## 6 HSAB Principle Revisited  
The physical equivalence of reactivity concepts formulated in the energy and resultant gradient-information representations has direct implications for OCT, in which one treats a molecule as an information network propagating signals of the AO origins of electrons in the bond system determined by the configuration occupied MO. It has been argued that elements of the CBO matrix \(\boldsymbol{\gamma}=\left[\gamma_{k,l}\right]\) of Equation (26), weighting factors in Equation (24), determine amplitudes of conditional probabilities defining molecular (direct) communications between AO. Entropic descriptors of such information channel generate the entropic bond orders and measures of their covalent/ionic components, which ultimately facilitate an IT understanding of molecular electronic structure in chemical terms [7; 19; 20; 21; 22; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. The communication \"noise\" (orbital indeterminicity) in this network, measured by the channel conditional entropy, is due to the electron delocalization in the bond system of a molecule. It represents the system overall bond \"covalency\", while the channel information \"capacity\" (orbital determinicity), reflected by the mutual information of the molecular communication network, measures its resultant bond \"iconicity\". The more scattering (indeterminate) is the molecular information system, the higher its covalent character; a more deterministic (less noisy) channel thus represents a more ionic molecular system. These two bond attributes thus compete with one another. In chemistry, the bond covalency, a common possession of electrons by interacting atoms, is indeed synonymous with an electron delocalization generating a communication noise. A classical example of a purely covalent interaction constitute bonds connecting identical atoms, e.g., hydrogens in H\({}_{2}\) or carbons in ethylene, when the interacting AO in the familiar MO diagrams of chemistry exhibit the same AO energies. The bond ionicity accompanies large differences in electronegativities, generating a substantial CT between the interacting atoms. Such bonds correspond to a wide separation of AO energies in MO diagrams. The ionic bond component diminishes noise and introduces more determinicity into AO communications, thus representing the bond mechanism competitive with the bond covalency. One of the celebrated (qualitative) rules of chemistry deals with stability preferences in molecular coordinations. The HSAB principle [84; 85; 106] predicts that chemically hard (H) acids prefer to coordinate hard bases in the [HH] complexes A-B, and soft (S) acids prefer to coordinate soft bases in the [SS] complexes, whereas the \"mixed\" [HS] or [SH] coordinations, of hard acids with soft bases or of soft acids with hard bases, are relatively unstable. Little is known about the communication implications of this principle. In such a communication perspective on reactive systems the H and S reactants correspond to internally ionic (deterministic) and covalent (noisy) substrate channels, respectively. The former involves relatively localized communications between AO, while the latter corresponds to delocalized probability scatterings between the basis states. In the reactivity context, the following additional questions arise:  
What is an overall character of communications responsible for the mutual interaction between reactants? How does the HSAB rule influence the inter-reactant propagations of information, i.e., how do the [HH] and [SS] preferences shape the inter-reactant communications in these complexes? Do the S substrates in [SS] complex predominantly interact \"covalently\", and H substrates in the [HH] complex \"ionically\"? In the frontier electron (FE) [81; 82; 83] approach to molecular interactions and CT phenomena, the orbital energy of the substrate highest occupied MO (HOMO) determines its donor (basic) level of the chemical potential, while the lowest unoccupied MO (LUMO) energy establishes its acceptor (acidic) capacity (see Figure 4).