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The time-dependent restricted-active-space self-consistent-field (TD-RASSCF)method is formulated based on the TD variational principle. In analogy with theconfiguration-interaction singles (CIS), singles-and-doubles (CISD),singles-doubles-and-triples (CISDT) methods in quantum chemistry, theTD-RASSCF-S, -SD, and -SDT methods are introduced as extensions of theTD-RASSCF dou- bles (-D) method [Phys. Rev. A 87, 062511 (2013)]. Based on ananalysis of the numerical cost and test calculations for one-dimensional (1D)models of atomic helium, beryllium, and carbon, it is shown that theTD-RASSCF-S and -D methods are computationally feasible for systems with manyelectrons and more accurate than the TD Hartree-Fock (TDHF) and TDCIS methods.In addition to the discussion of methodology, an analysis of electron dynamicsin the high-order harmonic generation (HHG) process is presented. For the 1Dberyllium atom, a state-resolved analysis of the HHG spectrum based on thetime-independent HF orbitals shows that while only single-orbital excitationsare needed in the region below the cutoff, single- and double-orbitalexcitations are es- sential beyond, where accordingly thesingle-active-electron (SAE) approximation and the TDCIS method break down. Onthe other hand, the TD-RASSCF-S and -D methods accurately describe themulti-orbital excitation processes throughout the entire region of the HHGspectrum. For the 1D carbon atom, our calculations show that multi-orbitalexcitations are essential in the HHG process even below the cutoff. Hence, inthis test system a very accurate treatment of electron correlation is required.The TD-RASSCF-S and -D approaches meet this demand, while the SAE approximationand the TDCIS method are inadequate.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

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