two-body classical Coulomb repulsion and the non-classical XC potentials were directly set up on the 3D CCG. Local-density approximated (LDA) XC functionals of the homogeneous electron gas in conjunction with the Hay-Wadt type pseudopotential was used. A multitude of quantities like viz., individual energy contributions to total energy, eigenvalues, potential energy curves, ionization energies, as well as atomization energies were investigated. The relevance and performance of the CCGs were judged on 12 molecules (from small to medium size) and 3 atoms. In each of these cases practically identical results as those from the ACG and grid-free results were obtained. Now, it is well-known that the local density functionals suffer from a number of problems and hence it is essential to use more accurate functionals, namely those incorporating the gradient and Laplacian corrections. We have a number of objectives in this article. Firstly, we want to assess the validity and efficacy of the aforementioned scheme of I for a larger set of species to justify and validate its future usage. Secondly its scope of applicability is broadened by incorporating the gradient corrected XC functionals (for demonstration, the popular non-local Becke exchange [24] and Lee-Yang- Parr (LYP) correlation [25] is used). First, a detailed test on the convergence of our results on 5 atoms and 12 molecules is made as in I for the BLYP XC functional. In the next step, additional 41 molecules are considered both at the LDA and BLYP level. Detailed comparison with reference theoretical and experimental results are made, wherever possible. Besides, we also report the highest-occupied molecular orbital (HOMO) energies obtained with the Leeuwen-Baerends (LB) [26, 27] exchange potential for the latter 41 molecules (see Section III for motivational details). In all cases, this significantly improves both LDA and BLYP HOMO energies. Section II gives a summary of the method of calculation and computational aspects. Section III presents a discussion on the results obtained. We end with a few concluding remarks about the future prospects in Section IV. This section sketches the essential steps involved in the ground-state calculation of a many-electron system within the KS DFT framework used in the present work; further details can be found in [23]. The KS MOs { ψ σ i ( r ) } , σ = α, β are linearly expanded in terms of a set of K known basis II. METHODOLOGY AND IMPLEMENTATION 4