/2. Further analysis of the time-dependent behaviors of the spin flux in these numerical simulations reveals (i) the spin flux induces rearrangement of the local spin structure, such as reduction of the spin polarization arising from the triplet O2 and (ii) the spin flux flows from O2 to CH3· in the reaction starting from spin configuration (a) and from CH3· to O2 in that starting from configuration (b), whereas no major intermolecular spin flux was observed in that starting from configuration (c). Our study thus establishes the mechanism of the spin flux that rearranges the local spin structures associated with chemical bonds.
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Affiliation(s)
- Kota Hanasaki
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
| | - Kazuo Takatsuka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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Arasaki Y, Takatsuka K. Energy natural orbital characterization of nonadiabatic electron wavepackets in the densely quasi-degenerate electronic state manifold. J Chem Phys 2023; 158:114102. [PMID: 36948795 DOI: 10.1063/5.0139288] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2023] Open
Abstract
Dynamics and energetic structure of largely fluctuating nonadiabatic electron wavepackets are studied in terms of Energy Natural Orbitals (ENOs) [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 154, 094103 (2021)]. Such huge fluctuating states are sampled from the highly excited states of clusters of 12 boron atoms (B12), which have densely quasi-degenerate electronic excited-state manifold, each adiabatic state of which gets promptly mixed with other states through the frequent and enduring nonadiabatic interactions within the manifold. Yet, the wavepacket states are expected to be of very long lifetimes. This excited-state electronic wavepacket dynamics is extremely interesting but very hard to analyze since they are usually represented in large time-dependent configuration interaction wavefunctions and/or in some other complicated forms. We have found that ENO gives an invariant energy orbital picture to characterize not only the static highly correlated electronic wavefunctions but also those time-dependent electronic wavefunctions. Hence, we first demonstrate how the ENO representation works for some general cases, choosing proton transfer in water dimer and electron-deficient multicenter chemical bonding in diborane in the ground state. We then penetrate with ENO deep into the analysis of the essential nature of nonadiabatic electron wavepacket dynamics in the excited states and show the mechanism of the coexistence of huge electronic fluctuation and rather strong chemical bonds under very random electron flows within the molecule. To quantify the intra-molecular energy flow associated with the huge electronic-state fluctuation, we define and numerically demonstrate what we call the electronic energy flux.
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Affiliation(s)
- Yasuki Arasaki
- Fukui Institute for Fundamental Chemistry, Kyoto University, 606-8103 Kyoto, Japan
| | - Kazuo Takatsuka
- Fukui Institute for Fundamental Chemistry, Kyoto University, 606-8103 Kyoto, Japan
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Sun X. Physical substance of recoil term in molecular dynamics. COMPUT THEOR CHEM 2022. [DOI: 10.1016/j.comptc.2022.113698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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6
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Hanasaki K, Takatsuka K. Spin current in chemical reactions. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2022.139462] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Hanasaki K, Takatsuka K. On the molecular electronic flux: Role of nonadiabaticity and violation of conservation. J Chem Phys 2021; 154:164112. [PMID: 33940814 DOI: 10.1063/5.0049821] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Analysis of electron flux within and in between molecules is crucial in the study of real-time dynamics of molecular electron wavepacket evolution such as those in attosecond laser chemistry and ultrafast chemical reaction dynamics. We here address two mutually correlated issues on the conservation law of molecular electronic flux, which serves as a key consistency condition for electron dynamics. The first one is about a close relation between "weak" nonadiabaticity and the electron dynamics in low-energy chemical reactions. We show that the electronic flux in adiabatic reactions can be consistently reproduced by taking account of nonadiabaticity. Such nonadiabaticity is usually weak in the sense that it does not have a major effect on nuclear dynamics, whereas it plays an important role in electronic dynamics. Our discussion is based on a nonadiabatic extension of the electronic wavefunction similar in idea to the complete adiabatic formalism developed by Nafie [J. Chem. Phys. 79, 4950 (1983)], which has also recently been reformulated by Patchkovskii [J. Chem. Phys. 137, 084109 (2012)]. We give straightforward proof of the theoretical assertion presented by Nafie using a time-dependent mixed quantum-classical framework and a standard perturbation expansion. Explicitly taking account of the flux conservation, we show that the nonadiabatically induced flux realizes the adiabatic time evolution of the electronic density. In other words, the divergence of the nonadiabatic flux equals the time derivative of the electronic density along an adiabatic time evolution of the target molecule. The second issue is about the accurate computationability of the flux. The calculation of flux needs an accurate representation of the (relative) quantum phase, in addition to the amplitude factor, of a total wavefunction and demands special attention for practical calculations. This paper is the first one to approach this issue directly and show how the difficulties arise explicitly. In doing so, we reveal that a number of widely accepted truncation techniques for static property calculations are potential sources of numerical flux non-conservation. We also theoretically propose alternative strategies to realize better flux conservation.
