Volume 150, number 3,4 CHEMICAL PHYSICS LETTERS 16 September 1988 zyxwvu TOPOLOGICAL PARTITIONING OF ELECTRON DENSITIES FROM SPIN-COUPLED WAVEFUNCTIONS David L. COOPER zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Department of Chemistry, University ofLiverpool, P.O. Box 147, Liverpool L69 3BX, UK and Neil L. ALLAN Research and Technology Department, ICI Chemicals and Polymers Ltd., P.O. Box 8, The Heath, Runcorn, Cheshire W A7 4QD, UK Received 12 May 1988; in final form 29 June 1988 The zero-flux surface criterion for partitioning the total molecular electron density is extended to deal with wavefunctions constructed directly from non-orthogonal orbitals. This topological analysis is used for total electron densities from spin-coupled wavefunctions to investigate the process of bond formation in the electronic ground states of LiH and BH, and to compare two different descriptions of the pyridine molecule. 1. Introduction An important concept in chemistry is that mole- cules are composed of atoms and functional groups with characteristic and transferable properties. Con- sequently, there have been many attempts to define the boundaries of atoms in molecules. One of the most interesting of these is based on an analysis of the topological properties of the gradient vector field Vp of the total charge density p. This approach has been developed extensively by Bader et al. [ 1,2]. The points at which the total electron density ex- hibits saddle points are known as “critical points”. It is possible to distinguish different types of critical point, such as those in bonds, rings and cages, ac- cording to the signs of the eigenvalues of the Hessian of p, A zero-flux surface is the set of trajectories of Vp which start at infinity (or another critical point) and terminate at a bond critical point. These are the only closed surfaces for which the gradient of the charge density normal to the surface is zero and they partition p into atomic fragments. This criterion for charge partitioning leads to additive fragment prop- erties which may be obtained by restricting the rel- evant integrations to the atomic subspaces. In particular, we may define the charges on individual atoms in molecules. In the present work, we extend this method to deal with wavefunctions constructed directly from non- orthogonal orbitals. We use topological partitioning of total electron densities from spin-coupled wave- functions to investigate the process of bond forma- tion in the electronic ground states of LiH and BH, and to compare two different descriptions of the pyr- idine molecule. The spin-coupled wavefunction #I consists of a single spatial configuration with one or- bital for each electron, and it includes all allowed modes of coupling together the spins of the electrons. The orbitals are expanded in a basis set of atom- centred functions, much as in MO theory, and are fully optimized without orthogonality or symmetry constraints. In general, the orbitals turn out to be distinct and non-orthogonal. This model produces accurate potential curves and properties, and its flex- ibility allows for all possible modes of dissociation. Additional electron correlation can be included in a Xi For recent reviews see ref. [ 31. 0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division ) 287