## 8 Communication Considerations  
These alternative coordinations in reactive systems can be also qualitatively approached within the communication theory of the chemical bond [9; 10; 11; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62]. To directly connect to the discussion of the preceding section, one again adopts the _site_-resolution on both reactants [see Equation (76)], in which the system communication (information) channel is defined by the network of conditional probabilities of observing in R\({}_{\alpha}\) the \"output\" (\"receiver\") fragment \(\lambda^{\prime}\), given the \"input\" (\"source\") site \(\lambda\):  
\[P_{\alpha}(\lambda^{\prime}|\lambda)=P_{\alpha}(\lambda^{\prime},\lambda)/P_{ \alpha}(\lambda)\equiv P_{\alpha}(\lambda{\rightarrow}\lambda^{\prime}), \qquad\quad\Sigma_{\lambda^{\prime}}\ P_{\alpha}(\lambda^{\prime}|\lambda)=1. \tag{103}\]  
Here, \(P_{\alpha}(\lambda)\) denotes the _site_-probability and \(P_{\alpha}(\lambda^{\prime},\lambda)\) stands for the _joint_-probability of the occurrence of the _two_-site event in the bond system of R\({}_{\alpha}\). They must satisfy the usual normalizations:\[\Sigma_{\lambda}\;[\Sigma_{\lambda^{\prime}}\;P_{\alpha}(\lambda^{\prime},\lambda)] =\Sigma_{\lambda}\;P_{\alpha}(\lambda)=1. \tag{104}\]  
The key CT sites in both reactants determine the overall chemical character of these subsystems in reactive complexes: the _acceptor_ (acidic) site in A, \(a_{\rm A}\), and the _donor_ (basic) site in B, \(b_{\rm B}\). These crucial fragments are accentuated by the bold symbols in Figure 3, where the dominating communications between the nearest neighbors in both coordinations are shown. The R\({}_{c}\) diagram in the Figure 3a shows that only the complementary arrangement exhibits the _direct_ communication \(b_{\rm B}{\rightarrow}a_{\rm A}\), reflected by a high conditional probability \(P_{c}(b_{\rm B}{\rightarrow}a_{\rm A})\), besides the _double_-cascade propagation \(b_{\rm B}{\rightarrow}[a_{\rm B}{\rightarrow}b_{\rm A}]{\rightarrow}a_{\rm A}\) of a relatively low probability,  
\[P_{c}(b_{\rm B}{\rightarrow}[a_{\rm B}{\rightarrow}b_{\rm A}]{\rightarrow}a _{\rm A})=P_{c}(b_{\rm B}{\rightarrow}a_{\rm B})\;P_{c}(a_{\rm B}{ \rightarrow}b_{\rm A})\;P_{c}(b_{\rm A}{\rightarrow}a_{\rm A})<<P_{c}(b_{\rm B }{\rightarrow}a_{\rm A}). \tag{105}\]  
The R\({}_{\rm HSAB}\) coordination Figure 3b generates two indirect (_single_-cascade) scatterings between the crucial sites \(a_{\rm A}\) and \(b_{\rm B}\):  
\[ \begin{array}{c}P_{\rm HSAB}(b_{\rm B}{\rightarrow}a_{\rm B}{\rightarrow}a _{\rm A})=P_{\rm HSAB}(b_{\rm B}{\rightarrow}a_{\rm B})\;P_{\rm HSAB}(a_{\rm B }{\rightarrow}a_{\rm A})\qquad\mbox{and}\\ P_{\rm HSAB}(b_{\rm B}{\rightarrow}b_{\rm A}{\rightarrow}a_{\rm A})=P_{\rm HSAB }(b_{\rm B}{\rightarrow}b_{\rm A})\;P_{\rm HSAB}(b_{\rm A}{\rightarrow}a_{ \rm A}).\end{array}  \tag{106}\]  
As indicated above, in communication theory the indirect scatterings involve products of the relevant direct propagations. Therefore, the conditional probability of the direct step \(b_{\rm B}{\rightarrow}a_{\rm A}\) in R\({}_{c}\) must dominate over all indirect communications between these sites. This provides additional rationale for the observed complementary preference in the acid-base coordination. Moreover, the soft (basic) fragment is predicted to overlap with the neighboring sites more strongly compared to the hard (acidic) fragment, thus giving rise to stronger electron communications:  
\[P_{\alpha}(b_{\rm X}{\rightarrow}\lambda)>P_{\alpha}(a_{\rm X}{\rightarrow} \lambda)\qquad\quad\mbox{and}\qquad\quad P_{\alpha}(\lambda{\rightarrow}b_{ \rm X})>P_{\alpha}(\lambda{\rightarrow}a_{\rm X}). \tag{107}\]  
Figure 3: The dominating (nearest neighbor) communications between the chemically bonded sites of the Acid–Base complexes R\({}_{c}\) (**a**) and R\({}_{\rm HSAB}\) (**b**), respectively.