Orbital-communication channels

Scheme 1.13 The orbital-communication channels for the localized M—La bond in the fixed-input approach, for P = Q = 1/2, and the singly occupied antibonding MO covalent (molecular input Panel a) and ionic (promolecular input Panel b).

After a brief summary of the molecular and MO-communication systems and their entropy/information descriptors in OCT (Section 2) the mutually decoupled, localized chemical bonds in simple hydrides will be qualitatively examined in Section 3, in order to establish the input probability requirements, which properly account for the nonbonding status of the lone-pair electrons and the mutually decoupled (noncommunicating, closed) character of these localized a bonds. It will be argued that each such subsystem defines the separate (externally closed) communication channel, which requires the individual, unity-normalized probability distribution of the input signal. This calls for the variable-input revision of the original and fixed-input formulation of OCT, which will be presented in Section 4. This extension will be shown to be capable of the continuous description of the orbital(s) decoupling limit, when AO subspace does not mix with (exhibit no communications with) the remaining basis functions. 

It should be emphasized that these entropy/information descriptors and the underlying probabilities depend on the selected basis set, for example, the canonical AO of the isolated atoms or the hybrid orbitals (HOs) of their promoted (valence) states, the localized MO (LMO), etc. In what follows we shall examine these IT descriptors of chemical bonds in illustrative model systems. The emphasis will be placed on the orbital decoupling in the molecular communication channels and the need for appropriate changes in their input probabilities, which weigh the contributions to the average information descriptors from each input. 

The OCT has recently been extended to cover many orbital effects in the chemical bond and reactivity phenomena [38, 68-70]. The orbital communications have also been used to study the bridge bond order components [71, 72] and the multiple probability scattering phenomena in the framework of the probability-amplitude channel [73]. The implicit bond-dependency origins of the indirect (bridge) interactions between atomic orbitals in molecules have also been investigated [74],... 

R.F. Nalewajski, Information origins of the chemical bond Bond descriptors from molecular communication channels in orbital resolution, Int. J. Quantum. Chem. 109 (2009) 2495. 

There are obvious normalization (sum) rules to be satisfied by these input-dependent probabilities. Consider first the completely coupled molecular channel, in which all orbitals interact chemically, thus exhibiting nonvanishing direct and/or indirect communications with the system remainder. In this case all molecular inputs have to be effectively probed to the full extent of the unit condensed probability of the molecule as a whole ... 

It follows from the input probabilities in Scheme 1.2 that in the limit of the decoupled (lone-pair) orbital doubly occupied AO in the channel input is then deterministically transmitted to the same AO in the channel output, with the other (unoccupied) AO not participating in the channel communications, so that both orbitals do not contribute to the resultant bond indices. Therefore, the flexible-input approach correctly accounts for the MO shape decoupling in the chemical bond, which was missing in the previous, fixed-input scheme. 

The orbital information system involves the complete sets of AO events in the channel input a = xJ and the channel output b = x j. In this description, the AO-> AO communication network is determined by the conditional probabilities... 

The conditional probabilities of Equation 8.24 determine the molecular information channel for the direct communications between AO, which generate the associated covalency (noise) and ionicity (information flow) descriptors of chemical bonds. One similarly derives the corresponding entropy/information mnltiplicities for the indirect interactions between the specified (terminal) orbitals Xj from descriptors of the associated AO information cascades, including the most important (chemical) bridges [10,58,60]. These directed indices of bridge interactions have been shown to compare favorably with the generalized Wiberg measures of Equation 8.43. 

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