R.F. Nalewajski, D.W. Szczepanik
, J. MrozekAdvances in Quantum Chemistry vol. 61
(ed. J.R. Sabin, E. Brandas), Chapter 1 (pp. 1−48), Elsevier, 2011. URL
Information-theoretic (IT) probe of molecular electronic structure, within the orbital-communication theory (OCT) of the chemical bond, uses the standard entropy/information descriptors of the Shannon theory of communication to characterize the scattering of electron probabilities and their information content throughout the system network of chemical bonds generated by the occupied molecular orbitals (MOs). Thus, the molecule is treated as information network, which propagates the "signals" of the electron allocation to constituent atomic orbitals (AOs) or general basis functions between the channel AO "inputs" and "outputs". These orbital "communications" are determined by the two-orbital conditional probabilities of the output AO events given the input AO events. It is argued, using the quantum-mechanical superposition principle, that these conditional probabilities are proportional to the squares of corresponding elements of the first-order density matrix of the AO charges and bond orders (CBO) in the standard self-consistent field (SCF) theory using linear combinations of AO (LCAO) to represent MO. Therefore, the probability of the interorbital connections in the molecular communication system is directly related to the Wiberg-type quadratic indices of the chemical bond multiplicity. Such probability propagation in molecules exhibits the communication "noise" due to electron delocalization via the system chemical bonds, which effectively lowers the information content in the output signal distribution, compared with that contained in probabilities determining its input signal, molecular or promolecular. The orbital information systems are used to generate the entropic measures of the chemical bond multiplicity and their covalent/ionic composition. The average conditional-entropy (communication noise, electron delocalization) and mutual-information (information capacity, electron localization) descriptors of these molecular channels generate the IT covalent and IT ionic bond components, respectively. A qualitative discussion of the mutually decoupled, localized bonds in hydrides indicates the need for the flexible-input generalization of the previous fixed-input approach, in order to achieve a better agreement among the OCT predictions and the accepted chemical estimates and quantum-mechanical bond orders. In this extension, the input probability distribution for the specified AO event is determined by the molecular conditional probabilities, given the occurrence of this event. These modified input probabilities reflect the participation of the selected AO in all chemical bonds (AO communications) and are capable of the continuous description of its decoupling limit, when this orbital does not form effective combinations with the remaining basis functions. The occupational aspect of the AO decoupling has been shown to be properly represented only when the separate communication systems for each occupied MO are used, and their occupation-weighted entropy/information contributions are classified as bonding (positive) or antibonding (negative) using the extraneous information about the signs of the corresponding contributions to the CBO matrix. This information is lost in the purely probabilistic model since the channel communications are determined by the squares of such matrix elements. The performance of this MO-resolved approach is then compared with that of the previous, overall (fixed-input) formulation of OCT for illustrative π-electron systems, in the Hückel approximation. A qualitative description of chemical bonds in octahedral complexes is also given. The bond differentiation trends in OCT have been shown to agree with both the chemical intuition and the quantum-mechanical description. The numerical Restricted Hartree-Fock (RHF) applications to diatomic bonds in representative molecular systems are reported and discussed. The probability weighted scheme for diatomic molecular fragments is shown to provide an excellent agreement with both the Wiberg bond orders and the intuitive chemical bond multiplicities.