Nonlinear pressure dependence of the bulk modulus of TmSe

We have calculated the total energy of TmSe within local-density theory over a wide range of volumes. Our results reproduce the nonlinear relation between the bulk modulus and pressure that is characteristic of valence transitions. The softening of the bulk modulus is directly related to the crossing of the 4f band by the conduction band. A comparison with experiment shows that the local-density approximation puts the 4f band about 40 mRy too high in energy. The tentative explanation given here for the discontinuous transition observed in some TmSe-TmTe alloys can be verified by experiments at low temperature.