Time-dependent restricted-active-space self-consistent-field theory with space partition

Abstract

Aiming at efficient numerical analysis of time-dependent (TD) many-electron dynamics of atoms involving multielectron continua, the TD restricted-active-space self-consistent-field theory with space partition (TD-RASSCF-SP) is presented. The TD-RASSCF-SP wave function is expanded in terms of TD configuration-interaction coefficients with Slater determinants composed of two kinds of TD orbitals: $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ orbitals are defined to be nonvanishing in the inner region ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{V}$), a small volume around the atomic nucleus, and $\stackrel{\ifmmode \check{}\else \v{}\fi{}}{M}$ orbitals are nonvanishing in the large outer region ($\stackrel{\ifmmode \check{}\else \v{}\fi{}}{V}$). For detailed discussion of the SP strategy, the equations of motion are derived by two different formalisms for comparison. To ensure continuous differentiability of the wave function across the two regions, one of the formalisms makes use of the property of the finite-element discrete-variable-representation (FEDVR) functions and introduces additional time-independent orbitals. The other formalism is more general and is based on the Bloch operator as in the $R$-matrix theory, but turns out to be less practical for numerical applications. Hence, using the FEDVR-based formalism, the numerical performance is tested by computing double-ionization dynamics of atomic beryllium in intense light fields. To achieve high accuracy, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ should be set large to take into account the strong many-electron correlation around the nucleus. On the other hand, $\stackrel{\ifmmode \check{}\else \v{}\fi{}}{M}$ can be set much smaller than $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ for capturing the weaker correlation between the two outgoing photoelectrons. As a result, compared with more accurate multiconfigurational TD Hartree-Fock (MCTDHF) method, the TD-RASSCF-SP method may achieve comparable accuracy in the description of the double-ionization dynamics. There are, however, difficulties related to the stiffness of the equations of motion of the TD-RASSCF-SP method, which makes the required time step for this method smaller than the one needed for the MCTDHF approach.