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Affiliation(s)
- Kota Hanasaki
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
| | - Kazuo Takatsuka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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Matsuoka T, Takatsuka K. Nonadiabatic electron wavepacket dynamics behind molecular autoionization. J Chem Phys 2018; 148:014106. [DOI: 10.1063/1.5000293] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Takahide Matsuoka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Sakyo-ku, Kyoto 606-8103, Japan
| | - Kazuo Takatsuka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Sakyo-ku, Kyoto 606-8103, Japan
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Yonehara T, Nakajima T. A quantum dynamics method for excited electrons in molecular aggregate system using a group diabatic Fock matrix. J Chem Phys 2017; 147:074110. [PMID: 28830170 DOI: 10.1063/1.4998746] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a practical calculation scheme for the description of excited electron dynamics in molecular aggregate systems within a local group diabatic Fock representation. This scheme makes it easy to analyze the interacting time-dependent excitation of local sites in complex systems. In addition, light-electron couplings are considered. The present scheme is intended for investigations on the migration dynamics of excited electrons in light-induced energy transfer systems. The scheme was applied to two systems: a naphthalene-tetracyanoethylene dimer and a 20-mer circle of ethylene molecules. Through local group analyses of the dynamical electrons, we obtained an intuitive understanding of the electron transfers between the monomers.
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Affiliation(s)
- Takehiro Yonehara
- RIKEN Advanced Institute for Computational Science, Kobe 650-0047, Japan
| | - Takahito Nakajima
- RIKEN Advanced Institute for Computational Science, Kobe 650-0047, Japan
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10
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Time-resolved photoelectron signals from bifurcating electron wavepackets propagated across conical intersection in path-branching dynamics. Chem Phys 2017. [DOI: 10.1016/j.chemphys.2017.06.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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11
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Li ZW, Yonehara T, Takatsuka K. Nonadiabatic electron wavepacket study on symmetry breaking dynamics of the low-lying excited states of cyclic-B4. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2015.10.012] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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12
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Electron wavepacket approaches to non-adiabatic transition processes in the internal rotational motion of H2CNH2+ – Charge oscillation due to electronic coherence. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.06.081] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Fujii M, Yamashita K. Semiclassical quantization of nonadiabatic systems with hopping periodic orbits. J Chem Phys 2015; 142:074104. [PMID: 25701999 DOI: 10.1063/1.4907910] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller's trace formula to a nonadiabatic form. The quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow DOF, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels. In addition to the semiclassical quantization condition, we also discuss chaotic dynamics involved in the classical limit of nonadiabatic dynamics.
