Atomic and molecular volumes from three crystal tessellations: a comparison of the QTAIM, Hirshfeld, and Voronoi data

The volumes of atoms and molecules obtained by means of quantum theory of atoms in molecules (V_AM) in previously reported π and σ complexes were compared with those revealed from the Hirshfeld surfaces (V_HS) and the Voronoi tessellation (V_VD). For metal atoms, V_HS and V_VD are close to V_AM values. The Voronoi tessellation underestimates volumes of heavy and low-coordinated metal atoms by 27% in average, while for s- and d-metal ions in σ-complexes V_VD deviates from V_AM by 6% in average only. The Hirshfeld surfaces underestimate volumes of metal atoms in π-complexes by 17% and overestimate those in σ-complexes by 30% in average. Any correlation between atomic volumes of non-metals is absent; however, V_HS and V_VD values for polyatomic (even diatomic) molecules deviated from V_AM by 11% in average. All three methods indicate constancy of molecular volumes in crystals. Sensitivity of three methods to detect trends in atomic and molecular volumes over different datasets was discussed.