Through-space and through-bridge interactions in the correlation analysis of chemical bonds

The formalism of the through-space and through-bridge communications proposed by Nalewajski within the framework of the Orbital Communication Theory is used to evaluate the correlation effect between electron populations of two chemical bonds. Proposed in this paper purely-probabilistic formalism defines the correlation between two chemical bonds as determined by the difference between appropriately normalized fourth-order joint probabilities corresponding to direct (through-space) and indirect (through-bridge) communication within a four-state time-homogeneous Markov chain. Alternative bond-correlation coefficient introduced earlier by Yamasaki and Goddard is based on the concept of the hierarchy of statistical covariance operators. The proposed correlation coefficient requires computing only the second-order probability terms when working within the condensed-atomic resolution and thus they are far less computationally expensive making them suitable for correlation analysis of chemical interactions between large molecular fragments. (C) 2013 Elsevier B.V. All rights reserved.