Electric field gradient in accurate quantum chemical calculations
The electric field gradients (EFGs) at the (non-spherical) nucleus contribute to atomic and molecular hyperfine structure and govern Nuclear Quadrupole Resonance (NQR) and M\"ossbauer spectra. EFGs provide a highly sensitive probe of local bonding, symmetry, and crystal defect geometry and electronic structure. The EFGs can be obtained from electronic structure calculations and can also be extracted from spectroscopic measurements, thus linking electronic structure theory and spectroscopic observables. In this work, we present a methodological study of EFGs for a range of molecules and crystalline materials, using both periodic boundary conditions and embedded cluster models, and compare the results with reported experimental data. We analyze the sensitivity of EFG values to details of the calculations, such as the selection of the model Hamiltonians, basis sets, and the geometries of molecules and crystals. We also address persistent differences in EFG sign conventions and tensor definitions employed in the literature and in widely used quantum chemistry codes. While the EFG sign does not affect zero B-field NQR spectra, they can become critical in Mossbauer spectroscopy or when the quadrupolar interactions are combined with other interactions of the nucleus with the environment. Together, our systematic study results provide practical guidelines for computing, interpreting, and exploiting EFGs as quantitative descriptors of electronic structure and chemical environment.