Spin-mapping approach for nonadiabatic molecular dynamics

• Published in: The Journal of chemical physics Vol. 151; no. 4; pp. 044119 - 44132
• Main Authors: Runeson, Johan E., Richardson, Jeremy O.
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 28.07.2019
• Subjects: Computer simulation; Correlation analysis; Electron states; Harmonic oscillators; Mapping; Molecular dynamics; Operators (mathematics); Spin dynamics; Zero point energy
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/1.5100506

We propose a trajectory-based method for simulating nonadiabatic dynamics in molecular systems with two coupled electronic states. Employing a quantum-mechanically exact mapping of the two-level problem to a spin-12 coherent state, we use the Stratonovich-Weyl transform to construct a classical phase space of a spin vector constrained to a spherical surface whose radius is consistent with the quantum magnitude of the spin. In contrast with the singly excited harmonic oscillator basis used in Meyer-Miller-Stock-Thoss (MMST) mapping, the theory requires no additional projection operators onto the space of physical states. When treated under a quasiclassical approximation, we show that the resulting dynamics are equivalent to those generated by the MMST Hamiltonian. What differs is the value of the zero-point energy parameter as well as the initial distribution and the measurement operators used in constructing correlation functions. For various spin-boson models, the results of the method are seen to be a significant improvement compared to both standard Ehrenfest dynamics and linearized semiclassical MMST mapping, without adding any computational complexity.