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.