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

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 (OAT-DCCD) 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.This document gives additional results to the main article. Included are demonstrations of non-collapsing OATDCCD and TDCCSD simulations of Be in the cc-pVDZ basis, discussion of controllable error in the twoparticle case for TDFCI and OATDCCD, Be in the cc-pVTZ basis, and systematic breaking of the TDCCSD and OATDCCD methods for LiH in the aug-cc-pVDZ basis by increasing the field strength.

A state-specific multireference coupled-cluster method based on the bivariational principle

“…This opens up the route to not only response theory 22 and the approximation of excited states, 2,23 but also real-time propagation of quantum systems far from the ground-state. [24][25][26][27]…”

Interpretation of Coupled-Cluster Many-Electron Dynamics in Terms of Stationary States

“…Although the reference determinant |Φ 0 should be constructed from time-dependent orthonormal 16,31,57 or biorthonormal 23,30,58 orbitals to capture the main effects of interactions between the electrons and external fields, we shall in this work use the static Hartree-Fock (HF) ground-state determinant for simplicity.…”

“…Yielding energies, structures, and properties with excellent accuracy for both ground-and excited states of weakly correlated systems, it has become one of the most trusted methods of molecular quantum chemistry. 15 Recent years have witnessed increasing interest in time-dependent CC (TDCC) theory [16][17][18][19][20] for numerical simulations of many-body quantum dynamics in nuclear, 21 and atomic and molecular [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] systems. In addition, TDCC theory plays a key role in recent work on finite-temperature CC theory for molecular 39,40 and extended 41 systems.…”

Effects of electronic correlation on the high harmonic generation in helium: a time-dependent configuration interaction singles vs time-dependent full configuration interaction study

“…The approaches known from quantum chemistry that have been extended to the time-domain can be generally classified into two categories: the orbital-based ones, which include time-dependent Hartree-Fock (TD-HF) [29][30][31][32][33][34][35] and time-dependent density functional theory (TD-DFT) [28,, and the wavefunction-based ones, such as time-dependent configuration interaction (TD-CI) [27,28,44,, time-dependent multiconfigurational self consistent field (TD-MCSCF) [74,[88][89][90][91][92][93][94][95] and time-dependent coupled cluster (TD-CC) [96][97][98][99][100][101][102][103]. Out of all these methods the one that gained an exceptional popularity in theoretical attoscience is the time-dependent configuration interaction with single excitations (TD-CIS) [27, 28, 44, 59-61, 63-65, 67-70, 75, 76, 78, 79, 82-87], due to its simple formalism and low computational costs.…”