Herman-Kluk propagator is free from zero-point energy leakage

Abstract

Semiclassical techniques constitute a promising route to approximate quantum dynamics based on classical trajectories starting from a quantum-mechanically correct distribution. One of their main drawbacks is the so-called zero-point energy (ZPE) leakage, that is artificial redistribution of energy from the modes with high frequency and thus high ZPE to that with low frequency and ZPE due to classical equipartition. Here, we show that an elaborate semiclassical formalism based on the Herman-Kluk propagator is free from the ZPE leakage despite utilizing purely classical propagation. This finding opens the road to correct dynamical simulations of systems with a multitude of degrees of freedom that cannot be treated fully quantum-mechanically due to the exponential increase of the numerical effort.

WavePacket: A Matlab package for numerical quantum dynamics. III. Quantum‐classical simulations and surface hopping trajectories

“…Future releases of WavePacket will also include some of the more recent developments in SHT techniques, above all the various decoherence corrections in FSSH, to keep up with the recent progress in surface hopping . Moreover, also class definitions for various semi‐classical approaches based on Gaussian packets in phase space shall be implemented. Of particular interest will be nonadiabatic extensions of Gaussian propagation methods, such as the multiple spawning technique, surface hopping Gaussian propagations, or adaptive variants thereof …”

Semiclassical Vibrational Spectroscopy of Biological Molecules Using Force Fields

“… 17 − 24 SC calculations can be also performed to reproduce IR transition intensities, 25 , 26 while the most recent advances have focused on fundamental physics aspects like zero-point energy leakage and deterministic chaos. Specifically, it has been shown that SC calculations are free of zero-energy leakage at least when a full sampling of the phase space is performed 27 and that the influence of chaotic classical trajectories can be largely reduced and sometimes completely avoided by adopting a preliminary adiabatic switching procedure to sample initial conditions. 28 …”

Machine learning for vibrational spectroscopy via divide-and-conquer semiclassical initial value representation molecular dynamics with application to N-methylacetamide

“…(1) is given by the time-averaging semiclassical initial value representation (TA-SCIVR) method. [14][15][16][17][18][19][20][21][22][23] This is obtained by applying a time-averaging filter to the Heller-Herman-Kluk-Kay (HHKK) propagator, [24][25][26][27][28][29][30][31][32][33][34][35][36] which defines the approximate quantum time evolution. The final TA-SCIVR expression of Eq.…”