The electronic structures of rare-earth elements in the hexagonal close-packed structure and Europium in the body-centered cubic structure are calculated using density-functional theory (DFT). X-ray photoemission spectroscopy (XPS) and bremsstrahlung isochromatic spectroscopy (BIS) simulations are made within DFT by implying that the f-electrons are excited by a large photon energy, either by removal from the occupied states in XPS or by addition to the unoccupied f-states in BIS. The results show sizable differences in the apparent position of the f-states compared to the f-band energy of the ground states. This result is fundamentally different from calculations assuming strong on-site correlation, since all the calculations are based on DFT. The spin–orbit coupling and multiplet splittings are not included, and the present simulation accounts for almost half of the difference between the f-level positions in the DFT ground states and the observed f-level positions. The electronic specific-heat at low T is compatible with the DFT ground state, where f-electrons often reside at the Fermi level.