Numerical stability of time-dependent coupled-cluster methods for many-electron dynamics in intense laser pulses

TL;DR

This paper compares the numerical stability of two time-dependent coupled-cluster methods for simulating many-electron dynamics in intense laser fields, highlighting the superior stability of the orbital-adaptive approach.

Contribution

It demonstrates that orbital-adaptive time-dependent coupled-cluster doubles (OATDCCD) offers improved numerical stability over traditional TDCCSD in intense laser pulse simulations.

Findings

OATDCCD shows significantly reduced oscillations in doubles amplitudes.

Stability is linked to the quality of the biorthonormal reference determinants.

Reference weight can diagnose potential instabilities.

Abstract

We investigate the numerical stability of time-dependent coupled-cluster theory for many-electron dynamics in intense laser pulses, comparing two coupled-cluster formulations with full configuration interaction theory. Our numerical experiments show that orbital-adaptive time-dependent coupled-cluster doubles (OATDCCD) theory offers significantly improved stability compared with the conventional Hartree-Fock-based time-dependent coupled-cluster singles-and-doubles (TDCCSD) formulation. The improved stability stems from greatly reduced oscillations in the doubles amplitudes, which, in turn, can be traced to the dynamic biorthonormal reference determinants of OATDCCD theory. As long as these are good approximations to the Brueckner determinant, OATDCCD theory is numerically stable. We propose the reference weight as a diagnostic quantity to identify situations where the TDCCSD and OATDCCD theories become unstable.