II. METHOD OF CALCULATION 4 ρ ( r ) = ∑ i | ψ i ( r ) | $^{2}$. [ − 1 2 ∇ 2 + v$_{es}$ ( r ) + v$_{xc}$ ( r ) ] ψ$_{i}$ ( r ) = ε$_{i}$ψ$_{i}$ ( r ) (1) v$_{es}$ ( r ) = − Z r + ∫ ρ ( r $^{′}$) | r − r $^{′}$| d r ′ (2) v$_{x}$ ( r ) = − ∫ r ∞ E$_{x}$ ( r ) · d l . (3) E$_{x}$ ( r ) = ∫ ρ$_{x}$ ( r , r $^{′}$)( r − r $^{′}$) | r − r $^{′}$| 3 d r . (4) The methodology as well as the numerical solution of the desired radial Kohn-Sham (KS) equation through GPS discretization scheme has been presented before [23,24,27-31]; hence not repeated. Only essentials details are given. Unless otherwise mentioned, atomic units employed throughout the article. Our interest is in the following single-particle nonrelativistic KS equation, where three terms in the left-hand side signify respectively the kinetic, electrostatic and exchange-correlation (XC) energy contributions. v$_{es}$ ( r ) contains the nuclear-attraction and classical internuclear Coulomb repulsion as, where Z corresponds to the nuclear charge. The local nonvariational exchange potential relates to the work required to move an electron against the electric field E$_{x}$ ( r ) arising out of its own Fermi-hole charge distribution, ρ$_{x}$ ( r , r $^{′}$), and given by the line integral [25], where For well-defined potentials, work done must be path-independent (irrotational), which is rigorously satisfied for spherically symmetric systems. This potential can be calculated ac- curately as the Fermi hole is known exactly in terms of the single-particle orbitals. Working within the central-field approximation, ψ$_{i}$ ( r ) = R$_{nl}$ ( r ) Y$_{lm}$ (Ω), employing a suitable corre- lation functional (here we use LYP potential, [26]), solution of the KS equation produces a self-consistent set of orbitals, which gives the electron density as, The radial KS equation is solved accurately and efficiently by means of the GPS method, which has shown remarkable success for structure and dynamics of Coulombic singular sys- tems such as atoms, molecules as well as other difficult and stronger singularities such as