Density-functional calculations for doubly excited states of He,Li⁺, Be²⁺ and B³⁺ (^1.3S^e,³P⁰,^1.3D^e,^1.3P⁰,¹G^e)

More than 200 low-lying and moderately high-lying doubly excited states (L.3Se, 3P0, L.3De, L.3F0, LGe) of He-isoelectronic systems (Z = 2 - 5) have been studied in the nonrelativistic Hohenberg - Kohn - Sham density-functional framework by incorporating the nonvariational work-function exchange potential suggested by Harbola and Sahni and a simple parametrized local Wigner-type correlation functional. In essence, a Kohn - Sham-type equation has been solved numerically. Our results on excited-state energies, excitation energies and differences between excitation energies are in good agreement with available experimental and theoretical results. In 50% of cases, the percentage deviation in the calculated excitation energy is less than unity. The estimates of the relatively small distances (0.02 - 0.1 au) of the He states below the corresponding N = 2, 3, 4 ionization thresholds are in error by 0.5 - 34.9%, indicating that the Wigner correlation functional needs to be improved for greater accuracy. The excited radial densities display expected structures. Some new states are reported