  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
closed-shell $N_{\rm e}$-electron systems, the TD-RASSCF-S wave function can be
fully converged using only $N_{\rm e}/2+1\le M\le N_{\rm e}$ spatial orbitals.
Importantly, based on the TD variational principle, the converged TD-RASSCF-S
wave function with $M= N_{\rm e}$ 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.