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Affiliation(s)
- Mikiya Fujii
- Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - Koichi Yamashita
- Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
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14
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Yamamoto K, Takatsuka K. Electronic quantum effects mapped onto non-Born-Oppenheimer nuclear paths: Nonclassical surmounting over potential barriers and trapping above the transition states due to nonadiabatic path-branching. J Chem Phys 2014; 140:124111. [DOI: 10.1063/1.4869191] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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15
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Yonehara T, Takatsuka K. Electron wavepacket dynamics in highly quasi-degenerate coupled electronic states: A theory for chemistry where the notion of adiabatic potential energy surface loses the sense. J Chem Phys 2012; 137:22A520. [DOI: 10.1063/1.4742155] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Nagashima K, Takatsuka K. Early-Stage Dynamics in Coupled Proton–Electron Transfer from the π–π* State of Phenol to Solvent Ammonia Clusters: A Nonadiabatic Electron Dynamics Study. J Phys Chem A 2012; 116:11167-79. [DOI: 10.1021/jp304781m] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kengo Nagashima
- Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
| | - Kazuo Takatsuka
- Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
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17
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Okuyama M, Takatsuka K. Dynamical Electron Mechanism of Double Proton Transfer in Formic Acid Dimer. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2012. [DOI: 10.1246/bcsj.20110237] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Michihiro Okuyama
- Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo
| | - Kazuo Takatsuka
- Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo
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18
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Yonehara T, Hanasaki K, Takatsuka K. Fundamental Approaches to Nonadiabaticity: Toward a Chemical Theory beyond the Born–Oppenheimer Paradigm. Chem Rev 2011; 112:499-542. [DOI: 10.1021/cr200096s] [Citation(s) in RCA: 154] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Takehiro Yonehara
- Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo Komaba, 153-8902 Tokyo, Japan
| | - Kota Hanasaki
- Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo Komaba, 153-8902 Tokyo, Japan
| | - Kazuo Takatsuka
- Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo Komaba, 153-8902 Tokyo, Japan
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Fujii M. Quantum and semiclassical theories for nonadiabatic transitions based on overlap integrals related to fast degrees of freedom. J Chem Phys 2011; 135:114102. [PMID: 21950845 DOI: 10.1063/1.3634025] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Alternative treatments of quantum and semiclassical theories for nonadiabatic dynamics are presented. These treatments require no derivative couplings and instead are based on overlap integrals between eigenstates corresponding to fast degrees of freedom, such as electronic states. Derived from mathematical transformations of the Schrödinger equation, the theories describe nonlocal characteristics of nonadiabatic transitions. The idea that overlap integrals can be used for nonadiabatic transitions stems from an article by Johnson and Levine [Chem. Phys. Lett. 13, 168 (1972)]. Furthermore, overlap integrals in path-integral form have been recently made available by Schmidt and Tully [J. Chem. Phys. 127, 094103 (2007)] to analyze nonadiabatic effects in thermal equilibrium systems. The present paper expands this idea to dynamic problems presented in path-integral form that involve nonadiabatic semiclassical propagators. Applications to one-dimensional nonadiabatic transitions have provided excellent results, thereby verifying the procedure. In principle these theories that are presented can be applied to multidimensional systems, although numerical costs could be quite expensive.
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Affiliation(s)
- Mikiya Fujii
- Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902, Tokyo, Japan.
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Takatsuka K, Yonehara T. Exploring dynamical electron theory beyond the Born-Oppenheimer framework: from chemical reactivity to non-adiabatically coupled electronic and nuclear wavepackets on-the-fly under laser field. Phys Chem Chem Phys 2011; 13:4987-5016. [PMID: 21321712 DOI: 10.1039/c0cp00937g] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Chemical theory and its application to dynamical electrons in molecules under intense electromagnetic fields is explored, in which we take an explicit account of nuclear nonadiabatic (kinematic) interactions along with simultaneous coupling with intense optical interactions. All the electronic wavefunctions studied here are necessarily time-dependent, and thereby beyond stationary state quantum chemistry based on the Born-Oppenheimer framework. As a general and tractable alternative framework with which to track the electronic and nuclear simultaneous dynamics, we propose an on-the-fly method to calculate the electron and nuclear wavepackets coupled along the branching non-Born-Oppenheimer paths, through which their bifurcations, strong quantum entanglement between nuclear electronic motions, and coherence and decoherence among the phases associated with them are properly represented. Some illustrative numerical examples are also reported, which are aimed at our final goals; real time tracking of nonadiabatic electronic states, chemical dynamics in densely degenerate electronic states coupled with nuclear motions and manipulation and/or creation of new electronic states in terms of intense lasers, and so on. Other examples are also presented as to how the electron wavepacket dynamics can be used to analyze chemical reactions, shedding a new light on some typical and conventional chemical reactions such as proton transfer followed by tautomerization.
