Refined approach to cellularization: going from Heller's thawed Gaussian approximation to the Herman--Kluk propagator

Abstract

We present a refined cellularization (Filinov filtering) scheme for the semiclassical Herman--Kluk propagator, which employs the inverse Weierstrass transform and optimal scaling of the cell's size with the number of cells, and was previously used only in the context of the dephasing representation. In the new methodology, the sampling density for the cell centers correlates with the cell size, allowing for an effective sampling of the phase space covered by the initial state of the system. The main advantage of the presented approach is that, unlike the standard cellularization, it converges to the original Herman--Kluk result in the limit of an infinite number of trajectories and to the thawed Gaussian approximation when a single trajectory is used. We illustrate the performance of the refined cellularization scheme by calculating autocorrelation functions and spectra of both integrable and chaotic model systems.

7 pages, 3 figures

References in corpus (14)

• Computing quantum dynamics in the semiclassical regime
• On-the-fly ab initio semiclassical dynamics: Identifying degrees of freedom essential for emission spectra of oligothiophenes
• Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions
• Dephasing representation of quantum fidelity for general pure and mixed states
• Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation
• The Importance of the Pre-exponential Factor in Semiclassical Molecular Dynamics
• Mixed Semiclassical Initial Value Representation Time-Averaging Propagator for Spectroscopic Calculations
• Simplified Approach to the Mixed Time-averaging Semiclassical Initial Value Representation for the Calculation of Dense Vibrational Spectra
• Validating and Implementing Modified Filinov Phase Filtration in Semiclassical Dynamics
• On-the-fly ab initio three thawed Gaussians approximation: A semiclassical approach to Herzberg-Teller spectra
• Beating the efficiency of both quantum and classical simulations with semiclassics
• Family of Gaussian wavepacket dynamics methods from the perspective of a nonlinear Schrödinger equation
• Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor
• A semiclassical hybrid approach to linear response functions for infrared spectroscopy