Studies on the hollow states of atomic lithium by a density functional approach

Abstract

Density functional calculations are performed for twelve $2l2l'$n$l"$ (n$\geq$2) triply excited hollow resonance series of Li, {\em viz.,} 2s$^2$ns $^2$S$^e$, 2s$^2$np $^2$P$^o$, 2s$^2$nd $^2$D$^e$, 2p$^2$ns $^2$D$^e$,$^4$P$^e$, 2s2pns $^4$P$^o$, 2s2pnp $^4$D$^e$, 2p$^2$np $^2$F$^o$,$^4$D$^o$, 2p$^2$nd $^2$G$^e$, $^4$F$^e$ and 2s2pnd $^4$F$^o$, covering a total of about 270 low-, moderately high- and high-lying states, with n as high as up to 25. The work-function-based exchange potential and the nonlinear gradient plus Laplacian included Lee-Yang-Parr correlation energy functional is used. The relevant Kohn-Sham-type equation is solved numerically using the generalized pseudospectral method offering nonuniform, optimal spatial discretization to obtain the orbitals and densities. Except for the one state, the discrepancy in the calculated state energies remains well within 0.98%, whereas the excitation energies deviate by 0.02--0.58% compared to the available experimental and other theoretical results. Additionally companion calculations are also presented for the 37 $3l3l'$n$l"$ (n$\geq$3) doubly hollow states (seven are n=3 intrashell type) of Li with both K and L shells empty (up to n=6) in the photon energy range 175.63--180.51 eV, with varying symmetries and multiplicities. Our calculation shows good agreement with the recent literature data for the only two such doubly hollow states reported so far, {\em viz.,} 3s$^2$3p $^2$P$^o$ and 3s3p$^2$ $^4$P$^e$. The resonance series are found to be inextricably entangled to each other, leading to complicated behavior in their positions. Many new states are reported here for the first time. This provides a simple, efficient and general scheme for the accurate calculation of these and other multiply excited Rydberg series of many-electron atomic systems within density functional theory.