Formal structure of the Conceptual Density Functional Theory (CDFT) has expanded over the years to the well-organized, quasi-thermodynamic system concentrated on exploration of the energy functional [ ( )] E  r in quantification of properties of molecules. The global quantities characterizing atomic and molecular entities are: Contracting these local quantities to atoms bonded in molecules has long been recognized as an important challenge on the way to CDFT applications in practical chemistry. However, the results have been limited to various types of approximations, far from expectations of chemistry where the reality of bonded atoms has been a cornerstone for consideration of reactivity. The difficulty has long been recognized: neither the QTAIM method, nor the Hirschfeld partition had produced more than a 'noumenon' -"an object of purely intellectual intuition (…) subject to arbitrary (but disciplined) personal choice when specificity is desired." For practical reasons, the closed system representation (canonical ensemble) has been dominating in the analyses:   been tentatively explored in analysis of local properties of atoms-in-molecules. Boisdenghien et al. has presented an electron energy expansion in the Taylor series; attractive two-and one-dimensional projections of the LRF as ( ,0)  r for atoms have resulted. 16,17 Another approach to LRF by the above authors was aimed via polarizability of atoms and molecules that has been reasonably reproduced by using computable results for ( , ')  rr . 18 The formal link between the LRF and the polarizability tensor has been first proposed by Vela and Gazques. It was dwelled upon by other authors and the polarization justified Fukui indices have been developed on this ground by Komorowski et al. The LRF condensed to atoms has been proposed by Sablon et al. by an arbitrary integration of the ( , ')  rr kernel;