CHAPTER 11: Time-dependent Restricted-active-space Self-consistent-field Theory for Electron Dynamics on the Attosecond Timescale

The time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory is a wavefunction-based theory for the TD many-electron problem. The RAS scheme allows an inclusion of specific orbital spaces. Hence, the theory allows an identification of the spaces that are most important for a given process. The RAS reduces the configuration space, i.e., the space describing all the possible arrangements of the electrons in the different orbitals by the imposed restrictions on the excitations between orbital spaces. The use of TD SCF orbitals additionally reduces the number of configurations because the orbitals adjust in an optimal manner during time propagation. The theoretical concepts underlying the TD-RASSCF theory are discussed. A derivation of the equations of motion is presented. It is discussed how to extract observables. Some properties including gauge invariance and numerical performance are discussed. Finally some illustrative applications in high-order harmonic generation and photoionization including time-delay studies are given. The TD-RASSCF theory is a many-electron theory that accounts for correlation between the electrons, and its evaluation is, accordingly, numerically demanding. Therefore, at present, its application to strong-field many-photon processes is restricted to one spatial dimension. For calculations in three spatial dimensions, application is best suited for few-photon processes in attosecond pulses.