Trajectory-Based Approaches for Quantum Statistics and Quantum Dynamics for Nonadiabatic Systems

Jian Liu
Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing, China
Lundi 24 Juin 2019, 14h00
bibliothèque LCT, tour 12 - 13, 4^ème étage

The first part of the talk is on thermdynamics for nonadiabatic systems. An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD) for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.
The second part of the talk is on nonadiabatic dynamics. We propose a new unified theoretical framework to construct equivalent representations of the multi-state Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional Hamiltonian onto an F+1 dimensional space, creation and annihilation operators are defined such that the F+1 dimensional space is complete for any combined excitation. Commutation and anti-commutation relations are then naturally derived, which show that the underlying degrees of freedom are neither bosons nor fermions. This sets the scene for developing equivalent expressions of the Hamiltonian operator in quantum mechanics and their classical/semiclassical counterparts. Six mapping models are presented as examples. The framework also offers a novel way to derive such as the Meyer-Miller model.
We then present a new perspective for developing nonadiabatic dynamics methods based on the unified framework. Such nonadiabatic dynamics approaches demonstrate overall reasonably accurate dynamics behaviors in comparison to exact results even in the asymptotic long time limit for various spin-boson models and site-exciton models. Further investigation may lead to practically useful approaches to study nonadiabatic processes in realistic molecular systems in condensed phase.
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References:
[1] X. Liu and J. Li, J. Chem. Phys. 2018, 148, 102319.
[2] Z. Zhang, X. Liu, Z. Chen, H. Zheng, K. Yan, and J. Liu, J. Chem. Phys. 2017, 147, 034109.
[3] J. Liu, D. Li, and X. Liu, J. Chem. Phys. 2016, 145, 024103.
[4] X. He and J. Liu, J. Chem. Phys. submitted.
[5] J. Liu, J. Chem. Phys. 2017, 146, 024110.
[6] J. Liu, J. Chem. Phys. 2016, 145, 204105.