# Ground and excited states of Li $^{−}$, Be− through a density-based approach 

Department of Chemistry and Biochemistry, University of California, Los Angeles, CA, 90095-1569, USA 

Amlan K. Roy ∗ 

Abraham F. Jalbout 

Institute of Chemistry, National Autonomous University of Mexico, Mexico City, Mexico 

## Abstract 

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 $^{e}$→ 1s2p $^{3 5}$S o of Li $^{−}$, [He]2s2p $^{2 4}$P $^{e}$→ [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. 

