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Shu Y, Truhlar DG. Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients. J Chem Theory Comput 2024; 20:4396-4426. [PMID: 38819014 DOI: 10.1021/acs.jctc.4c00424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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Schürger P, Engel V. Differential Shannon entropies and correlation measures for Born-Oppenheimer electron-nuclear dynamics: numerical results and their analytical interpretation. Phys Chem Chem Phys 2023; 25:28373-28381. [PMID: 37842823 DOI: 10.1039/d3cp03573e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2023]
Abstract
We study the Born-Oppenheimer dynamics within a model for a coupled electron-nuclear motion. Differential Shannon entropies are calculated from the time-dependent probability densities of the combined system and, using single particle densities, entropies for the electronic and nuclear degrees of freedom are derived. These functions provide information on details of the wave packet motion. From the entropies, we determine the mutual information which characterizes particle correlations. This quantity is compared to other measures of electron-nuclear entanglement. Numerical results are interpreted within an analytically solvable approach, and it is documented how these functions depend on properties of the Born-Oppenheimer wave function and, in particular, how dynamical effects like wave packet focusing and dispersion influence the correlation between the particles.
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Affiliation(s)
- Peter Schürger
- Universität Würzburg, Institut für Physikalische und Theoretische Chemie, Emil-Fischer-Str. 42, 97074 Würzburg, Germany.
| | - Volker Engel
- Universität Würzburg, Institut für Physikalische und Theoretische Chemie, Emil-Fischer-Str. 42, 97074 Würzburg, Germany.
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Blavier M, Gelfand N, Levine R, Remacle F. Entanglement of electrons and nuclei: A most compact representation of the molecular wave function. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2022.139885] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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4
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Stetzler J, Rassolov VA. Comparison of Born–Oppenheimer approximation and electron-nuclear correlation. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2106321] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Julian Stetzler
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC, USA
| | - Vitaly A. Rassolov
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC, USA
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Zhang C, Chen G, Si Y, Liu M. Surface modeling of photocatalytic materials for water splitting. Phys Chem Chem Phys 2021; 24:1237-1261. [PMID: 34935801 DOI: 10.1039/d1cp04352h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
The photocatalyst surface is central to photocatalytic reactions. However, it has been a challenge to explicitly understand both the surface configuration and the structure-dependent photocatalytic properties at the atomic level. First-principles density functional theory (DFT) calculations provide a versatile method that makes up for the lack of experimental surface studies. In DFT calculations, the initial surface model greatly affects the accuracy of the calculation results. Consequently, establishing a more realistic and more reliable material surface models is undoubtedly the first step and the most important link in theoretical calculations. The aim of this Perspective is to provide a general understanding of the methods for the surface modeling of photocatalytic materials in recent years. We begin with a discussion of the basic theories applied in photocatalytic surface research, followed by an explanation of the importance of surface modeling in photocatalysis. We then elaborate on the advantages and disadvantages of the basic surface model and briefly describe the latest surface modeling methods. Finally, we evaluate the rationality of current surface modeling methods. We summarize this Perspective by prospecting the developing directions of photocatalytic surface research in the future. It is believed that a reasonable surface model should be verified by both experimental characterization and theoretical computation with negative feedback.
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Affiliation(s)
- Chunyang Zhang
- International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China.
| | - Guijun Chen
- International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China.
| | - Yitao Si
- International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China.
| | - Maochang Liu
- International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China. .,Suzhou Academy of Xi'an Jiaotong University, Suzhou, Jiangsu 215123, P. R. China
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Schirò M, Eich FG, Agostini F. Quantum-classical nonadiabatic dynamics of Floquet driven systems. J Chem Phys 2021; 154:114101. [PMID: 33752379 DOI: 10.1063/5.0043790] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a trajectory-based approach for excited-state molecular dynamics simulations of systems subject to an external periodic drive. We combine the exact-factorization formalism, allowing us to treat electron-nuclear systems in nonadiabatic regimes, with the Floquet formalism for time-periodic processes. The theory is developed starting with the molecular time-dependent Schrödinger equation with the inclusion of an external periodic drive that couples to the system dipole moment. With the support of the Floquet formalism, quantum dynamics is approximated by combining classical-like, trajectory-based, nuclear evolution with electronic dynamics represented in the Floquet basis. The resulting algorithm, which is an extension of the coupled-trajectory mixed quantum-classical scheme for periodically driven systems, is applied to a model study, exactly solvable, with different field intensities.
