  Density functional calculations are performed for ground [He]2s$^2$
$^1$S$^e$, and three metastable bound excited states, 1s2s2p$^2$ $^5$P$^e$,
1s2p$^3$ $^5$S$^o$, 1s2s2p3p $^5$P$^e$ of Li$^-$ and [He]2s2p$^2$ $^4$P$^e$,
[He]2p$^3$ $^4$S$^o$, 1s2s2p$^3$ $^6$S$^o$ of Be$^-$ each. The
work-function-based exchange potential is used, while the correlation effects
are included by employing the Lee-Yang-Parr potential. The relevant
nonrelativistic KS equation is solved by means of a generalized pseudospectral
discretization scheme offering nonuniform and optimal spatial grid. Computed
total energies, radial densities, selected density moments, as well as two
transition wavelengths (1s2s2p$^2$ $^5$P$^e \to$1s2p$^3$ $^5$S$^o$ of Li$^-$,
[He]2s2p$^2$ $^4$P$^e \to$ [He]2p$^3$ $^4$S$^o$ of Be$^-$) show reasonably good
agreement with the available theoretical and experimental data. The term
energies show an absolute deviation of 0.007--0.171% with the largest deviation
being observed for the even-parity $^5$P state of Li$^-$. The transition
wavelengths of Li$^-$, Be$^-$ are calculated within 0.891 and 0.438% of the
experimental values. This offers a simple practical route towards accurate
reliable calculation of excited states of anions within density functional
theory.
