Efficient simulation of wave-packet dynamics on multiple coupled potential surfaces with split potential propagation

TL;DR

This paper introduces a method to significantly accelerate quantum wave-packet simulations involving multiple coupled potential surfaces by splitting the potential matrix, reducing computational effort while maintaining accuracy.

Contribution

The authors develop a potential splitting technique that reduces matrix exponentiation steps, halving the simulation time for wave-packet dynamics on coupled surfaces.

Findings

Potential splitting reduces potential propagation time by approximately 70%.

The introduced method maintains accuracy with minimal additional error.

Applicable to multi-surface quantum dynamics simulations.

Abstract

We present a simple method to expedite simulation of quantum wave-packet dynamics by more than a factor of $2$ with the Strang split-operator propagation. Dynamics of quantum wave-packets are often evaluated using the the \emph{Strang} split-step propagation, where the kinetic part of the Hamiltonian $\hat{T}$ and the potential part $\hat{V}$ are piecewise integrated according to $e^{- i \hat{H} \delta t} \approx e^{- i \hat{V} \delta t/2} e^{- i \hat{T}\delta t} e^{- i \hat{V} \delta t/2}$, which is accurate to second order in the propagation time $\delta t$. In molecular quantum dynamics, the potential propagation occurs over multiple coupled potential surfaces and requires matrix exponentiation for each position in space and time which is computationally demanding. Our method employs further splitting of the potential matrix $\hat{V}$ into a diagonal space dependent part $\hat{V}_{D}(R)$ and an off-diagonal time-dependent coupling-field $\hat{V}_{OD}(t)$, which then requires only a single matrix exponentiation for each time-step, considerably reducing the calculation time even in the simplest two-surface interaction ($\sim$70\% reduction observed in potential propagation time). We analyze the additional error due to the potential splitting and show it to be small compared to the inherent error associated with the kinetic/potential splitting.