# Periodic Hirshfeld Atom Refinement

## TL;DR

This paper introduces a new method called periodic Hirshfeld Atom Refinement (pHAR) that improves the accuracy of structural data for periodic materials containing B–H and N–H bonds.

## Contribution

The novel contribution is pHAR, a periodic version of HAR that extends its applicability to periodic-network structures.

## Key findings

- pHAR results show close agreement with neutron-diffraction data for X–H bond lengths.
- pHAR nearly doubled the available reliable experimental data on B–H bonds.
- The method is compatible with conventional HAR using Gaussian orbitals and Bloch wave formalism.

## Abstract

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.