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.