Time-dependent restricted-active-space self-consistent-field singles method for many-electron dynamics

Abstract

The time-dependent restricted-active-space self-consistent-field singles (TD-RASSCF-S) method is presented for investigating TD many-electron dynamics in atoms and molecules. Adopting the SCF notion from the muticonfigurational TD Hartree-Fock (MCTDHF) method and the RAS scheme (single-orbital excitation concept) from the TD configuration-interaction singles (TDCIS) method, the TD-RASSCF-S method can be regarded as a hybrid of them. We prove that, for closedshell N e -electron systems, the TD-RASSCF-S wave function can be fully converged using only N e /2 + 1 ≤ M ≤ N e spatial orbitals. Importantly, based on the TD variational principle, the converged TD-RASSCF-S wave function with M = N e is more accurate than the TDCIS wave function. The accuracy of the TD-RASSCF-S approach over the TDCIS is illustrated by the calculation of high-order harmonic generation spectra for one-dimensional models of atomic helium, beryllium, and carbon in an intense laser pulse. The electronic dynamics during the process is investigated by analyzing the behavior of electron density and orbitals. The TD-RASSCF-S method is accurate, numerically tractable, and applicable for large systems beyond the capability of the MCTDHF method.

Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules

“…[32], and in an SCF setting in Refs. [27][28][29]. The idea of selecting determinants by their importance, and thus truncating the CI expansion, has a long tradition in atomic and molecular physics [58].…”

“…[32], and variations thereof in Refs. [27][28][29]. In this work, we use a generalized scheme based on the construction and manipulation of types of excitation classes which is particularly suited for GAS calculations and which has previously been successfully applied in Coupled-Cluster theory [60,61].…”

“…Further, MCT-DHF calculations are feasible for N el 10 with highlyoptimized codes. Currently, progress towards larger systems is made in the combination of restricted-active spaces time-dependent orbitals [27][28][29].…”

“…This makes the method infeasible for systems having more than a few electrons interacting with a strong field. The TD complete-active-space self-consistent-field method (TD-CASCF) [26], and the more general TD restricted-active space SCF (TD-RASSCF) [27][28][29] cure this scaling by imposing restrictions on the active orbital spaces, while keeping the attractive SCF notion of the MCTDHF approach, i.e., the orbitals are time-dependent and optimally updated in each time-step.…”

Instabilities and inaccuracies of multi-configuration time-dependent Hartree-Fock

“…In equation (16), we assume that the orbitals are sorted in descending order with respect to their occupation and that U only acts on the virtual orbitals. For his calculation, we have chosen (17) as the unitary transformation which is applied to the virtual orbitals. The matrix K in equation (17) is an arbitrary Hermitian matrix which we define as…”