High order relativistic corrections on the electric field gradient within the LRESC formalism

In this work we present relativistic corrections to the electric field gradient (EFG) given by the Linear Response Elimination of the Small Component (LRESC) scheme at 1/c^2 order and including for the first time spin-dependent (SD) corrections at 1/c^4 order. We show that these new terms improve the performance of LRESC as results with this methodology are very close to those calculated at four-component Dirac-Hartree-Fock (4c-DHF) level. We assess the new corrections in Br Y and At Y di-halogen ( Y = F, Cl, Br, I, At) and XZY bi-lineal molecules ( Z = Zn, Cd, Hg; X, Y = F, Cl, Br, I, At). At 4c-DHF level, we analyse the contributions coming from the large and small components of the relativistic 4c wave function to the electronic part of EFG and compare them with the LRESC corrections to their electronic origin. For Hg X2 ( X = Cl, Br, I) subset, when the SD correcting terms are included, LRESC calculations match very well with 4c-DHF ones and those from the literature, with differences less than 1% for molecules containing up to three heavy atoms. We show that LRESC gives accurate values of EFG allowing the analysis of the electronic origin of relativistic effects in terms of well known nonrelativistic operators.