TABLE IV: Comparison of the kinetic ( 〈 T 〉 ), potential ( 〈 V 〉 ), total ( E ) energies and N for several atoms and molecules with the reference grid-DFT results [30]. BLYP results in a.u. PW=Present Work. See text for details. System 〈 T 〉 −〈 V 〉 −〈 E 〉 N PW Ref. [30] PW Ref. [30] PW Ref. [30] PW Ref. [30] Na 2 0.14723 0.14723 0.52871 0.52871 0.38148 0.38148 1.99999 2.00000 Mg 0.24935 0.24935 1.06017 1.06017 0.81082 0.81083 1.99999 1.99999 NaH 0.60093 0.60088 1.34698 1.34693 0.74606 0.74605 1.99997 1.99999 P 2.38891 2.38890 8.78249 8.78248 6.39358 6.39358 4.99999 4.99999 As 2.10490 2.10494 8.14207 8.14211 6.03717 6.03717 4.99999 4.99999 S 3.73143 3.73145 13.73598 13.73599 10.00455 10.00454 6.00000 5.99999 Br 4.27022 4.27043 17.36122 17.36148 13.09100 13.09105 7.00000 6.99999 NaCl 5.83959 5.83957 21.01698 21.01694 15.17739 15.17737 8.00003 7.99999 H 2 S 4.98071 4.98066 16.21919 16.21913 11.23848 11.23846 8.00000 7.99999 PH 3 4.18229 4.18224 12.40101 12.40096 8.21871 8.21872 7.99999 7.99999 Br 2 8.66533 8.66527 34.88603 34.88596 26.22070 26.22069 13.99999 14.00000 H 2 S 2 8.88238 8.88240 30.16535 30.16538 21.28297 21.28298 13.99999 13.99999 MgCl 2 11.75947 11.75999 42.54049 42.54103 30.78102 30.78104 16.00004 15.99999 Na 2 Cl 2 11.68815 11.68842 42.12410 42.12438 30.43595 30.43595 16.00002 15.99999 SiH 2 Cl 2 14.14948 14.14945 49.04463 49.04461 34.89515 34.89516 19.99999 20.00000 deviation in total energy is only 0.0013% (for NaH). Table V displays the calculated negative HOMO energies, − ϵ$_{HOMO}$ (in a.u.) and estimated atomization energies (in kcals/mole) for the same 12 molecules in Table V of I, using the BLYP XC density functional. These are compared with the theoretical [30] as well the experimental results from the NIST database [43]. Same grid parameters as those in the previous table are employed for these. The − ϵ$_{HOMO}$ values completely agree with those from the theoretical literature results [30], except in two occasions (MgCl$_{2}$, Na$_{2}$Cl$_{2}$), where the absolute discrepancy remains only 0.0001 a.u. The calculated atomization energies also show very good agreement with the reference theoretical values [30]. For Na$_{2}$ HCl, NaCl and H$_{2}$S, our values are identical as those from reference. The largest discrepancy (0.248%) is observed for Br$_{2}$. However, both quantities differ significantly from the experimental values; but that is a separate issue (not directly related to the main theme of this work). These could possibly be improved further by employing more appropriate basis functions and/or better XC functionals, and may be considered in future works. The previous work of [23] as well as the ongoing discussion amply demonstrates that the approach can produce good-quality results for both LDA and gradient-corrected non-local 11