Semiclassical dynamics in the mixed quantum-classical limit

Abstract

The semiclassical Double Herman-Kluk Initial Value Representation is an accurate approach to computing quantum real time correlation functions, but its applications are limited by the need to evaluate an oscillatory integral. In previous work, we have shown that this `sign problem' can be mitigated using the modified Filinov filtration technique to control the extent to which individual modes of the system contribute to the overall phase of the integrand. Here we follow this idea to a logical conclusion: we analytically derive a general expression for the mixed quantum-classical limit of the semiclassical correlation function - AMQC-IVR, where the phase contributions from the `classical' modes of the system are filtered while the `quantum' modes are treated in the full semiclassical limit. We numerically demonstrate the accuracy and efficiency of the AMQC-IVR formulation in calculations of quantum correlation functions and reaction rates using three model systems with varied coupling strengths between the classical and quantum subsystems. We also introduce a separable prefactor approximation that further reduces the computational cost, but is only accurate in the limit of weak coupling between the quantum and classical subsystems.

arXiv comment11 pages, 4 figures

References in corpus (11)

• Direct simulation of electron transfer using ring polymer molecular dynamics: Comparison with semiclassical instanton theory and exact quantum methods
• Impediments to mixing classical and quantum dynamics
• Kinetically Constrained Ring-Polymer Molecular Dynamics for Non-adiabatic Chemical Reactions
• Semiclassical "Divide-and-Conquer" Method for Spectroscopic Calculations of High Dimensional Molecular Systems
• 'Divide-and-conquer' semiclassical molecular dynamics: An application to water clusters
• Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation
• The Importance of the Pre-exponential Factor in Semiclassical Molecular Dynamics
• "Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems
• Simplified Approach to the Mixed Time-averaging Semiclassical Initial Value Representation for the Calculation of Dense Vibrational Spectra
• Herman-Kluk propagator is free from zero-point energy leakage
• Validating and Implementing Modified Filinov Phase Filtration in Semiclassical Dynamics

Cited by in corpus (5)

• Improved semiclassical dynamics through adiabatic switching trajectory sampling
• A Semiclassical Framework for Mixed Quantum Classical Dynamics
• A Linearized Semiclassical dynamics study of the multi-quantum vibrational relaxation of NO scattering from a Au(111) Surface
• Non-Linear Correlation Functions and Zero-Point Energy Flow in Mixed Quantum-Classical Semiclassical Dynamics
• Semiclassical Dynamics in Wigner Phase Space I : Adiabatic Hybrid Wigner Dynamics