Molecular information channels

In OCT, the entropy/information indices of the covalent/ionic components of all chemical bonds in a molecule represent the complementary descriptors of the average communication noise and the amount of information flow in the molecular information channel. The molecular input p(a) = p generates the same distribution in the output of the molecular channel,... 

Scheme 1.4 The molecular information channel of it electrons in allyl and its overall IT bond indices.

R.F. Nalewajski, Orbital resolution of molecular information channels and stockholder atoms, Mol. Phys. 104 (2006) 2533. 

R.F. Nalewajski, Chemical bond descriptors from molecular information channels in orbital resolution, Int. J. Quantum. Chem. 109 (2009) 425. 

In typical SCF LCAO MO calculations, the lone pairs of the valence and inner electronic shells can strongly affect the overall IT descriptors of the chemical bonds. Elimination of such lone-pair contributions in the resultant IT bond indices requires an ensemble (flexible input) approach [9,10,55]. In this scheme of determining the IT bond descriptors of diatomic fragments in molecules, the joint (bond) probabilities of two AO centered on different atoms constitute the input probabilities of the molecular information channel. Indeed, such probabilities reflect the simultaneous participation of the given pair of basis functions in interatomic chemical bonds so that this ensemble approach effectively projects out the spurious contributions attributable to inner-shell and outer-shell AO, which are excluded from mixing into the... 

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. 

Keywords Bond information probes Bond localization Chemical bonds Chemical reactivity Contra-gradience criterion Covalent/ionic bond components Direct/indirect bond multiplicities Entropic bond indices Fisher information Information theory Molecular information channels Orbital... 

The conditional probabilities of Eq. (26) determine the molecular information channel for the mutual communications between AO, which generate the associated... 

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. 

Scheme 1.1 The molecular information system modeling the chemical bond between two basis functions /=(o,b) and its entropy/information descriptors. In Panel b, the corresponding nonbonding (deterministic) channel due to the lone-pair hybrid 6° is shown. For the molecular input p = (P, Q), the orbital channel of Panel a gives the bond entropy-covalency represented by the binary entropy function H[P). For the promolecular input p° = (1/2,1/2), when both basis functions contribute a single electron each to form the chemical bond, one thus predicts H[p°] = 1 and the bond information ionicity / = 1 — H(P). Hence, these two bond components give rise to the conserved (P-independent) value of the single overall bond multiplicity N = I + S = 1.

Scheme 1.9 The molecular partial information channels and their entropy/information descriptors of the chemical interaction between the adjacent (Panel a) and terminal (Panel b) AO in the jt-electron system of allyl.

This situation is also encountered if one considers the coupling between two intramolecular manifolds A and B. Here, the energy that can be captured by B from A is of interest. On its transfer path from A to B, via a molecular coupling channel, the energy can be transformed by a molecular rotor into motion [30]. Lloyd concluded that any quantum system that can obtain information (energy) about another quantum system can form the basis of a quantum demon [32]. Problematic is that a non-invasive observer is required to measure this exchange of information energy between the two nanosystems... 

Knowledge of the underlying nuclear dynamics is essential for the classification and description of photochemical processes. For the study of complicated systems, molecular dynamics (MD) simulations are an essential tool, providing information on the channels open for decay or relaxation, the relative populations of these channels, and the timescales of system evolution. Simulations are particularly important in cases where the Bom-Oppenheimer (BO) approximation breaks down, and a system is able to evolve non-adiabatically, that is, in more than one electronic state. 

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