Post-Hartree-Fock methods for Hirshfeld atom refinement: are they necessary? Investigation of a strongly hydrogen-bonded molecular crystal

Hirshfeld atom refinement (HAR) is a method for refining X-ray crystal structures that is able to provide bond lengths involving hydrogen atoms in statistical agreement with those derived from neutron diffraction data, provided the data reach 0.8 Å resolution. Rather than using tabulated spherical atomic structure factors, HAR uses “tailor made” aspherical atomic structure factors obtained directly from quantum chemical calculations. Despite the very good results obtained so far, which make HAR an emerging refinement method of modern crystallography, until now all the Hirshfeld atom refinements were exclusively based on Hartree-Fock (HF) or density functional theory (DFT) methods, but never on the so-called post-HF techniques of quantum chemistry. Post-HF methods exploit more sophisticated multi-determinant wavefunctions and, consequently, should provide more accurate electron densities for the refinements. For this reason, for the first time we have performed HARs based on two well-known post-HF strategies (MP2 and Coupled Cluster) combined with three different basis-sets (def2-SVP, def2-TZVP and def2-TZVPP). The obtained results have been afterwards analyzed and compared to those resulting from neutron and other Hirshfeld atom refinements, the latter relying on Hartree-Fock and DFT (BLYP and B3LYP) calculations in order to evaluate if the use of more sophisticated and expensive approaches of quantum chemistry can improve the performances of the HAR technique.