  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.

Chemical Physics;Atomic Physics