Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

Abstract

The electrostatic contribution to the Mössbauer isomer shift of mercury for the series HgF n (n = 1, 2, 4) with respect to the neutral atom has been investigated in the framework of four-and two-component relativistic theory. Replacing the integration of the electron density over the nuclear volume by the contact density (that is, the electron density at the nucleus) leads to a 10% overestimation of the isomer shift. The systematic nature of this error suggests that it can be incorporated into a correction factor, thus justifying the use of the contact density for the calculation of the Mössbauer isomer shift. The performance of a large selection of density functionals for the calculation of contact densities has been assessed by comparing with finite-field four-component relativistic coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] calculations. For the absolute contact density of the mercury atom, the Density Functional Theory (DFT) calculations are in error by about 0.5%, a result that must be judged against the observation that the change in contact density along the series HgF n (n = 1, 2, 4), relevant for the isomer shift, is on the order of 50 ppm with respect to absolute densities. Contrary to previous studies of the 57 Fe isomer shift (F Neese, Inorg Chim Acta 332:181, 2002), for mercury, DFT is not able to reproduce the trends in the isomer shift provided by reference data, in our case CCSD(T) calculations, notably the non-monotonous decrease in the contact density along the series HgF n (n = 1, 2, 4). Projection analysis shows the expected reduction of the 6s 1/2 population at the mercury center with an increasing number of ligands, but also brings into light an opposing effect, namely the increasing polarization of the 6s 1/2 orbital due to increasing effective charge of the mercury atom, which explains the nonmonotonous behavior of the contact density along the series. The same analysis shows increasing covalent contributions to bonding along the series with the effective charge of the mercury atom reaching a maximum of around ?2 for HgF 4 at the DFT level, far from the formal charge ?4 suggested by the oxidation state of this recently observed species. Whereas the geometries for the linear HgF 2 and square-planar HgF 4 molecules were taken from previous computational studies, we optimized the equilibrium distance of HgF at the four-component Fock-space CCSD/aug-cc-pVQZ level, giving spectroscopic constants r e = 2.007 Å and x e = 513.5 cm -1 .Dedicated to Professor Pekka Pyykkö on the occasion of his 70th birthday and published as part of the Pyykkö Festschrift Issue.Electronic supplementary material The online version of this article

Modeling nuclear volume isotope effects in crystals

“…DHF calculations with the enhanced triple-ζ basis set used by Knecht et al (29) suggest that the double-ζ basis set used in this study slightly underestimates contact densities (and their sensitivity to the chemical environment) by roughly 3% relative to a set constructed with additional, sharp basis functions to describe wave functions near the Hg nucleus. CCSD(T) Hg/ 198 Hg substitution, for either functional.…”

“…Contact densities and isotopic energy shifts calculated with DHF, CCSD(T), and DFT-PAW models are also well correlated for mercury-bearing species. The main exception is HgF 4 , which Knecht et al (29) studied and discussed in detail as an example of an electronic structure that is not reproduced well by either DFT or DHF methods. In the present study and in that by Knecht et al, DFT models get the relative change in contact density from HgF 2 to HgF 4 backward, whereas the CCSD(T) results are correct in sense and magnitude; DHF models get the sense correct but overestimate the magnitude.…”

Perspective: Relativistic effects

“…184 DFT was compared to CCSD(T) reference data and found to under-perform. Isomer shift calculations have traditionally relied on determining the "contact" density, i.e., the density value at the nucleus of interest.…”

Theoretical 57Fe Mössbauer spectroscopy: isomer shifts of [Fe]-hydrogenase intermediates

“…Detailed analysis 25 shows that in a relativistic framework the contact density ρ 0 has contributions from atomic s 1/2 and p 1/2 orbitals only, from the large and small components, respectively. These contributions are compiled in Table Table 7 for the neutral iron atom.…”

“…23,24 The use of effective densities and the inclusion of relativity has also been considered by others and both effects have been shown to be of quantitative importance for heavier nuclei. 25,26 On the contrary, for iron both the role of relativity and the use of effective densities rather than contact densities remains less clear. An open question is thus to what extent relativistic effects should be included and whether spin-orbit coupling influences the isomer shift.…”