Additive and non-additive information channels in orbital communication theory of the chemical bond

The molecular communication system in the resolution of the basis functions chi = {chi (X)} contributed by the molecule constituent atoms {X}, the key concept of the Orbital Communication Theory (OCT) of the chemical bond, is introduced and its information-theoretic (IT) bond descriptors are summarized. The additive and non-additive components of these molecular information channels are identified. The former involve only the internal (one-center) communications {X -> X} between the basis functions chi (X) of each bonded atom X, determined by the associated (diagonal) block P(chi (X)|chi (X)) of the molecular conditional probabilities, which are responsible for the intra-atom promotion to its effective valence state. The latter accordingly involve only the external (two-center) communications between the contributed AO of each pair of bonded atoms, {Y -> X and X -> Y}, generated by the off-diagonal blocks of conditional probabilities P(chi (X)|chi (Y)) and P(chi (Y)|chi (X)),X not equal Y, respectively, which are responsible for the inter-atomic bonding effects in the molecule. Both these probability scatterings ultimately determine the resultant multiplicities of the system chemical bonds. The input-ensemble average value of the channel conditional-entropy, which measures its communication "noise" due to electron delocalization via all chemical bonds, measures the IT-covalency in the molecule, while the complementary descriptor of the ensemble average value of the network mutual-information (information-capacity) reflects the electron localization effects and measures the system IT-ionic component. The illustrative example of the localized chemical bond originating from the interaction between two atomic orbitals is reexamined in some detail and the bond-weighted ensemble approach to chemical interactions in diatomic molecular fragments is discussed within the standard Restricted Hartree-Fock theory. In diatomic systems such treatment exactly reproduces the familiar bond index of Wiberg and provides its resolution into the complementary IT-covalent and IT-ionic components. The operator formulation of the probability-scattering phenomena in molecules is given and the probability-amplitude channel defined by the first-order density matrix is introduced. The AIM internal and external eigenvalue problems of this Charge-and-Bond-Order matrix are introduced and a similar approach to probability propagation matrices/operators is suggested.