The full topology of the Laplacian of the electron density: scrutinising a physical basis for the VSEPR model Nathaniel O. J. Malcolmy and Paul L. A. Popelier* Dept. of Chemistry, UMIST, Manchester, UK M60 1QD Received 22nd November 2002, Accepted 16th January 2003 First published as an Advance Article on the web 14th May 2003 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. 1. Introduction Chemistry benefits from consistency between its concepts and the properties of molecular wave functions obtained by modern computational schemes. In other words, the rules, models and explanations that chemists have introduced over the years ultimately need to find a physical basis. Quantum chemical topology (QCT) 1–3 is an attractive way to accomplish this goal. QCT captures chemical information emerging from contemporary mathematical expressions of molecular wave functions. In this paper we focus on finding a physical basis for the valence shell electron pair repulsion (VSEPR) model by examining the full topological characteristics of the function L(r) ¼c 2 r(r), which is the negative of the Laplacian of the electron density. The VSEPR model, 4,5 also known as the Gillespie–Nyholm rules, 6 has for many years provided a rationale for molecular geometry in the spirit of Lewis structures. The predecessor of the VSEPR model, already formulated in 1940 by Sidgwick and Powell, 7 stated, on the basis of structures of singly bonded AX n molecules known at the time, that two pairs of electrons in a valence shell have y Current address: Tripos UK Ltd., Sunningdale House, Caldecotte Lake Drive, Milton Keynes, UK MK7 8LF. DOI: 10.1039/b211650m Faraday Discuss., 2003, 124, 353–363 353 This journal is # The Royal Society of Chemistry 2003