Orbital density functional as a means to restore the discontinuities in the total-energy derivative and the exchange-correlation potential

The local density approximation ( LDA) to the density functional theory ( DFT) has a continuous derivative of the total energy as a function of the number of electrons and continuous exchange - correlation potential, while in exact DFT both functions should be discontinuous as the number of electrons goes through an integer value. We propose an ad hoc orbital density functional ( ODF) ( with orbitals defined as Wannier functions) that by construction obeys this discontinuity condition. Taking its variation, the one- electron equations are obtained with a potential in the form of a projection operator. This operator increases the separation between occupied and empty bands, thus curing an LDA deficiency - systematic underestimation of the energy gap value. The minimization of the ODF gives the ground- state orbital and total electron densities. In addition to that we define the ODF fluctuation Hamiltonian that allows one to treat dynamical correlation effects. The dynamical mean- field theory ( DMFT) with the quantum Monte Carlo ( QMC) method for an effective impurity problem was used to solve this Hamiltonian. We have applied the ODF method to the problem of the metal - insulator transition in lanthanum trihydride LaH3-x. In the LDA calculations for all values of hydrogen nonstoichiometry x the ground state of this material is metallic, while experimentally the system is insulating for x < 0.3. The ODF method gave a paramagnetic insulator solution for LaH3 and LaH2.75 but metallic state for LaH2.5.