  Thiolate containing mercury(II) complexes of the general formula
[Hg(SR)$_n$]$^{2-n}$ have been of great interest since the toxicity of mercury
was recognized. $^{199}$Hg nuclear magnetic resonance spectroscopy (NMR) is a
powerful tool for characterization of mercury complexes. In this work, the Hg
shielding constants in a series of [Hg(SR)$_n$]$^{2-n}$ complexes are therefore
investigated computationally with particular emphasis on their geometry
dependence. Geometry optimizations and NMR chemical shift calculations are
performed at the density functional theory (DFT) level with both the
zeroth-order regular approximation (ZORA) and four-component relativistic
methods. The four exchange-correlation (XC) functionals PBE0, PBE, B3LYP and
BLYP are used in combination with either Dyall's Gaussian-type (GTO) or
Slater-type orbitals (STOs) basis sets. Comparing ZORA and four-component
calculations, one observes that the calculated shielding constants for a given
molecular geometry have a constant difference of $\sim$1070 ppm. This confirms
that ZORA is an acceptable relativistic method to compute NMR chemical shifts.
The combinations of 4-component/PBE0/v3z and ZORA/PBE0/QZ4P are applied to
explore the geometry dependence of the isotropic shielding. For a given
coordination number the distance between mercury and sulfur is the key factor
affecting the shielding constant, while changes in bond and dihedral angles and
even different side groups have relatively little impact.
