Relativistic corrections to the electric field gradient given by linear response elimination of the small component formalism

Abstract

This article is concerned with the analysis of relativistic corrections to the electric field gradients (EFGs) via the linear response elimination of the small component scheme (LRESC). Originally developed for magnetic shielding constant, LRESC has been applied in many molecular properties and presented in this work describing EFG for the first time. Within LRESC we obtain relativistic corrections to EFG in terms of 1/c (the speed of light) formally showing that, up to first order (1/c 2), there are no virtual pair contributions; recovering the so‐called “no‐pair” approximation. Virtual pair contributions and triplet corrections arise at second order (1/c 4). To assess the LRESC description of EFGs at Hartree‐Fock and DFT levels, we applied it to a simple heavy atom containing set of benchmark molecular systems, HX (X = F, Cl, Br, I, and At), and to linear HgX 2 (X = Cl, Br, and I) molecules. Fully relativistic four‐component calculations were also done and taken as reference. The most important relativistic correction given by LRESC is a Mass‐velocity related contribution (ΔMv) which represents close to 80% of the nonrelativistic result for At in HAt molecule. For Hg in HgX 2 molecular systems, ΔMv is also the most important correction representing close to 60% of the nonrelativistic part. We also describe the overall behavior of LRESC corrections in HgX 2 molecules showing low varying results when the weight of the halogen, X , increases. In this kind of molecular system, correlation effects appear in combination to relativity, making them a challenging group to be studied. LRESC results are in very good agreement with previous results for halogen halides, but it shows a need of inclusion of higher order contributions, beyond 1/c 2, when applied to Hg in HgX 2 set, although LRESC describes accurately At atom, heavier than Hg.