The generalized active space concept for the relativistic treatment of electron correlation. III. Large-scale configuration interaction and multiconfiguration self-consistent-field four-component methods with application to UO2

Abstract

We present an implementation for large-scale relativistic electronic structure calculations including spin-dependent contributions and electron correlation in a fully variational procedure. The modular implementation of the double group configuration interaction ͑CI͒ program into a multiconfiguration self-consistent-field ͑MCSCF͒ code allows for the treatment of large CI expansions in both the spinor optimization step and the post-MCSCF dynamic electron correlation step. As an illustration of the potential of the new code, we calculate the spectroscopic properties of the UO 2 molecule where we study the ground state and a few excited states in vertical and adiabatic calculations.

A Fock space coupled cluster study on the electronic structure of the UO2, UO2+, U4+, and U5+ species

“…Is this large discrepancy caused by the differences induced by the argon matrix, by deficiencies in the calculation, such as limits on the size of the active space used, or by both? The generalized active space configuration interaction ͑GASCI͒ results by Fleig et al 23 agree better with experiment and with older spin-orbit configuration interaction calculations of Chang 22 but both calculations were done in rather modest basis sets and could suffer from basis set incompleteness errors. It is therefore clear that more theoretical work is desirable.…”

“…SOC is rather large, leading to significant admixture of 3 ⌬ u character in both the 2u ground state and the 3u first excited state ͑better described in a jj-coupling picture as pure 5f 5/2 1 7s 1/2 1 states͒. Actual calculations on gas phase UO 2 by Chang, 22 Gagliardi et al 4,18 and Fleig et al 23 reproduce this splitting well. The manifold of SOC-split grade states does not have two so closely spaced states at low energy.…”

“…31 858 40% ͑5f 5f ͒ +18%͑5f 5f ͒ +16%͑6d ␦ 6d lier CASPT2 calculations, but the GASCI calculation of Fleig et al 23 and also the multireference configuration interaction ͑MRCI͒ calculations of Tyagi 63 give a significantly smaller value for the excitation from 5f ,5/2u to 5f ␦,3/2u . This is probably due to the fact that fewer electrons were correlated in these CI calculations; if we correlate only 14 electrons we also obtain smaller energy differences of 1621 and 1911 cm −1 .…”

Relativistic kinetic-balance condition for explicitly correlated basis functions

“…(97) in the appendix) to match the partitioning of the wave function according to Eq. (26). We then obtain the following block structure for the two-fermion Hamiltonian defined in Eq.…”

“…Four-component methods rely on the kinetic-balance condition for variational stability. This condition is well-defined for single fermions [9][10][11][12][13][14][15][16] and can therefore straightforwardly be applied to orbital-based methods such as the DiracHartree-Fock approach and electron-correlation methods based on it [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. For orbital-based theories with explicit correlation factors, recent work focused on four-component second-order Møller-Plesset perturbation theory with positiveenergy-states projection operators in combination with the one-electron kineticbalance condition [31].…”