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Affiliation(s)
- Kazuo Takatsuka
- Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902, Tokyo, Japan.
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Yonehara T, Takatsuka K. Non-Born–Oppenheimer quantum chemistry on the fly with continuous path branching due to nonadiabatic and intense optical interactions. J Chem Phys 2010; 132:244102. [DOI: 10.1063/1.3439396] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Takatsuka K, Yonehara T. Nonadiabatic Chemical Dynamics in Intermediate and Intense Laser Fields. ADVANCES IN CHEMICAL PHYSICS 2010. [DOI: 10.1002/9780470564318.ch2] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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23
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Yonehara T, Takatsuka K. Characterization of electron-deficient chemical bonding of diborane with attosecond electron wavepacket dynamics and laser response. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2009.09.001] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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24
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Nagashima K, Takatsuka K. Electron-Wavepacket Reaction Dynamics in Proton Transfer of Formamide. J Phys Chem A 2009; 113:15240-9. [DOI: 10.1021/jp905583s] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Kengo Nagashima
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, 153-8902 Tokyo, Japan
| | - Kazuo Takatsuka
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, 153-8902 Tokyo, Japan
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25
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Yonehara T, Takahashi S, Takatsuka K. Non-Born–Oppenheimer electronic and nuclear wavepacket dynamics. J Chem Phys 2009; 130:214113. [DOI: 10.1063/1.3151684] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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27
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Yonehara T, Takatsuka K. Phase-space averaging and natural branching of nuclear paths for nonadiabatic electron wavepacket dynamics. J Chem Phys 2008; 129:134109. [DOI: 10.1063/1.2987302] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Yonehara T, Takatsuka K. Nonadiabatic electron wavepacket dynamics of molecules in an intense optical field: An ab initio electronic state study. J Chem Phys 2008; 128:154104. [DOI: 10.1063/1.2904867] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Takatsuka K. Generalization of classical mechanics for nuclear motions on nonadiabatically coupled potential energy surfaces in chemical reactions. J Phys Chem A 2007; 111:10196-204. [PMID: 17676718 DOI: 10.1021/jp072233j] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To cope with this problem, we propose a generalization of classical mechanics that provides a path even in cases where multiple potential energy surfaces are involved in a single event and the Born-Oppenheimer approximation breaks down. This generalization is made by diagonalization of the matrix representation of nuclear forces in nonadiabatic dynamics, which is derived from a mixed quantum-classical representation of the electron-nucleus entangled Hamiltonian [Takatsuka, K. J. Chem. Phys. 2006, 124, 064111]. A manifestation of quantum fluctuation on a classical subsystem that directly contacts with a quantum subsystem is discussed. We also show that the Hamiltonian thus represented gives a theoretical foundation to examine the validity of the so-called semiclassical Ehrenfest theory (or mean-field theory) for electron quantum wavepacket dynamics, and indeed, it is pointed out that the electronic Hamiltonian to be used in this theory should be slightly modified.
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Affiliation(s)
- Kazuo Takatsuka
- Department of Basic Science, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
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30
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Yagi K, Takatsuka K. Nonadiabatic chemical dynamics in an intense laser field: electronic wave packet coupled with classical nuclear motions. J Chem Phys 2007; 123:224103. [PMID: 16375466 DOI: 10.1063/1.2130335] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Dynamics of molecules in an intense laser field is studied in terms of the quantum electronic wave packet coupled with classical nuclear motions. The equations of motion are derived taking a proper account of molecular interactions with the vector potential of a classical electromagnetic field, along with the nonadiabatic interaction due to the breakdown of the Born-Oppenheimer approximation. With the aid of electronic structure calculations, the present method enables us to track, in an ab initio manner, the dynamics of polyatomic molecules in an intense field. Preliminary calculations are carried out for the vibrational state of LiF and a collision of Li+F under an intense laser pulse, which are limited to the domain of no ionization.
