Irreducible Charge Density Matrices for Analysis of Many-Electron Wave Functions

A novel procedure for deriving multicenter bond indices on the basis of irreducible spinless charge density matrices that are naturally introduced as in the Ursell–Mayer theory is presented. Unlike earlier schemes using central moments of the charge operator, the procedure presented here leads to a proper definition of multicenter bond indices for an arbitrary number of atoms. Formal relationships and numerical techniques for the typical configuration interaction (CI) approaches, up to full CI, are given and illustrated with simple molecular systems. Comparison of the molecular orbital and full CI results indicates strong electron correlation effects, especially for the 3-center and 4-center bond indices. Excited state multicenter bond indices are described within the CI singles approach. The problem of proper definition of atomic valence and bond indices for electronic states with nonzero spin is raised. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem 102: 582–601, 2005