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 matrix and the other expressed as the correlation of fluctuations (covariance) of the number of electrons between the atomic centers. Although these definitions lead to identical formulae for mono-determinantal SCF wavefunctions, they predict different bond orders for correlated wavefunctions. It is shown that, in this case, the fluctuation-based definition leads to slightly lower values of the bond order than does the exchange-based definition, provided one uses an appropriate space-partitioning technique like that of Baderʹs topological theory of atoms in a molecule; however, use of Mulliken partitioning in this context leads to unphysical behaviour. The example of H2 is discussed in detail.