PACS 71.15.Mb, 71.15.Nc, 71.20.Eh, 71.28.+d The ground state configuration of the monochalcogenides of Sm and Eu is determined from total energy calculations using the self-interaction corrected local-spin-density approximation. The Sm chalcogenides, with the exception of SmO, are characterized by divalent f 6 Sm ions, while all the Eu chalcogenides have divalent f 7 Eu ions in the ground state. With pressure, the Eu and Sm chalcogenides exhibit isostructural transitions into an intermediate valent state, which in the total energy calculations is represented by localized f 5 configurations on the Sm ions (f 6 on Eu ions) together with a partly occupied f-band at the Fermi level. The energy of the fundamental f → d transition, which determines the value of the semiconducting gap, is determined by total energy calculations of the charged rare earth ion (Eu + or Sm + ) in a supercell approach with one f-electron removed. The pressure coefficients are in excellent agreement with experiment, and the occurrence of isostructural transitions is intimately related to the closure of the band gap.