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In this paper, we analyze the detailed quantum-classical behavior of two alternative approaches to simulating molecular dynamics with electronic transitions: the popular fewest switches surface hopping (FSSH) method, introduced by Tully in 1990 [Tully, \textit{J.~Chem.~Phys.}, 1990, \textbf{93}, 1061] and our recently developed quantum trajectory surface hopping (QTSH) method [Martens, \textit{J.~Phys.~Chem.~A}, 2019 \textbf{123}, 1110]. Both approaches employ an independent ensemble of trajectories that undergo stochastic transitions between electronic surfaces. The methods differ in their treatment of energy conservation, with FSSH imposing conservation of the classical kinetic plus potential energy by rescaling of the classical momenta when a surface hop occurs, while QTSH incorporates quantum forces throughout the dynamics which lead naturally to the conservation of the full quantum-classical energy. We investigate the population transfer and energy budget of the surface hopping methods for several simple model systems and compare with exact quantum result. In addition, the detailed dynamics of the trajectory ensembles in phase space are compared with the quantum evolution in the Wigner representation. Conclusions are drawn.
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Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states
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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- Award ID(s):
- 2102402
- PAR ID:
- 10520186
- Publisher / Repository:
- jcp
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 160
- Issue:
- 5
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0177778
