Chemical bond descriptors from molecular information channels in orbital resolution

The inter and intraorbital flows of the Fisher and Shannon informations in the molecular communication networks defined in the condensed atomic orbital (AO) resolution are investigated, and the effect of the basis set overlap is examined. The Schrödinger equation is interpreted as solution of the variation principle for the extreme Fisher information, subject to the wave‐function‐normalization (geometric) and potential‐energy (physical) constraints. Its orbital contributions determine the information scattering of the underlying Fisher channel in the adopted AO basis set. This communication network is compared with the associated information system of the Shannon theory of communication. The new set of conditional probabilities between orbitals is compared to that used in the previous, sequential‐cascade approach to the effective information promotion of AO in the molecular environment. Both geometrical and physical probabilities are reexamined using the quantum‐mechanical superposition principle. The former characterizes the whole orbital space, whereas the latter describes only its occupied part, which determines the system chemical bonds. It is argued that the squares of corresponding elements of the charge and bond‐order (CBO) matrix of the LCAO MO theory replace in the physical set of conditional probabilities the corresponding squares of the overlap integrals, which determine the geometrical set. The chain‐rule interpretation of conditional probabilities is given. The modified 2‐AO channel reproduces fully the earlier predictions from the molecular information channel in atomic resolution. The familiar bond criteria for an effective mixing of AO into molecular orbitals (MO) are shown to remain valid in the communication theory of the chemical bond (CTCB). © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009