Fast real-time time-dependent density functional theory calculations with the parallel transport gauge

TL;DR

This paper introduces a gauge optimization method using parallel transport in RT-TDDFT, significantly increasing the simulation time step and computational speed for ultrafast electronic dynamics.

Contribution

The authors develop a parallel transport gauge approach that reduces oscillations in RT-TDDFT, enabling larger time steps and faster simulations across various electronic structure calculations.

Findings

Achieves 5-10 times speedup over standard methods.

Allows time steps of 10-100 attoseconds in planewave basis.

Demonstrates over 10 times faster wall clock time for silicon systems.

Abstract

Real-time time-dependent density functional theory (RT-TDDFT) is known to be hindered by the very small time step (attosecond or smaller) needed in the numerical simulation due to the fast oscillation of electron wavefunctions, which significantly limits its range of applicability for the study of ultrafast dynamics. In this paper, we demonstrate that such oscillation can be considerably reduced by optimizing the gauge choice using the parallel transport formalism. RT-TDDFT calculations can thus be significantly accelerated using a combination of the parallel transport gauge and implicit integrators, and the resulting scheme can be used to accelerate any electronic structure software that uses a Schr\"odinger representation. Using absorption spectrum, ultrashort laser pulse, and Ehrenfest dynamics calculations for example, we show that the new method can utilize a time step that is on the order of $10\sim 100$ attoseconds in a planewave basis set, and is no less than $5\sim 10$ times faster when compared to the standard explicit 4th order Runge-Kutta time integrator. Thanks to the significant increase of the size of the time step, we also demonstrate that the new method is more than 10 times faster in terms of the wall clock time when compared to the standard explicit 4th order Runge-Kutta time integrator for silicon systems ranging from 32 to 1024 atoms