HgH₂meets relativistic quantum crystallography. How to teach relativity to a non-relativistic wavefunction

Abstract

The capability of X-ray constrained wavefunction (XCW) fitting to introduce relativistic effects into a non-relativistic wavefunction is tested. It is quantified how much of the reference relativistic effects can be absorbed in the non-relativistic XCW calculation when fitted against relativistic structure factors of a model HgH2 molecule. Scaling of the structure-factor sets to improve the agreement statistics is found to introduce a significant systematic error into the XCW fitting of relativistic effects.

Accurate crystal structures and chemical properties from NoSpherA2

“…Therefore, to overcome these drawbacks, it is necessary to collect both very high-quality low-order data to capture the hydrogen-atom signal and high-resolution data to reduce truncation errors. 97 However, the experimental X-ray diffraction data of compounds containing heavy elements are very often affected by systematic problems such as significant absorption and radiation-damage effects. 39,98 Here, we test to which extent a very sophisticated theoretical electron-density model underlying the refinement (see Section 2.5) can help to interpret the diffraction pattern of the osmium hexahydride OsH 6 (PC 12 H 19 ) 2 .…”

“…It is worth noting that the OsH 6 (PC 12 H 19 ) 2 measurement used here is not of especially inferior quality, but rather represents a standard measurement as it is nowadays routinely obtained for service measurements of coordination and organometallic compounds. Therefore, we use this example to have a closer look at the problem of truncation effects caused by limited resolution because it was shown recently in ref. 97 that even at resolutions as high as d = 0.20 Å, core and outer-core electron-density distributions of a mercury hydride cannot be reproduced at all from structure factors, regardless of the sophistication of the quantum-crystallographic model.…”

“…Therefore, we use this example to have a closer look at the problem of truncation effects caused by limited resolution because it was shown recently in ref. 97 that even at resolutions as high as d ¼ 0.20 Å, core and outer-core electron-density distributions of a mercury hydride cannot be reproduced at all from structure factors, regardless of the sophistication of the quantum-crystallographic model. Fig.…”

“…Therefore, to overcome these drawbacks, it is necessary to collect both very high-quality low-order data to capture the hydrogen-atom signal and high-resolution data to reduce truncation errors. 97 However, the experimental X-ray diffraction data of compounds containing heavy elements are very oen affected by systematic problems such as signicant absorption and radiation-damage effects. In all HARs reported in Table 4, the Os-H distances were rened freely, while some restraints on the hydrogen atom anisotropic displacement parameters were applied, and one hydrogen atom was rened isotropically.…”

X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review

“…XCWs have also been obtained from structure factors generated from theoretical ab initio wavefunctions, with the aim of understanding to what extent (magnitude, accuracy) electron correlation, polarization by the crystal field and relativistic effects could be retrieved from the structure factors (Buc ˇinsky ´et al, 2016;Genoni et al, 2017;Ernst et al, 2020;Podhorsky ´et al, 2021;Macetti et al, 2021). For example, Genoni et al (2017) demonstrated that electron correlation effects in the valence region of the electron density could be recovered, provided high-resolution data was downweighted, whereas Buc ˇinsky ´et al (2016) quantified relativistic effects in the electron density, and under what conditions such effects might be detected experimentally.…”