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Affiliation(s)
- Marco Schirò
- JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11 Place Marcelin Berthelot, 75321 Paris Cedex 05, France
| | - Florian G Eich
- HQS Quantum Simulations GmbH, Haid-und-Neu-Straße 7, D-76131 Karlsruhe, Germany
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
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Pieroni C, Marsili E, Lauvergnat D, Agostini F. Relaxation dynamics through a conical intersection: Quantum and quantum-classical studies. J Chem Phys 2021; 154:034104. [PMID: 33499611 DOI: 10.1063/5.0036726] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Abstract
We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys. Chem. B 104 1146 (2000)] to reproduce, with a minimal model, the main features of the 11-cis to all-trans isomerization of the retinal of rhodopsin. In particular, we focus on the performance of various trajectory-based schemes to nonadiabatic dynamics, and we compare quantum-classical results to the numerically exact quantum vibronic wavepacket dynamics. The purpose of this work is to investigate, by analyzing electronic and nuclear observables, how the sampling of initial conditions for the trajectories affects the subsequent dynamics.
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Affiliation(s)
- Carlotta Pieroni
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Emanuele Marsili
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - David Lauvergnat
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
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Talotta F, Agostini F, Ciccotti G. Quantum Trajectories for the Dynamics in the Exact Factorization Framework: A Proof-of-Principle Test. J Phys Chem A 2020; 124:6764-6777. [PMID: 32786992 DOI: 10.1021/acs.jpca.0c03969] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.
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Affiliation(s)
- Francesco Talotta
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France.,Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405, Orsay, France
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France.,Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405, Orsay, France
| | - Giovanni Ciccotti
- CNR, Institute for Applied Computing "Mauro Picone" (IAC), Via dei Taurini 19, 00185 Rome, Italy.,School of Physics, University College of Dublin UCD - Belfield, Dublin 4, Ireland.,Dipartimento di Fisica, Università di Roma La Sapienza, P. le A. Moro 5, 00185 Roma, Italy
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You P, Chen D, Lian C, Zhang C, Meng S. First‐principles dynamics of photoexcited molecules and materials towards a quantum description. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1492] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Peiwei You
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics Chinese Academy of Sciences Beijing China
- School of Physical Sciences University of Chinese Academy of Sciences Beijing China
| | - Daqiang Chen
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics Chinese Academy of Sciences Beijing China
- School of Physical Sciences University of Chinese Academy of Sciences Beijing China
| | - Chao Lian
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics Chinese Academy of Sciences Beijing China
| | - Cui Zhang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics Chinese Academy of Sciences Beijing China
- Songshan Lake Materials Laboratory Dongguan China
| | - Sheng Meng
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics Chinese Academy of Sciences Beijing China
- School of Physical Sciences University of Chinese Academy of Sciences Beijing China
- Songshan Lake Materials Laboratory Dongguan China
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Ibele LM, Nicolson A, Curchod BFE. Excited-state dynamics of molecules with classically driven trajectories and Gaussians. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1665199] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Lea M. Ibele
- Department of Chemistry, Durham University, Durham, UK
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11
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Agostini F, Curchod BFE. Different flavors of nonadiabatic molecular dynamics. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1417] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Federica Agostini
- Laboratoire de Chimie Physique UMR 8000 CNRS/University Paris‐Sud Orsay France
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