Hirshfeld atom like refinement with alternative electron density partitions

Abstract

Hirshfeld atom refinement is one of the most successful methods for the accurate determination of structural parameters for hydrogen atoms from X-ray diffraction data. This work introduces a generalization of the method [generalized atom refinement (GAR)], consisting of the application of various methods of partitioning electron density into atomic contributions. These were tested on three organic structures using the following partitions: Hirshfeld, iterative Hirshfeld, iterative stockholder, minimal basis iterative stockholder and Becke. The effects of partition choice were also compared with those caused by other factors such as quantum chemical methodology, basis set, representation of the crystal field and a combination of these factors. The differences between the partitions were small in terms of R factor (e.g. much smaller than for refinements with different quantum chemistry methods, i.e. Hartree-Fock and coupled cluster) and therefore no single partition was clearly the best in terms of experimental data reconstruction. In the case of structural parameters the differences between the partitions are comparable to those related to the choice of other factors. We have observed the systematic effects of the partition choice on bond lengths and ADP values of polar hydrogen atoms. The bond lengths were also systematically influenced by the choice of electron density calculation methodology. This suggests that GAR-derived structural parameters could be systematically improved by selecting an optimal combination of the partition and quantum chemistry method. The results of the refinements were compared with those of neutron diffraction experiments. This allowed a selection of the most promising partition methods for further optimization of GAR settings, namely the Hirshfeld, iterative stockholder and minimal basis iterative stockholder.

Keywords: GAR; HAR; Hirshfeld atom refinement; electron density partition; generalized atom refinement.

Figure 1

Hydrogen atom labelling schemes for the studied structures (a) urea and (b) oxalic acid dihydrate, produced using the iterative stockholder partition refinement with B3LYP/cc-pVTZ theory level and surrounding multipoles cluster. ADP values are shown at the 50% probability level (Mercury, Macrae et al., 2020 ▸).

Figure 2

Comparison of neutron and X-ray parameters of polar hydrogen atoms for refinements with various basis sets: (a) ΔR – the difference between X-ray and neutron measured bond lengths (error bars correspond to the X-ray bond length uncertainties), (b) 〈|ΔU _ij|〉 – the average absolute difference of the ADP tensor components, (c) ADP similarity index S ₁₂, (d) V _X/V _N ratio of X-ray and neutron thermal ellipsoids.

Figure 3

Comparison of the neutron and X-ray parameters of polar hydrogen atoms for refinements with various quantum chemistry methods: (a) ΔR – the difference between X-ray and neutron measured bond length (error bars correspond to the X-ray bond length uncertainties), (b) 〈|ΔU _ij|〉 – average absolute difference of ADP tensor components, (c) ADP similarity index S ₁₂, (d) V _X/V _N ratio of X-ray and neutron thermal ellipsoids.

Figure 4

Comparison of the neutron and X-ray parameters of polar hydrogen atoms for refinements with various representations of the crystal field (see text): (a) ΔR – the difference between X-ray and neutron measured bond lengths (error bars correspond to the X-ray bond length uncertainties), (b) 〈|ΔU _ij|〉 – the average absolute difference of ADP tensor components, (c) ADP similarity index S ₁₂, (d) V _X/V _N ratio of X-ray and neutron thermal ellipsoids.

Figure 5

Comparison of neutron and X-ray parameters of polar hydrogen atoms for refinements with HAR, TAAM and a model with standardized neutron bond lengths: (a) ΔR – the difference between X-ray and neutron measured bond lengths in mÅ (error bars correspond to the X-ray bond length uncertainties), (b) 〈|ΔU _ij|〉 – the average absolute difference of ADP tensor components, (c) ADP similarity index S ₁₂, (d) as in (a) but the least accurate methods were omitted to improve readability.

Figure 6

Hydrogen atoms in SPAnPS coloured according to the group (see text): (1) – green, (2) – white, (3) – dark red and (4) – cyan. Iterative Hirshfeld partition refinement with B3LYP/cc-pVTZ theory level and surrounding multipoles cluster. ADP values are shown at the 50% probability level (Mercury, Macrae et al., 2020 ▸).

Figure 7

Comparison of the neutron and X-ray parameters of polar hydrogen atoms for refinement with various electron density partitions: (a) ΔR (mÅ) – the difference between X-ray and neutron measured bond lengths (error bars correspond to the X-ray bond length uncertainties), Fig. S2 also includes B partition, (b) 〈|ΔU _ij|〉 – average absolute difference of ADP tensor components, (c) ADP similarity index S ₁₂, (d) V _X/V _N ratio of X-ray and neutron thermal ellipsoids.