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with respect to α , a value within the range of 6–8 seemed satisfactory and we employed 7 for all the results reported in this work. This has produced highly satisfying results for a modest number of atomic (3) and molecular (12) systems in our previous work [23]. The short-range Fourier integral is calculated analytically, whereas the long-range part is obtained from FFT of the real-space values. 

As already mentioned, a major thrust of the current communication is to demonstrate the feasibility and viability of our current scheme in the context of so-called “non-local” (gradient and Laplacian-dependent) XC functionals which would be necessary for future chemical applications. For this, we first test this with two of the widely used functionals, namely the Becke exchange [24] and LYP correlation [25] (for convenience, an alternative equivalent form [33] containing only the first derivative has been mostly used in practice). The homogeneous electron-gas correlation of Vosko-Wilk-Nusair (VWN) [34] is used in all the LDA calculations. Following [35], the gradient-dependent functionals can be treated without evaluating the density Hessians by using a finite-orbital basis expansion. To this end, XC contributions of the KS matrix is written in the following working form, 

<img src='content_image/336259.jpg'>

where γ$_{αα}$ = |∇ ρ$_{α}$ | $^{2}$, γ$_{αβ}$ = ∇ ρ$_{α}$ · ∇ ρ$_{β}$ , γ$_{ββ}$ = |∇ ρ$_{β}$ | 2 and f is a function only of the local quantities ρ$_{α}$ , ρ$_{β}$ and their gradients. The BLYP functionals are implemented using the Density Functional Repository program [36]. The two-electron matrix elements cannot be evaluated analytically; here we use direct numerical integrations on the CCG grid. Note that some of the existing DFT codes [37] use an alternative route of fitting these by an auxiliary basis set, the so-called discrete variational method [38–40]. The generalized matrix- eigenvalue problem is solved using the standard LAPACK routine [41] accurately efficiently. Self-consistent set of MOs, density and energy are obtained in the usual manner subject to the convergence of (a) potential (b) total energy and (c) eigenvalues. Tolerance of 10 − 6 a.u. was used for (b) and (c), while a value of 10 − 5 for (a). Atomic units employed, unless otherwise mentioned. 

