On the flexibility of the multipole model refinement. A DFT benchmark study of the tetra­kis­(μ-acetato)di­aquadicopper model system

The refinement flexibility of the Hansen–Coppens multipole model is tested on DFT calculated structure factors for the tetra­kis­(μ-acetato)di­aquadicopper model system. The Cu scattering factor performs the best of all the options tried for most of the monitored parameters despite the Cu²⁺ nature of the complex studied. The Hansen–Coppens model performs similarly well when comparing deviations among computational chemistry methods.

In this study, the flexibility of the multipole Hansen–Coppens (HC) model refinement is investigated on calculated structure factors from a DFT reference for the tetra­kis­(μ-acetato)di­aquadicopper model system (CCDC reference 1811668). The effect of the resolution [sin(θ)/λ], the Cu scattering factor, the inclusion of anisotropic displacement parameters and the positions of the atoms in the refinement are considered in terms of statistical error analysis, residual and deformation density maps, Atoms In Molecules parameters, d-orbital populations, and others. The choice of the neutral Cu scattering factor in the HC refinement is found to give the most satisfactory results for most of the monitored parameters, despite the formal Cu²⁺ nature of copper in the studied complex. In order to put the difference between the HC model and the reference DFT (BLYP functional) results on the right scale, several computational chemistry methods (B3LYP, Hartree–Fock, Møller–Plesset perturbation theory and Coupled Clusters Singles and Doubles) were compared with the chosen DFT reference. Differences in the magnitudes of the structure factors and AIM parameters are presented, including considerations of relativistic effects and periodic boundary conditions, i.e. a comparison of a molecular crystal calculation versus an isolated molecule in the crystal.