Numerical Tests of a Fixed Vibrational Basis/Gaussian Bath Theory for Small Molecule Dynamics in Low-Temperature Media

Abstract

A recently framed quantum/semiclassical treatment for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium (Chapman, C. T.; Cina, J. A. J. Chem. Phys.2007,127, 114502) is further analyzed and subjected to initial tests of its numerical implementation. In the illustrative context of a 1D system interacting with a 1D medium, we rederive the fixed vibrational basis/gaussian bath (FVB/GB) equations of motion for the parameters defining the gaussian bath wave packet accompanying each of the energy eigenkets of the quantum mechanical system. The conditions of validity for the gaussian-bath approximation are shown to coincide with those supporting approximate population conservation. We perform initial numerical tests of the FVB/GB scheme and illustrate the semiclassical description it provides of coherent motion in the medium by comparing its predictions with the exact results for a high-frequency system harmonic oscillator bilinearly coupled to a lower-frequency bath oscillator. Linear vibronic absorption spectra or, equivalently, ultrafast wave packet interferometry signals are shown to be readily and accurately calculable within the FVB/GB framework.

Quantum dynamics and spectroscopy of dihalogens in solid matrices. I. Efficient simulation of the photodynamics of the embedded I2Kr18 cluster using the G-MCTDH method

“…The system-environment perspective of the G-MCTDH description is the same as in the Fixed Vibrational Basis/Gaussian Bath (FVB/GB) approach developed by Cina and coworkers [44][45][46] and successfully applied to the I 2 : Kr system. In the FVB/GB method a different ansatz is used: The energy eigenstates of the system are calculated and the time-dependent wavefunction is obtained by combining each eigenstate with one variationally evolving 'thawed' Gaussian wave packet (i. e. with time-dependent position and width).…”

“…A similar approach is the local coherent state approximation (LCSA) of Martinazzo et al, 42 in which the vibrational basis is replaced by a discrete variable representation (DVR). More recently, Kovac and Cina 43 , described the photodynamics of a I 2 Kr 6 model cluster using the fixed vibrational basis/Gaussian bath theory (FVB/GB), [44][45][46] in which the wavefunction for the system coordinate (the I-I stretch) is represented on a conventional basis of vibrational eigenstates, and each level is accompanied by a Gaussian wave packet describing the bath. In all of these approaches, the propagation is fully based on the time-dependent variational principle.…”

Compact MCTDH Wave Functions for High-Dimensional System-Bath Quantum Dynamics

“…The basic model adopted in this work is the celebrated independent oscillator model, also known as the Caldeira–Leggett model, ,, where a system degree of freedom x (the “system”) couples to a number N of harmonic oscillators q k (the “bath”), H = p 2 2 m + V ( x ) + prefix∑ k = 1 N { p k 2 2 + 1 2 ω k 2 ( q k − c k f false( x false) ω k 2 ) 2 } Here the bath is represented in mass-weighted coordinates, p ,{ p k } are the corresponding momenta, m is the system mass, V ( x ) is a bare system potential which is chosen to be of Morse form, V ( x ) = D e e –α x (e –α x – 2), and f ( x ) is a coupling function f ( x ) = 1 − normale − α x α such that f ( x ) ≈ x close to the equilibrium position, but with a finite limit as x → ∞. The Morse potential parameters were set to D e = 1.55 eV and α = 1.238 a 0 –1 and are representative of a hydrogen atom chemisorbed on a graphene layer; correspondingly, in the following m is the mass of a H atom.…”

“…A similar development in the context of dynamics at conical intersections has been proposed in ref 37. Further developments in line with more approximate treatment of the secondary modes, e.g., using Gaussian basis sets, 26,28,38,39 will be considered in the near future.…”

“Divide-and-conquer” semiclassical molecular dynamics: An application to water clusters

“…SCIVR builds a bridge between classical and quantum physics, since it allows to approximate the quantum propagator reliably by using only dynamical quantities that are generated from a classical simulation. [64][65][66][67][68][69][70][71][72][73][74][75][76] Specifically, the time averaged version of the quantum propagator is able to detect quantum effects on small-and medium-sized molecules accurately. [77][78][79][80][81][82][83][84][85][86][87][88][89][90] Recently, we have proposed a method called Divide-and-Conquer Semiclassical Initial Value Representation (DC SCIVR) 91,92 which makes semiclassical dynamics viable also for large molecules.…”