  The time-dependent restricted-active-space self-consistent-field (TD-RASSCF)
method is formulated based on the TD variational principle. In analogy with the
configuration-interaction singles (CIS), singles-and-doubles (CISD),
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 dou- bles (-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 es- sential 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
multi-orbital excitation processes throughout the entire region of the HHG
spectrum. For the 1D carbon atom, our calculations show that multi-orbital
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.
