We present the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory as a new framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory by incorporating the restrictedactive-space scheme well known in time-independent quantum chemistry. Optimization of the orbitals as well as the expansion coefficients at each time step makes it possible to construct the wave function accurately while using only a relatively small number of electronic configurations. In numerical calculations of high-order harmonic generation spectra of a one-dimensional model of atomic beryllium interacting with a strong laser pulse, the TD-RASSCF method is reasonably accurate while largely reducing the computational complexity. The TD-RASSCF method has the potential to treat large atoms and molecules beyond the capability of the MCTDHF method.

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), 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 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.

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.

The formation and decay of doubly excited methane in photon and electron interactions have been investigated through measuring (i) the cross sections for the emission of the Lyman-α fluorescence in the photoexcitation of CH4 as a function of incident photon energy in the range 18–51 eV and (ii) the electron-energy-loss spectrum of CH4 tagged with the Lyman-α photons at 80 eV incident electron energy and 10° electron scattering angle in the range of the energy loss 20–45 eV. Five superexcited states have been found, three of which are doubly excited states with the others being singly excited states. It has been found that the electron interaction with CH4 at 80 eV incident electron energy and 10° electron scattering angle accelerates the double excitation against the single excitation as compared with the photon interaction.

The angular correlation of two Lyman-α photons generated by the linearly polarized single-photon absorption of H2(X 1Σg+) followed by the neutral dissociation of the doubly excited Q21Πu(1) state has been theoretically investigated with the second-order correlation function in quantum optics. A strong angular correlation has been obtained even for the molecules randomly oriented in space, due to the complicated entanglement of two H(2p) atoms in the intermediate state. It has been revealed how the symmetry properties in the electronic state are transferred to the two-photon state and how they manifest themselves in the angular correlation function.