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.