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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Semiclassical quantization in Liouville space for vibrational dynamics.

Scott M Gruenbaum¹, Roger F Loring

¹Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA.

The Journal of Physical Chemistry. B

|March 8, 2011

Summary

This study simplifies semiclassical calculations for quantum mechanics using the mean-trajectory (MT) approximation. The new method efficiently includes quantum coherence effects in complex molecular dynamics simulations.

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Area of Science:

Quantum mechanics
Physical chemistry
Computational chemistry

Background:

Semiclassical approximations, like the Herman-Kluk (HK) propagator, incorporate quantum coherence into classical mechanics for dynamical calculations.
The HK method reproduces quantum effects in nonlinear vibrational response functions but is computationally intensive for multiple degrees of freedom.
Quantum coherence in HK arises from interference between classical trajectories.

Purpose of the Study:

To simplify semiclassical calculations of response functions by elucidating the mechanism of quantum effect reproduction in quasiperiodic dynamics.
To derive a mean-trajectory (MT) approximation for the Liouville space time evolution operator, extending its applicability beyond response functions.

Main Methods:

Developed a mean-trajectory (MT) approximation by treating the phase space difference between trajectories perturbatively.
Performed analytical integration over trajectory differences and numerical integration over mean trajectories.
Derived an MT approximation for the Liouville space time evolution operator that propagates the density operator.

Main Results:

The MT approximation significantly simplifies semiclassical calculations of response functions in quasiperiodic dynamics.
The derived MT approximation is applicable to linear and nonlinear vibrational response functions for both isolated and coupled anharmonic motions.
The analysis clarifies the relationship between semiclassical quantization of wave function propagators and density operator propagators.

Conclusions:

The MT approximation offers a practical and efficient route for incorporating quantum coherence effects in complex molecular dynamics.
This work extends the utility of semiclassical methods to the time evolution of the density operator, broadening its application in quantum dynamics.
The findings bridge the understanding of semiclassical propagators for wave functions and density operators.