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The standard fewest switches surface hopping algorithm fails to conserve momentum in systems with spin-orbit coupling and an odd number of electrons. A solution involves using phase-space electronic Hamiltonians to ensure momentum conservation in semiclassical simulations.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Fewest switches surface hopping (FSSH) is a standard algorithm for simulating non-adiabatic dynamics.
  • Systems with spin-orbit coupling and an odd number of electrons present unique challenges for FSSH.
  • Conservation of linear and angular momentum is crucial for accurate simulations.

Purpose of the Study:

  • To identify the limitations of the standard FSSH algorithm in conserving momentum.
  • To propose a modified approach for accurate semiclassical simulations.
  • To address the coupling of nuclear, electronic orbital, and electronic spin degrees of freedom.

Main Methods:

  • Analysis of momentum conservation in FSSH for systems with spin-orbit coupling.
  • Investigation of time-reversibility in adiabatic dynamics.
  • Development of a solution using phase-space electronic Hamiltonians H(R, P).

Main Results:

  • The standard FSSH algorithm violates linear and angular momentum conservation in specific systems.
  • The violation stems from propagating dynamics along non-time-reversible surfaces.
  • Running dynamics along eigenvalues of phase-space electronic Hamiltonians with specific electronic-nuclear coupling resolves the issue.

Conclusions:

  • A modified semiclassical approach is necessary for accurate simulations involving coupled nuclear, electronic orbital, and spin dynamics.
  • The proposed method using phase-space Hamiltonians provides a pathway for improved simulations.
  • This work is relevant for systems exhibiting chiral-induced spin selectivity.