title: Information-scattering perspective on orbital hybridization.
abstract: Within the communication theory of the chemical bond, the transformation of atomic orbitals (AO) into molecular orbitals (MO) generates the information system for the associated electronic promotion of AOs in a molecule. It consists of the two orbital-mixing stages involving AOs and MOs, and one MO-occupation subchannel. The conditional-entropy and mutual-information descriptors of this resultant "communication" system, which measure the average "noise" and the amount of information in the molecular channel, provide novel information-theoretic measures of the system bond covalency and ionicity, respectively. This information-theoretic approach to the many-center probability-scattering in AO resolution is now applied to the one-center orbital transformations to examine the entropic indices of an effective promotion of the canonical AO in alternative valence states of an atom, identified by different occupations of hybrid orbitals (HO). This phenomenon is first illustrated and tested using the simplest scheme of mixing two atomic orbitals in a generalized sp hybridization. The conditions for the maximum of the AO-promotion covalency are examined, and the shape independence of the orbital channels and their entropy/information descriptors for the equalized probability weights of HO in the specified atomic valence state is commented upon. Entropic indices are then generated for selected valence states of the carbon atom, resulting from different hybridization schemes, in order to characterize their complementary aspects of the system electron polarization (one-center ionicity) and electron delocalization (one-center covalency). The interpretation of these components as measures of a degree of the acquired "order" and surviving "disorder" (electron uncertainty) in the valence state is also given. These results are found to generally agree with intuitive expectations. The exact HO-occupation subchannel is derived, which reproduces the average AO occupations in the valence state. This approach is also proposed for the multicenter probability scattering in molecules, via the system occupied MO, in probing the system chemical bonds.
authors.affiliation: Department of Theoretical Chemistry, Jagiellonian University, Ingardena 3, 30-060 Cracow, Poland. nalewajs@chemia.uj.edu.pl
authors.forename: Roman F
authors.initials: RF
authors.lastname: Nalewajski