A DFT approach for the accurate calculation of triply excited hollow and doubly-hollow Rydberg resonances in lithium isoelectronic sequence

Density functional calculations are performed for the $2l2l'nl'' (n \ge 2)$ triply excited \emph{hollow} resonances in lithium isoelectronic sequence. An amalgamation of the local nonvariational work-function-based exchange potential and LYP correlation functional is used. Radial KS equation is solved accurately through the Generalized pseudospectral method, leading to a nonuniform and optimal spatial discretization. Results are presented on the excited-state energy, excitation energy, radial density and other expectation values. A large number of states are studied, covering low, moderately-high and high-lying excitations, with $n$ \emph{as high as up to 25}, having varied symmetries and multiplicities. Companion calculations are made for the $3l3l'nl'' (n \ge 3)$ \emph{doubly-hollow} states of Li in the photon energy range of 176-181 eV. Detailed comparisons with recent theoretical and experimental results show excellent agreement. Many \emph{new} resonances are presented for the first time, which can provide useful guidelines for future studies. This provides a simple, efficient and general scheme for reliable and accurate treatment of multiply excited Rydberg resonances in atoms within DFT.