Two-component relativistic calculations of electric-field gradients using exact decoupling methods: Spin-orbit and picture-change effects

Electric field gradients (EFGs) for heavy nuclei in diatomic molecules (hydrogen halides and group-13 iodides), uranyl (UO2 ²⁺), and a uranyl carbonate complex, were computed with different formally exactly (or nearly exactly) decoupled two-component relativistic Hamiltonians: the "exact two-component" (X2C) method, the Barysz-Sadlej-Snijders (BSS) approach, and up to 35th order in the Douglas-Kroll-Hess (DKH) expansion, utilizing a new implementation in the open-source NWChem quantum chemistry package. Results from two-component Hartree-Fock and density functional theory (DFT) calculations at the scalar relativistic approximation as well as including spin-orbit coupling are reported. Picture-change corrected EFGs obtained with X2C, BSS, and high-order DKH are shown to be numerically equivalent. Effects from spin-orbit coupling on the EFGs tend to be moderate but should not be excluded for reliable predictions. Picture-change effects on the EFG of a heavy atom can be as large as the correct picture-change corrected value, as is shown for the uranium EFG in the uranyl systems. The results demonstrate the necessity of simultaneously including spin-orbit and picture-change effects in calculations of heavy atom EFGs.