## III. RESULTS AND DISCUSSION 

At first, Table I shows a comparison of our calculated ground-state energy components with respect to the number of mesh points N$_{r}$ ( r ∈ { x, y, z } ) as well as the grid spacing h$_{r}$ , for Cl$_{2}$ and HCl at internuclear distances 4.2 and 2.4 a.u respectively employing the BLYP density functional. In this occasion, we adopt a similar presentation strategy as in I. A series of calculations were performed in the same fashion to test the convergence of our results with respect to the grid parameters. These numerical experiments produced very similar conclusions as reached in for LDA XC-case in I. Hence out of eight, we eventually report here the results from two such sets only (to avoid too many entries in the table), viz., (i) Set A with N$_{r}$ = 64, h$_{r}$ = 0 . 3, (ii) Set B with N$_{r}$ = 128, h$_{r}$ = 0 . 2, which suffices to illustrate the important points. The reference theoretical results presented in this and all other tables throughout the article imply those obtained from the GAMESS quantum chemistry program [30]. They use same basis set, effective core potential and employing the “grid” option. The corresponding results from the “gridfree” option are quoted in footnotes for convenience, in several occasions. Now onwards, we will refer to them as grid and grid-free theoretical reference results. The former uses the Euler-McLaurin quadrature for the radial integrations and Gauss-Legendre quadrature for the angular integrations. The convergence of energies and other quantities with respect to the radial and angular grid was monitored by performing two extra set of calculations (i) N$_{r}$, N$_{θ}$, N$_{φ}$ = 96, 36, 72 (ii) N$_{r}$, N$_{θ}$, N$_{φ}$ = 128, 36, 72, besides the default grid option ( N$_{r}$, N$_{θ}$, N$_{φ}$ = 96, 12, 24), where the three integers denote the respective number of integration points in r, θ, φ directions. Note that all the 3 grids offered very similar results; for example, out of the 17 atoms and molecules, total energies remain same upto 5th decimal place for 8 species for all 3 grids. In the remaining cases, they differed slightly among each other as the grid parameters changed; the largest deviation in total energy being 0.00064 a.u. for Na$_{2}$Cl$_{2}$ and for all others it is well below 0.00007 a.u. However, passing from the default grid to (ii) gradually improves N . In this and all other tables in the article, we have quoted (ii) results for the reference grid -DFT values. The grid-free implementation uses the resolution of identity to simplify the molecular integrals enabling their analytical evaluation and obviating the necessity of using grid quadratures. Quantities considered are the same as those in I, viz., various energies such as kinetic ( T ), total nucleus-electron attraction ( V ne t ), classical Coulomb repulsion ( E$_{h}$ ), exchange ( E$_{x}$ ), 

