Electron correlation in beryllium: Effects in the ground state, short-pulse photoionization, and time-delay studies

Abstract

We apply a three-dimensional (3D) implementation of the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) method to investigate effects of electron correlation in the ground state of Be as well as in its photoionization dynamics by short XUV pulses, including time-delay in photoionization. First, we obtain the ground state by propagation in imaginary time. We show that the flexibility of the TD-RASSCF on the choice of the active orbital space makes it possible to consider only relevant active space orbitals, facilitating the convergence to the ground state compared to the multiconfigurational time-dependent Hartree-Fock method, used as a benchmark to show the accuracy and efficiency of TD-RASSCF. Second, we solve the equations of motion to compute photoelectron spectra of Be after interacting with a short linearly polarized XUV laser pulse. We compare the spectra for different RAS schemes, and in this way we identify the orbital spaces that are relevant for an accurate description of the photoelectron spectra. Finally, we investigate the effects of electron correlation on the magnitude of the relative Eisenbud-Wigner-Smith (EWS) timedelay in the photoionization process into two different ionic channels. One channel, the ground state channel in the ion, is accessible without electron correlation. The other channel is only accessible when including electron correlation. For theory beyond the mean-field time-dependent HartreeFock, the EWS time-delay for the photon energy analyzed is quite insensitive to the considered active orbital spaces.

Colloquium : Multiconfigurational time-dependent Hartree approaches for indistinguishable particles

“…(i) From the computed wavefunction, one extracts the expectation value of the radial distance in a given direction, r(t) , as a function of time and the linear momentum of the photoelectron, k that can be evaluated in different ways. For instance k , can be evaluated via integrating only in the outer part of the simulation volume (Omiste et al, 2017;Omiste and Madsen, 2018). (ii) Using r(t) and k the effective ionization time,…”

“…For example in beryllium, photoionization of the ground state into the channel Be + [(1s 2 2p) 2 P o ]+e − (s or d) changes two orbitals in the dominant configurations by the action of the one-body photoionization operator. Therefore, that process can not be described by TDHF (Omiste et al, 2017).…”

Effects of core space and excitation levels on ground-state correlation and photoionization dynamics of Be and Ne

“…For instance, the ground-state energy for MCTDHF with 5 orbitals is −14.6171, larger than the value −14.6192 in Ref. [40] which was taken as the most bound ground-state solution without taking into account any symmetry considerations. In the present work, we consider ground-state wave functions belonging to the same family of solutions, i. e., functions with even parity, M L = 0 for each configuration and orbitals with well defined magnetic quantum number.…”

“…In these methods the number of orbitals can be reduced by introducing time-dependent orbitals, which therefore implies a smaller number of configurations. The most commonly used SCF methods which include correlation are multiconfigurational time-dependent Hartree-Fock (MCTDHF) 14,[20][21][22][23][24][25][26][27][28][29][30][31] , time-dependent completeactive-space SCF (TD-CASSCF) [32][33][34][35][36] and time-dependent restricted-active-space SCF (TD-RASSCF) 33,[37][38][39][40][41][42] approaches. Specifically, TD-RASSCF not only reduces the number of orbitals, but also the number of configurations can be reduced by appropriately choosing the restricted-active-space (RAS).…”

Electron correlation effects in enhanced ionization of diatomic molecules in near-infrared fields

“…Over the past years, various timedependent many-electron methods have been developed to address dynamic electron correlation in strong-field ionization of atoms and molecules. Among those, the timedependent R-matrix approach [35][36][37][38], the time-dependent Feshbach close-coupling (TDFCC) method [39], the multiconfigurational time-dependent Hartree-Fock (MCTDHF) method [40][41][42][43][44][45], and the time-dependent restricted-activespace self-consistent-field (TD-RAS-SCF) theory [46][47][48][49][50][51][52][53] have been used to understand dynamics. The time-dependent restricted-active-space configuration-interaction (TD-RASCI) method [54], and the time-dependent generalized-activespace configuration-interaction (TD-GASCI) method [33,34,55] take electron correlation into account through a configuration-interaction (CI) expansion by selectively choosing important Slater determinants relevant to the physical process of interest.…”