  Photon-induced electronic excitations are ubiquitously observed in organic
chromophore. In this context, we present a simple, alternative time-independent
DFT procedure, for computation of single-particle excitation energies, in
particular, the lower bound excited singlet states, which are of primary
interest in photochemistry. This takes inspiration from recently developed
Becke's exciton model, where a key step constitutes the accurate evaluation of
correlated singlet-triplet splitting energy. It introduces a non-empirical
model, both from "adiabatic connection theorem" and "virial theorem" to analyze
the role of 2e$^-$ integral in such calculations. The latter quantity is
efficiently mapped onto a real grid and computed accurately using a purely
numerical strategy. Illustrative calculations are performed on 10
$\pi$-electron organic chromophores within a Cartesian-grid implementation of
pseudopotential Kohn-Sham (KS) DFT, developed in our laboratory, taking
SBKJC-type basis functions within B3LYP approximation. The triplet and singlet
excitation energies corresponding to first singly excited configuration, are
found to be in excellent agreement with TD-B3LYP calculations. Further, we
perform the same for a set of larger molecular systems using the asymptotically
corrected LC-BLYP, in addition to B3LYP. A systematic comparison with
theoretical best estimates demonstrates the viability and suitability of
current approach in determining optical gaps, combining predictive accuracy
with moderate computational cost.
