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functions as, 

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where the set { χ$_{µ}$ ( r ) } denotes the contracted gaussian functions centered on the constituent atoms while { C σ $_{µi}$} contains the contraction coefficients for the orbital ψ σ i ( r ). The individual spin-densities are given by, 

where P σ stands for the respective density matrices. 

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Substitution of these terms into the energy expression, followed by minimization with respect to unknown coefficients C σ $_{µi}$, subject to the orthogonality constraint leads to the following matrix KS equation which is akin to the unrestricted Pople-Nesbet equation in Hartree-Fock (HF) theory, 

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Here S and F denote the K × K real, square symmetric overlap and total KS matrices respectively. C stands for the eigenvector matrix containing the expansion coefficients C σ µi while the orbital energies ϵ$_{i}$ are embedded in the diagonal matrix ϵ . The KS matrix is conveniently written as, 

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where the first two terms in the right-hand side signify the matrices of one-electron bare- nucleus Hamiltonian and the classical Coulomb repulsion. The one-electron overlap, kinetic- energy and nuclear-attraction integrals involved are the same as encountered in the GTF- based HF schemes and are computed using standard recursion algorithm [28, 29]. The pseudopotential matrix elements in the gaussian basis are taken taken from the GAMESS quantum chemistry program output [30]. The Coulomb potential is evaluated using a Fourier convolution technique [31, 32], which effectively uses a Ewald summation type decomposition in terms of short- and long-range contributions, 

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Here erf(x) and erfc(x) identify the error function and complimentary error function respec- tively. Note that the latter goes to zero exponentially fast at large r . The parameter α controls the range on which v short c is nonzero. After a thorough check on the convergence 

