## 7 Partial Electronic Flows  
It is also of interest to establish energy contributions due to all partial electronic flows shown in the flux patterns in Equation (48), of both P and CT origins. As observed above, all such spontaneous responses of the reactive system contribute the stabilizing (negative) contributions to the reaction energy. The P-currents represent the _intra_-reactant responses created by a presence of the other substrate and the external CT. The P/CT resolved flow patterns in Equation (48) and the associated energy terms call for the _site_-resolution of the polarized reactive system, now corresponding to the mutually-closed reaction sites on the internally- and mutually-closed reactants \(\text{A}=(a_{\text{A}}\mid b_{\text{A}})\) and \(\text{B}=(a_{\text{B}}\mid b_{\text{B}})\) (see Figure 1), for the external potential \(\
u(\alpha)\) of Equation (64),  
\[\text{R}_{\alpha}=[\text{A}(\alpha)\mid\text{B}(\alpha)]=[a_{\text{A}}(\alpha )\mid b_{\text{A}}(\alpha)\mid a_{\text{B}}(\alpha)\mid b_{\text{B}}(\alpha)]. \tag{75}\]  
Their functional fragments, the acidic and basic sites in both reactants,  
\[ \begin{array}{c}\Lambda(\text{R}_{\alpha})=\{\lambda_{\alpha}(\text{X})\equiv [a_{\text{X}}(\alpha),\,b_{\text{X}}(\alpha)]\}\\ \equiv\{a_{\text{A}}(\alpha),\,b_{\text{A}}(\alpha),\,a_{\text{B}}(\alpha),\,b _{\text{B}}(\alpha)\}\equiv\{\lambda_{1},\,\lambda_{2},\,\lambda_{3},\,\lambda_ {4}\},\end{array}  \tag{76}\]  
which contain \(n(\text{R}_{\alpha})=\{n_{\lambda}(\alpha)\}\) electrons, are then characterized by different levels of the site chemical potentials  
\[u(\text{R}_{\alpha})=\partial E_{\alpha}[n(\text{R}_{\alpha});\,\
u(\alpha)] /\partial u=\{u_{\alpha}(\lambda)=\partial E_{\alpha}/\partial n_{\lambda} \equiv u_{\lambda}\}, \tag{77}\]  
measured by the partial energy derivatives with respect to average electron populations:  
\[n(\text{R}_{\alpha})=\{n_{\alpha}(\lambda)\equiv n_{\lambda}\}=\{n_{\alpha}( \text{X})=[n_{\alpha}(a_{\text{X}}),\,n_{\alpha}(\text{X})]\}. \tag{78}\]The site-hardness descriptors are similarly defined by the corresponding matrix of the second populational derivatives of the energy in this resolution level:  
\[\mathbf{h}(\mathrm{R}_{\alpha})=\langle h_{\lambda,\lambda^{\prime}}=\partial^{2 }E_{\alpha}/\partial n_{\lambda}\ \partial n_{\lambda^{\prime}}=\partial u_{\alpha}(\lambda)/\partial n_{\lambda^{ \prime}}\rangle. \tag{79}\]  
In this more resolved perspective, one also applies the biased estimates of the fragment chemical potentials, measured either by the site negative ionization potential (\(u_{\lambda}=-I_{\lambda}\)) or its negative electron affinity (\(u_{\lambda}=-A_{\lambda}\)), when this fragment acts as an external electron donor or acceptor, respectively. A reference to Figure 1 and Equation (48) shows that the given site \(\lambda\) can act in the following three ways:  
(1) As internal (P) and external (CT) _donor_ of electrons, e.g., \(b_{\mathrm{B}}\) site in \(\mathrm{R}_{\mathrm{HSAB}}\);  
(2) As internal and external _acceptor_, e.g., \(a_{\mathrm{A}}\) site in \(\mathrm{R}_{\mathrm{HSAB}}\);  
(3) As _flow_-through fragment, e.g., all sites in \(\mathrm{R}_{c}\) and (\(a_{\mathrm{B}}\), \(b_{\mathrm{A}}\)) parts of \(\mathrm{R}_{\mathrm{HSAB}}\). (80)  
In the latter category the inflow/outflow currents, either of CT or P origins, compete with one another, thus minimizing the site net electron accumulation or depletion.