Theoretical Chemistry Accounts

, Volume 129, Issue 3–5, pp 631–650 | Cite as

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

  • Stefan Knecht
  • Samuel Fux
  • Robert van Meer
  • Lucas Visscher
  • Markus Reiher
  • Trond SaueEmail author
Regular Article


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 57Fe 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 non-monotonous 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 HgF4 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 HgF2 and square-planar HgF4 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 ω e = 513.5 cm−1.


Mössbauer spectroscopy Relativistic quantum chemistry Density functional theory Coupled cluster Contact density Mercury compounds Picture change effects 



We dedicate this paper to Pekka Pyykkö, a pioneer of relativistic quantum chemistry. With a unique combination of impressive chemical insight and judicious pragmatism, he has picked many of the bigger berries in the field, but graciously left some for others as well. We would like to thank one of the unknown referee’s for her/his elaborate report and comments which led to the discovery of an initial computational problem in the calculation of reaction energies and contact densities of the HgF4 compound. This issue has then been solved for the final version of this paper. S.K. thanks l’Université de Strasbourg (UDS) for a post-doctoral research grant and the supercomputer centers at ETH Zürich as well as UDS for ample computing time. M.R. and S.F. gratefully acknowledge financial support by ETH Zürich (Grant TH-26 07-3) and the Swiss national science foundation SNF (project no. 200020-132542/1). L.V. has been supported by NWO through the VICI programme.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Stefan Knecht
    • 1
  • Samuel Fux
    • 2
  • Robert van Meer
    • 3
  • Lucas Visscher
    • 3
  • Markus Reiher
    • 2
  • Trond Saue
    • 4
    Email author
  1. 1.Institute de Chimie de StrasbourgCNRS et Université de Strasbourg, Laboratoire de Chimie QuantiqueStrasbourgFrance
  2. 2.ETH Zurich, Laboratorium für Physikalische ChemieZurichSwitzerland
  3. 3.Amsterdam Center for Multiscale ModelingVU University AmsterdamHV AmsterdamThe Netherlands
  4. 4.Laboratoire de Chimie et Physique Quantique (CNRS UMR 5626), IRSAMCUniversité Paul SabatierToulouse cedexFrance

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