We report on X-ray photoelectron spectroscopy and ab initio electronic structure investigations of the skutterudite-related R5Rh6Sn18 superconductors, where R = Sc, Y, and Lu. These compounds crystallise with a tetragonal structure (space group I4(1)/acd) and are characterised by a deficiency of R atoms in their formula unit (R5-delta Rh6Sn18, delta << 1). Recently, we documented that the vacancies delta and atomic local defects (often induced by doping) are a reason for the enhancement in the superconducting transition temperature T-c of these materials, as well as metallic (delta = 0) or semimetallic (delta not equal 0) behaviours in their normal state. Our band structure calculations show the pseudogap at a binding energy of -0.3 eV for the stoichiometric compounds, which can be easily moved towards the Fermi level by vacancies delta. As a result, dychotomic nature in electric transport of R5Rh6Sn18 (metallic or semimetallic resistivity) depends on delta, which has not been interpreted before. We have shown that the densities of states are very similar for various R5Rh6Sn18 compounds, and they practically do not depend on the metal R, while they are determined by the Rh d-and Sn s- and p-electron states. The band structure calculations for Sc Sc5Rh6Sn18 have not been reported yet. We also found that the electronic specific heat coefficients gamma(0) for the stoichiometric samples were always larger with respect to the gamma(0) of the respective samples with vacancies at the R sites, which correlates with the results of ab initio calculations.