Towards improved accuracy of Hirshfeld atom refinement with an alternative electron density partition

Hirshfeld atom refinement (HAR) is generally the chosen method for obtaining accurate hydrogen atom parameters from X-ray diffraction data. Still, determination can prove challenging, especially in the case of atomic displacement parameters (ADPs). We demonstrate that such a situation can occur when the ADP values of the bonding partner of the hydrogen atom are not determined accurately. Atomic electron densities partially overlap and inaccuracies in the bonding neighbour ADPs can be partially compensated for with modifications to the hydrogen ADPs. We introduce a modified version of the original Hirshfeld partition: the exponential Hirshfeld partition, parameterized with an adjustable parameter (n) to allow control of the overlap level of the atomic electron densities which, for n = 1, is equivalent to the Hirshfeld partition. The accuracy of the HAR-like procedure using the new partition (expHAR) was tested on a set of organic structures using B3LYP and MP2 electron densities. Applying expHAR improved the hydrogen atom parameters in the majority of the structures (compared with HAR), especially in cases with the highest deviations from the reference neutron values. X-H bond lengths and hydrogen ADPs improved for 9/10 of the structures for B3LYP-based refinement and 8/9 for MP2-based refinement when the ADPs were compared with a newly introduced scale-independent similarity measure.