## 5 Current Coherence in Donor-Acceptor Systems
As shown in Figure 1, at finite separations between the two subsystems, spontaneous (primary) CT displacements between reactants trigger the induced (secondary) polarizational flows [P\({}_{\rm X}\)] within each reactant, which restore the intra-substrate equilibria initially displaced by the presence of the other fragment and the inter-reactant CT:  
\[ \begin{array}{ccccc}a_{\rm B}&\leftarrow&b_{\rm A}&&a_{\rm B}&\rightarrow& a_{\rm A}\\ \vdots&&\uparrow&\text{, }R_{\rm HSAB}:&\uparrow&&\uparrow\\ b_{\rm B}&\rightarrow&a_{\rm A}&&b_{\rm B}&\rightarrow&b_{\rm A}\end{array}  \tag{48}\]  
It has been inferred from the (energetic) electronegativity Equalization principle [95] that the electronic CT and P flows in \(R_{c}\) generate the _concerted_ pattern shown in Figure 1 and Equation (48), which exhibits the maximum current (phase-gradient) coherence. It implies the least population activation on both reactants, which also energetically favors the complementary complex relative to the regional HSAB arrangement. Indeed, in \(R_{\rm HSAB}\) coordination the energy-preferred _disconcerted_ flow pattern implies a more exaggerated depletion of electrons on \(b_{\rm B}\) and their more accentuated accumulation on \(a_{\rm A}\). In fact, these partial flows of electrons signify the \"bridge\" CT between the key (\"diagonal\") sites \(b_{\rm B}\) and \(a_{\rm A}\), via the intermediate (\"off-diagonal\") sites \(a_{\rm B}\) and \(b_{\rm A}\). In the complementary arrangement of both reactants, the partial fluxes involving the four active sites indicate the \"flow-through\" behavior of all these fragments, which combines the external (CT) and internal (P) currents. One observes that the acidic sites accept electrons as a result of charge transfer between reactants and donate electrons through the substrate polarization. The opposite behavior of the basic sites is observed: they receive electrons due to P-mechanism and lose electrons as a result of CT. In the HSAB complex, one observes a similar flow-through pattern only on the \(a_{\rm B}\) and \(b_{\rm A}\) sites, \(b_{\rm B}\) exclusively donates electrons both internally (P) and externally (CT), while \(a_{\rm A}\) only accepts electrons from its complementary fragment \(b_{\rm A}\) (P) and \(a_{\rm B}\) (CT) part of the other reactant. To summarize, in \(R_{c}\), one observes the concerted flow of electrons involving all four active sites of both reactants, with small net changes in electron populations on these fragments, while the charge reconstruction in \(R_{\rm HSAB}\) can be regarded as a transfer of electrons from \(b_{\rm B}\) to \(a_{\rm A}\) through the remaining (intermediate) sites \(a_{\rm B}\) and \(b_{\rm A}\). The energetical preference of the complementary arrangement of reactants [94; 95] also signifies the maximum _phase_-gradient coherence on each site, with its P or CT _inflow_ part being accompanied by the associated outflow flux. Such a flow pattern thus corresponds to the least populated displacements on all constituent active sites. The above \"activation\" perspective then provides a natural physical explanation of the observed preference of the complementary coordination. The energetically favored, concerted pattern of electronic fluxes in \(R_{c}\) can be realized only by an appropriate coherence of the site effective phase-gradients, of the pure or mixed states \(\{\Psi_{\lambda}\}\) describingthe mutually-closed fragments \(\lambda\in\{a_{\rm A}=1,\,b_{\rm A}=2,\,a_{\rm B}=3,\,b_{\rm B}=4\}\) of both reactants. These states define the average resultant currents on each site, weighted by the site electron probability distribution \(p_{\lambda}(\mathbf{r})\),  
\[\langle j\rangle_{\lambda}=\int p_{\lambda}(\mathbf{r})\;j_{\lambda}(\mathbf{r})\;d\bm {r}\equiv j(\lambda),\qquad\quad\int p_{\lambda}(\mathbf{r})\;d\mathbf{r}=1, \tag{49}\]  
already accounting for the average outflows-from and inflows-to the part in question, caused by the CT or P displacements in the system electronic structure.