The electronic structures of adamantane, 1-chloroadamantane, cyclohexane, and chlorocyclohexane and their interaction potentials with He*(2(3)S) metastable atoms are studied by two-dimensional (collision- and electron-energy-resolved) Penning ionization electron spectroscopy and model potential calculations. The model potential calculations are performed for the target-Li system based on a well-known resemblance between a metastable excited He*(2(3)S) atom and a ground-state Li(2(2)S) atom. Assignments of the electron spectra are made on the basis of ab initio and outer-valence Green's function calculations. Strong repulsive interactions between the saturated hydrocarbons and the metastable atom and strength sequence sigma(CC) > sigma(CH) observed experimentally are consistent with the anisotropic potential calculations. It is noted that attractive interaction in the region where lone-pair n(Cl) electrons are distributed for 1-chloroadamantane is weaker than that for chlorocyclohexane, because of the stronger steric shielding effect by the larger adamantane skeleton. Through comparison with the previous results on the saturated chloro-hydrocarbons, we find that the attractive interaction around the n(Cl) electron distribution does not become stronger as the energy level of the highest occupied molecular orbital becomes higher, which is the result of competition between effects of low exterior electron distributions and high energy levels.