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Affiliation(s)
- Kiyoshi Yagi
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, 153-8902 Tokyo, Japan.
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31
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Cardoza D, Pearson BJ, Weinacht T. Dissociative wave packets and dynamic resonances. J Chem Phys 2007; 126:084308. [PMID: 17343449 DOI: 10.1063/1.2437198] [Citation(s) in RCA: 17] [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 authors examine the role of dynamic resonances in laser driven molecular fragmentation. The yields of molecular fragments can undergo dramatic changes as an impulsively excited dissociative wave packet passes through a dynamic resonance. The authors compare three different kinds of dynamic resonances in a series of molecular families and highlight the possibility of characterizing the dissociative wave function as it crosses the resonance location.
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Affiliation(s)
- David Cardoza
- Department of Physics, Stony Brook University, Stony Brook, New York 11794, USA
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Mechanisms of the Elementary Processes of Electron Wavepacket Dynamics Coupled with Proton Transfer and Hydrogen-Atom Migration in H2O+H3O+. Angew Chem Int Ed Engl 2007. [DOI: 10.1002/ange.200603553] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Ushiyama H, Takatsuka K. Mechanisms of the Elementary Processes of Electron Wavepacket Dynamics Coupled with Proton Transfer and Hydrogen-Atom Migration in H2O+H3O+. Angew Chem Int Ed Engl 2007; 46:587-90. [PMID: 17152107 DOI: 10.1002/anie.200603553] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Hiroshi Ushiyama
- Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
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Takahashi S, Takatsuka K. On the validity range of the Born-Oppenheimer approximation: A semiclassical study for all-particle quantization of three-body Coulomb systems. J Chem Phys 2006; 124:144101. [PMID: 16626174 DOI: 10.1063/1.2173997] [Citation(s) in RCA: 24] [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 validity range of the Born-Oppenheimer (BO) approximation is studied with respect to the variation of the mass (m) of negatively charged particle by substituting an electron (e) with muon (mu) and antiproton (p) in hydrogen molecule cation. With the use of semiclassical quantization applied to these (ppe), (ppmu), and (ppp) under a constrained geometry, we estimate the energy difference of the non-BO vibronic ground state from the BO counterpart. It is found that the error in the BO approximation scales to the power of 3/2 to the mass of negative particles, that is, m(1.5). The origin of this clear-cut relation is analyzed based on the original perturbation theory due to Born and Oppenheimer, with which we show that the fifth order term proportional to m(5/4) is zero and thereby the first correction to the BO approximation should arise from the sixth order term that is proportional to m(6/4). Therefore, the validity range of the Born-Oppenheimer approximation is wider than that often mistakenly claimed to be proportional to m(1/4).
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Affiliation(s)
- Satoshi Takahashi
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, 153-8902 Tokyo, Japan.
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Takatsuka K. Non-Born-Oppenheimer path in anti-Hermitian dynamics for nonadiabatic transitions. J Chem Phys 2006; 124:64111. [PMID: 16483200 DOI: 10.1063/1.2167648] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
A serious difficulty in the semiclassical Ehrenfest theory for nonadiabatic transitions is that a path passing across the avoided crossing is forced to run on a potential averaged over comprising adiabatic potential surfaces that commit the avoided crossing. Therefore once a path passes through the crossing region, it immediately becomes incompatible with the standard view of "classical trajectory" running on an adiabatic surface. This casts a fundamental question to the theoretical structure of chemical dynamics. In this paper, we propose a non-Born-Oppenheimer path that is generated by an anti-Hermitian Hamiltonian, whose complex-valued eigenenergies can cross in their real parts and avoid crossing in the imaginary parts in the vicinity of the nonadiabatic transition region. We discuss the properties of this non-Born-Oppenheimer path and thereby show its compatibility with the Born-Oppenheimer classical trajectories. This theory not only allows the geometrical branching of the paths but gives the nonadiabatic transition amplitudes and quantum phases along the generated paths.
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Affiliation(s)
- Kazuo Takatsuka
- Department of Basic Science, The University of Tokyo, Komaba, Japan.
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