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

Density functional calculations are performed for 12 2l2l'nl'' (n >= 2) triply excited hollow resonance series of Li, namely, 2s²ns ²S^e, 2s²np ²P^o, 2s²nd ²D^e, 2p²ns ²D^e, ⁴P^e, 2s2pns ⁴P^o, 2s2pnp ⁴D^e, 2p²np ²F^o, ⁴D^o, 2p²nd ²G^e, ⁴F^e and 2s2pnd ⁴F^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 non-uniform, optimal spatial discretization to obtain the orbitals and densities. The present single determinantal approach yields fairly accurate results for the nonrelativistic energies, excitation energies as well as the radial densities and other expectation values. Except for 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 made for the 37 3l3l'nl'' (n >= 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, namely, 3s²3p ²P^o and 3s3p^{2 4}P^e. The resonance series are found to be inextricably entangled with each other, leading to complicated behaviour 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.