Atomic orbital-based cubic response theory for one-, two-, and four-component relativistic self-consistent field models

Relativistic four-component calculations of Buckingham birefringence using London atomic orbitals

“…For CO 2 , CS 2 and CSe 2 , we compare our results with previous nonrelativistic ab initio [17] data and with experiment [29][30][31][32][33][34]. The atomic-orbital-driven (AO-driven) scheme recently introduced by Bast et al [35] for calculating time-dependent molecular properties with one-, two-and four-component relativistic methods is extended to first-order frequency-dependent magnetic perturbations with London atomic orbitals (LAOs) [36][37][38][39][40], thereby ensuring gaugeorigin independence of the calculated results. The present work can also be considered an extension of our recent analytic implementation of Buckingham birefringence [22] to Kohn-Sham (KS) density-functional theory (DFT).…”

“…Being formulated in the AO basis, the approach is transparent to the explicit form of the molecular Hamiltonian and to the parametrization of the self-consistent-field wave function. We have previously utilized this feature to extend the approach to two-and four-component relativistic wave functions for the calculation of higherorder molecular properties involving one-electron operators [35]. Here, this approach is extended further to include KS exchange-correlation (XC) contributions using perturbation-dependent basis sets to first order.…”

“…The response vectors obtained are subsequently transformed back to the AO basis and converted into the homogeneous components of the perturbed density matrix, which is used in the calculation of the response functions that determine the Buckingham birefringence. For details, we refer to the literature describing the various aspects of the procedure [35,60,72].…”

“…As in our previous study of nonlinear electric responses in the relativistic domain [35], we determine the homogeneous component of the perturbed densities by solving a linear set of equations of the general form [60]…”

Gauge-origin independent calculations of Jones birefringence

“…The six first-order and nine second-order perturbed density matrices are determined by solving a set of linear response equations, either in the atomic or the molecular orbital basis. 19,[54][55][56][57] The specific case of determining perturbed densities for external frequencydependent magnetic fields, when using London atomic orbitals, have been described in detail in our previous work on the Cotton-Mouton effect, 44 and the interested reader is referred to this paper for more information about the details of the approach.…”