Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics. II. Extended formulation and numerical analysis

Abstract

The time-dependent restricted-active-space self-consistent-field (TD-RASSCF) method is formulated based on the TD variational principle. The SCF based TD orbitals contributing to the expansion of the wave function are classified into three groups, between which orbital excitations are considered with the RAS scheme. In analogy with the configuration-interaction singles (CIS), singles-and-doubles (CISD), and singles-doubles-and-triples (CISDT) methods in quantum chemistry, the TD-RASSCF-S, -SD, and -SDT methods are introduced as extensions of the TD-RASSCF-doubles (-D) method [Phys. Rev. A 87, 062511 (2013)]. Based on an analysis of the numerical cost and test calculations for one-dimensional (1D) models of atomic helium, beryllium, and carbon, it is shown that the TD-RASSCF-S and -D methods are computationally feasible for systems with many electrons and more accurate than the TD Hartree-Fock (TDHF) and TDCIS methods. In addition to the discussion of methodology, an analysis of electron dynamics in the high-order harmonic generation (HHG) process is presented. For the 1D beryllium atom, a state-resolved analysis of the HHG spectrum based on the time-independent HF orbitals shows that while only single-orbital excitations are needed in the region below the cutoff, single- and double-orbital excitations are essential beyond, where accordingly the single-active-electron (SAE) approximation and the TDCIS method break down. On the other hand, the TD-RASSCF-S and -D methods accurately describe the multiorbital excitation processes throughout the entire region of the HHG spectrum. For the 1D carbon atom, our calculations show that multiorbital excitations are essential in the HHG process even below the cutoff. Hence, in this test system a very accurate treatment of electron correlation is required. The TD-RASSCF-S and -D approaches meet this demand, while the SAE approximation and the TDCIS method are inadequate.