Ab initio theoretical study of three-centre bonding on the basis of bond index

Various methods of derivation of a multi-centre bond index and its physical significance are briefly discussed. The usefulness of the bond index model for the study of three-centre (3c) bonding is illustrated by taking a number of examples chosen from earlier calculations. The origin of the sign of 3c bond indices (I-ABC) predicted for three-centre two-electron (3c-2e) and three-centre four-electron (3c-4e) bonds is investigated using simple models with different bonding topologies. Some examples are given highlighting the role of I-ABC in elucidating the nature of bonding in controversial molecules. The bond index and the effective pair population models are compared and shown to be equivalent for an RHF wave function and even-centre bond indices. It is concluded that despite some inherent limitations such as the basis set sensitivity the bond index model provides a quite satisfactory description of 3c bonding. (C) 2000 Elsevier Science B.V. All rights reserved.