The full topology of the Laplacian of the electron density: scrutinising a physical basis for the VSEPR model

Abstract

Within the framework of quantum chemical topology (QCT) the function L(r), which equals the negative of the Laplacian of the electron density, has been proposed before as a physical basis for the valence shell electron pair repulsion (VSEPR) model. The availability of a new algorithm to integrate property densities over the basins of L(r) enabled a re-evaluation of this physical basis. We optimised a set of nine molecules at B3LYP/6-311+G(2d,p) level and partitioned the corresponding L(r) function for each molecule into basins. For the first time we visualise these basins in L(r), by directly showing their boundaries. We identify the basins in L(r) with the domains of the VSEPR model. Observations drawn from the populations and volumes of L-basins are contrasted with the three subsidiary VSEPR postulates. We find unexpectedly small populations, nearer to one than to two, for non-hydrogen cores and bonding domains, and populations much larger than two for non-bonding domains. We conclude that non-bonding or lone pairs have larger domains than bonding pairs in the same valence shell, in accordance with VSEPR. We also confirm that double and triple bond domains are larger than single-bond domains. However we cannot substantiate the effect of the electronegativity of central atom or ligand on the volume of bonding domains. In summary, the full topology of L(r) supports two out of three subsidiary VSEPR postulates.