Relativistic corrections of the electric field gradient in dihalogen molecules XY (X, Y = F, Cl, Br, I, At) within the linear response elimination of the small component formalism

Abstract

We analyze the performance of the linear response elimination of the small component (LRESC) scheme to describe the electric field gradient (EFG), in dihalogen molecular systems, and also to give insight of the relativistic corrections. LRESC shows a good performance, providing results close to four-component (4c) ones for molecules containing atoms belonging up to the fifth row of the Periodic Table . When heavier nuclei are involved the difference among LRESC and 4c values reaches up to 5%. The main relativistic correction represents 80% of the nonrelativistic part for the heaviest molecule. LRESC can be applied at Hartree-Fock as well as Density Functional Theory levels, therefore we also analyze correlation effects on EFG showing that relativity enhances correlation effects and both effects are not additive. As an application of LRESC method, nuclear quadrupole moment calculations of some halogen nuclei are also carried out and compared with the most recent data.

Electric Field Gradient in Chiral and Tetrahedral Molecules within High-Order LRESC Formalism

“…for the bromine and iodine nuclei. For the astatine atom, the LRESC-HF result differs by less than 0.8 a.u from the 4c-DHF result; this represents a difference of only 3.1%, showing the good performance of the LRESC scheme reproducing the ⟨ q zz ⟩ value for an atom belonging to the sixth row of the periodic table. − For light atoms, such differences are vanishingly small.…”

“…4c-DHF and 4c-DFT calculations were carried out with the Dirac program package, 39 and the UKB prescription was applied, as in previous works, since EFG results are improved with respect to the restricted kinetic balance (RKB) prescription. 37,38,50 For ν(N) calculations using eq 11, the molecules were centered at the center of mass, and the EFG tensor was rotated into the principal axis system of the inertia tensor moment, following the convention used in refs 19 and 51. The nuclear contribution of EFG was added to the electronic contribution according to eq 1, while the nuclear quadrupole moments Q(N) for H, Cl, Br, and I were taken from ref 52.…”

“…Finally, Δ pqp comes from the application of the Dirac relation to the electronic contribution of the EFG coming from the small components of the 4c wave function, including the momentum operator p . All of them were first presented and evaluated in refs and . Finally, eqs and correspond to the spin-dependent relativistic corrections coming from the small and large components of the 4c wave function, respectively.…”

“…Dyall.cv4z basis sets were used for all nuclei in the 4c and NR calculations of EFG as well as the LRESC corrections. 4c-DHF and 4c-DFT calculations were carried out with the Dirac program package, and the UKB prescription was applied, as in previous works, since EFG results are improved with respect to the restricted kinetic balance (RKB) prescription. ,, …”

“…LRESC was first presented to describe the NMR nuclear magnetic shielding tensor as corrections of the relativistic molecular ground state with a nonconserving total number of particles. In the past decade, LRESC was developed to calculate several properties, and more recently, it was applied for EFG calculation. − …”