Covalent bond orders and atomic valences from correlated wavefunctions

A comparison is made between two alternative definitions for covalent bond orders: one derived from the exchange part of the two-particle density matr ix and the other expressed as the correlation of fluctuations (covariance) of the number of electrons between the atomic centers. Although these defin itions lead to identical formulae for mono-determinantal SCF wavefunctions, they predict different bond orders for correlated wavefunctions. It is sho wn that, in this case, the fluctuation-based definition leads to slightly l ower values of the bond order than does the exchange-based definition, prov ided one uses an appropriate space-partitioning technique like that of Bade r's topological theory of atoms in a molecule; however, use of Mulliken par titioning in this context leads to unphysical behaviour. The example of H-2 is discussed in detail, (C) 1999 Elsevier Science B.V. All rights reserved .