Development of efficient time evolution method based on operator transformation

Abstract

Real-time propagation (RT) of time-dependent theories, such as time-dependent Hartree-Fock (TDHF) method and time-dependent density functional theory (TDDFT), have been applied to theoretically describing electron dynamics. However, RT calculations are computationally demanding, because of evaluation of time-evolution operator by conventional numerical integration such as the Runge-Kutta method. In this study, we developed the three-term recurrence-relation (3TRR) method as an efficient time-evolution method for electron dynamics, being inspired by the real-wave-packet method for nuclear wave packet dynamics with time-dependent Schrödinger equation. The basic formula of this approach was derived by introducing a transformation of the operator using the arcsine function. Since this operator transformation causes transformation of time, we derived the relation between original and transformed time. We applied this 3TRR method to equation of motion for density matrix in RT-THDF/TDDFT. 3TRR method achieved about four times faster RT-TDHF calculation than conventional fourth-order Runge-Kutta method.