3 most powerful and promising tools for electronic structure and dynamical studies of many- electron atoms, molecules, solids. While it enjoyed remarkable success for the ground states, same for excited states came much later. In the last decade, a work-function-based DFT prescription has been shown to be fairly successful for general atomic excited states (see for example, [23, 24] and the references therein). This proposed the use of a nonvariational local work-function-based exchange potential [25], which is computationally advantageous compared to the nonlocal HF potential. Usually, the gradient and Laplacian-included cor- relation functional of Lee-Yang-Parr (LYP) [26] was employed in conjunction. Recently this was extended for higher excitations through a generalized pseudospectral (GPS) implemen- tation which allowed to solve the resultant radial KS equation in a non-uniform, optimal spatial grid accurately efficiently [27]-[31]. This enabled us to study, for the first time, within the framework of DFT, a broad range of important physical processes in atomic ex- cited states such as multiple excitations, valence as well as core excitations, satellite states, high-lying Rydberg states etc. However with the exception of 8 triply excited states of He − [23], all of these works dealt with either neutral atom and cations. The current work aims at investigating the spectra of two most important and widely studied case of negative ions through the above DFT method, with an objective to assess and judge the performance of this simple single-determinantal approach in the context of excited states of negative ions. In other words can a density-based approach as ours, produce satisfactory and physically meaningful results for these intricate excited states; and if so how good do they perform in comparison to the traditional wave function-based methodologies, which are prevalent for their studies? To answer these questions, we investigate the term energies, radial densities, transition wavelengths as well as expectation values of some position operators for 4 states of Li $^{−}$, viz., [He]2s $^{2 1}$S $^{e}$, 1s2s2p $^{2 5}$P $^{e}$, 1s2p $^{3 5}$S $^{o}$, 1s2s2p3p $^{5}$P $^{e}$, and 3 states of Be $^{−}$, viz., [He]2s2p $^{2 4}$P $^{e}$, [He]2p $^{3 4}$S o and 1s2s2p $^{3 6}$S $^{o}$. Comparison with available theoretical and ex- perimental results are made, wherever possible. The article is organized as follows: Section II gives basic elements of the formalism as well as its numerical implementation, Section III makes a discussion on the results while we end with a few concluding remarks in Section IV.