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Wu Y, Subotnik JE. A quantum-classical Liouville formalism in a preconditioned basis and its connection with phase-space surface hopping. J Chem Phys 2023; 158:024115. [PMID: 36641414 DOI: 10.1063/5.0124835] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
We revisit a recent proposal to model nonadiabatic problems with a complex-valued Hamiltonian through a phase-space surface hopping (PSSH) algorithm employing a pseudo-diabatic basis. Here, we show that such a pseudo-diabatic PSSH (PD-PSSH) ansatz is consistent with a quantum-classical Liouville equation (QCLE) that can be derived following a preconditioning process, and we demonstrate that a proper PD-PSSH algorithm is able to capture some geometric magnetic effects (whereas the standard fewest switches surface hopping approach cannot capture such effects). We also find that a preconditioned QCLE can outperform the standard QCLE in certain cases, highlighting the fact that there is no unique QCLE. Finally, we also point out that one can construct a mean-field Ehrenfest algorithm using a phase-space representation similar to what is done for PSSH. These findings would appear extremely helpful as far as understanding and simulating nonadiabatic dynamics with complex-valued Hamiltonians and/or spin degeneracy.
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Affiliation(s)
- Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Takatsuka K. Quantum Chaos in the Dynamics of Molecules. ENTROPY (BASEL, SWITZERLAND) 2022; 25:63. [PMID: 36673204 PMCID: PMC9857761 DOI: 10.3390/e25010063] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 12/22/2022] [Accepted: 12/22/2022] [Indexed: 06/17/2023]
Abstract
Quantum chaos is reviewed from the viewpoint of "what is molecule?", particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is "bifurcation and merging" of quantum wavepackets, rather than "stretching and folding" of the baker's transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule.
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Affiliation(s)
- Kazuo Takatsuka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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Wu Y, Bian X, Rawlinson JI, Littlejohn RG, Subotnik JE. A phase-space semiclassical approach for modeling nonadiabatic nuclear dynamics with electronic spin. J Chem Phys 2022; 157:011101. [DOI: 10.1063/5.0093345] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. However, for electronic systems with spin degrees of freedom, there are few if any applicable and practical quasiclassical methods. Here, we show that for nonadiabatic dynamics with two electronic states and a complex-valued Hamiltonian that does not obey time-reversal symmetry (as relevant to many coupled nuclear-electronic-spin systems), the optimal semiclassical approach is to generalize Tully’s surface hopping dynamics from coordinate space to phase space. In order to generate the relevant phase-space adiabatic surfaces, one isolates a proper set of diabats, applies a phase gauge transformation, and then diagonalizes the total Hamiltonian (which is now parameterized by both R and P). The resulting algorithm is simple and valid in both the adiabatic and nonadiabatic limits, incorporating all Berry curvature effects. Most importantly, the resulting algorithm allows for the study of semiclassical nonadiabatic dynamics in the presence of spin–orbit coupling and/or external magnetic fields. One expects many simulations to follow as far as modeling cutting-edge experiments with entangled nuclear, electronic, and spin degrees of freedom, e.g., experiments displaying chiral-induced spin selectivity.
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Affiliation(s)
- Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Jonathan I. Rawlinson
- School of Mathematics, The University of Manchester, Oxford Rd., Manchester M13 9PL, United Kingdom
| | - Robert G. Littlejohn
- Department of Physics, University of California, 366 Physics North MC 7300, Berkeley, California 94720-7300, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Takatsuka K. Electron Dynamics in Molecular Elementary Processes and Chemical Reactions. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2021. [DOI: 10.1246/bcsj.20200388] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Kazuo Takatsuka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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Curchod BFE, Agostini F, Gross EKU. An exact factorization perspective on quantum interferences in nonadiabatic dynamics. J Chem Phys 2016; 145:034103. [DOI: 10.1063/1.4958637] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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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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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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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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Shenvi N. Phase-space surface hopping: Nonadiabatic dynamics in a superadiabatic basis. J Chem Phys 2009; 130:124117. [DOI: 10.1063/1.3098321] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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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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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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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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