Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics. II. Extended formulation and numerical analysis

Abstract

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.

Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules

“…[32], and in an SCF setting in Refs. [27][28][29]. The idea of selecting determinants by their importance, and thus truncating the CI expansion, has a long tradition in atomic and molecular physics [58].…”

“…[32], and variations thereof in Refs. [27][28][29]. In this work, we use a generalized scheme based on the construction and manipulation of types of excitation classes which is particularly suited for GAS calculations and which has previously been successfully applied in Coupled-Cluster theory [60,61].…”

“…Further, MCT-DHF calculations are feasible for N el 10 with highlyoptimized codes. Currently, progress towards larger systems is made in the combination of restricted-active spaces time-dependent orbitals [27][28][29].…”

“…This makes the method infeasible for systems having more than a few electrons interacting with a strong field. The TD complete-active-space self-consistent-field method (TD-CASCF) [26], and the more general TD restricted-active space SCF (TD-RASSCF) [27][28][29] cure this scaling by imposing restrictions on the active orbital spaces, while keeping the attractive SCF notion of the MCTDHF approach, i.e., the orbitals are time-dependent and optimally updated in each time-step.…”

Zombie states for description of structure and dynamics of multi-electron systems

“…For example, several versions of Multiconfigurational TimeDependent Hartree-Fock (MCTDH-F) techniques have been developed, 7,18-25 which can treat numerically many-body fermionic systems. Time-Dependent Restricted-Active-Space Self-Consistent Field (TD-RASSCF) theory [26][27][28][29] has been proposed to treat laser-driven many-electron dynamics at lower computational cost. Another example is B-spline TimeDependent Algebraic Diagrammatic Construction (B-spline TD-ADC) approach 30 that has been used to calculate the spectra of High-Harmonic generation in many-electron systems.…”