Periodic Hirshfeld Atom Refinement

Hirshfeld Atom Refinement (HAR) is a quantum crystallographic method for analyzing single-crystal X-ray diffraction data, providing accurate and precise structural parameters. Despite its success in predicting hydrogen-atom parameters, the application of HAR is fundamentally limited to molecular crystals. Inspired by two recently developed HAR versions that employ periodic-boundary conditions, here we introduce a new variant of periodic HAR (pHAR) that is applicable to any periodic-network structure while remaining compatible with conventional HAR by using atom-centered Gaussian orbitals with a Bloch wave formalism. pHAR was tested against high-quality single-crystal diffraction data for boranes and borates comprising N–H and B–H bonds in different chemical environments. The results demonstrate a close agreement of X–H bond lengths with reference data from neutron-diffraction experiments with improved precision. Using pHAR, this study has nearly doubled the previously available body of reliable experimental structural data on B–H bonds.