, Volume 51, Issue 1, pp 7-20,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 06 Oct 2012

Information-theoretic multiplicities of chemical bond in Shull’s model of H2

Abstract

Alternative information-theoretic (IT) measures of the chemical bond multiplicity and its covalent/ionic composition in the orbital communication theory (OCT) are examined using Shull’s natural orbital (NO) model of the homopolar bond in H2. In OCT a molecule is treated as an information (probability-scattering) system, generated by the network of conditional probabilities (from the quantum mechanical superposition principle) linking elementary events of the adopted perspective. For the first time this atomic orbital (AO) invariant, two-NO description of Shull allows one to examine in several alternative representations the behavior of the previously adopted IT indices, of the channel average communication noise (OCT-covalency) and information flow (OCT-ionicity), with changing internuclear distance R, from the united atom (R = 0 ) to the separated atoms limit (SAL) (R → ∞). The adopted references include the two-electron atomic and ionic functions of the model, as well as the alternative one-electron functions, of the AO and NO sets, respectively. The numerical results for the Wang function description of H2 are reported and a general agreement with the accepted chemical intuition is tested. Joint probabilities of Shull’s reference states are linked to the energy partitioning. The incorrect SAL behavior of the OCT-ionicity index, giving rise to the constant (interaction independent) overall multiplicity measure, emphasizes a need for a revision of these IT bond descriptors. The modified set of indices is proposed, reflecting the complementary localization (determinicity) and delocalization (indeterminicity) aspects of the communication system in question. The novel IT-ionicity now reflects the diagonal (intra-orbital, additive) information propagation in the molecular channel, while the modified IT-covalency accordingly measures the effect of its off-diagonal (inter-orbital, nonadditive) probability scatterings. These components are shown to give rise to the interaction strength dependent overall IT bond-order, which adequately reflects the chemical intuition.

Here A, A, and A respectively denote the scalar quantity, row vector and a square/rectangular matrix. The logarithm of the information measure is taken to an arbitrary but fixed base: log = log2 corresponds to information measured in bits (binary digits), while log = ln expresses the amount of information in nats (natural units): 1 nat = 1.44 bits.