Density-functional calculations on singly and doubly excited Rydberg states of many-electron atoms

Nearly 100 low-, moderately high-, and high-lying singly and doubly excited states of He, Li, and Be have been calculated using a nonvariational, work-function-based exchange potential within the nonrelativistic Hohenberg-Kohn-Sham density-functional theory (DFT). The nonlinear gradient included in the Lee-Yang-Parr correlation functional is used to incorporate the correlation potential. The generalized pseudospectral method is used for nonuniform and optimal spatial grid discretization and solution of the Kohn-Sham equation to obtain accurate eigenvalues, expectation values, and radial densities for both ground and excited states. The results are compared with the available theoretical and experimental data. The discrepancy in the calculated singly excited state energies is within about 0.01% for He (for other atoms, it is less than 0.2%), while that for the doubly excited states of He is well within 3.6%. The deviations in the calculated single- and double-excitation energies for 31 selected states are in the error ranges 0.009-0.632 % and 0.085-1.600 %, respectively. The overall agreement of the present results is quite gratifying, especially in the light of DFT's difficulties in dealing with excited states. The exchange-only results are practically of Hartree-Fock quality, and the correlation-included results are usually slightly overestimated. The present method offers a simple, computationally efficient and general scheme for accurate calculation of multiply excited Rydberg states within DFT