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## II. METHOD OF CALCULATION 

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, 

<img src='content_image/343407.jpg'>

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, 

<img src='content_image/343408.jpg'>

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 

<img src='content_image/343409.jpg'>

<img src='content_image/343410.jpg'>

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, 

<img src='content_image/343406.jpg'>

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 

