1 January 1999 Ž . Chemical Physics Letters 299 1999 1–8 Covalent bond orders and atomic valences from correlated wavefunctions ´ a, ) b b Janos G. Angyan , Edina Rosta , Peter R. Surjan ´ ´ ´ ´ a Laboratoire de Chimie theorique, UMR CNRS No. 7565, Institut Nanceien de Chimie Moleculaire, UniÕersite Henri Poincare, B.P. 239, ´ ´ ´ ´ ´ 54506 VandoeuÕre-les-Nancy, France ` b Theoretical Chemistry Laboratory, UniÕersity EotÕos Lorand, P.O. Box 32, H-1518 Budapest 112, Hungary ¨ ¨ ´ Received 22 October 1998 Abstract A comparison is made between two alternative definitions for covalent bond orders: one derived from the exchange part Ž . 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 Bader’s topological theory of atoms in a molecule; however, use of Mulliken partitioning in this context leads to unphysical behaviour. The example of H is discussed in 2 detail. q 1999 Elsevier Science B.V. All rights reserved. 1. Introduction The concept of bond order has proved to be a valuable tool for extracting chemical information wx coded in molecular wavefunctions 1 . A great deal of effort has been spent in the past to find an appropriate definition for this quantity, which is not w x observable in the usual sense 2–13 . The progress in this field has been reviewed up to 1992 by Sanni- w x grahi 14 . A class of particularly successful bond-order defi- w x nitions has emerged 5,6,8 from ab initio calcula- tions by a generalization of the earlier concept of ) Corresponding author. Fax: q33 3 8391 2530; e-mail: janos.angyan@lctn.u-nancy.fr wx Wiberg indices 4 , widely used in the past for semi-empirical wavefunctions. Perhaps the most sys- tematic work has been done by Mayer, who showed that one can establish a direct relationship between wx the bond order 8 and the energy partitioning in the w x ‘chemical hamiltonian approach’ 15 . The leading monopole term of the diatomic contribution to the total molecular energy has been found to be: E monopole s qq rR AB A B AB ˆ ˆ ˆ ˆ ² :² : ² : y N N y NN rR , 1 Ž. ž / A B A B AB ˆ ² : where q s Z y N is the net atomic charge of A A A ˆ atom A and N is the operator of the number of A electrons on atom A, bearing a nuclear charge of Z . A In addition to the classical Coulomb interaction of 0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 98 01255-X