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

Abstract

The local density approximation (LDA) to the density functional theory (DFT) has acontinuous derivative of the total energy as a function of the number of electrons andcontinuous exchange–correlation potential, while in exact DFT both functions should bediscontinuous as the number of electrons goes through an integer value. We propose an adhoc orbital density functional (ODF) (with orbitals defined as Wannier functions)that by construction obeys this discontinuity condition. Taking its variation, theone-electron equations are obtained with a potential in the form of a projectionoperator. This operator increases the separation between occupied and empty bands,thus curing an LDA deficiency—systematic underestimation of the energy gapvalue. The minimization of the ODF gives the ground-state orbital and totalelectron densities. In addition to that we define the ODF fluctuation Hamiltonianthat allows one to treat dynamical correlation effects. The dynamical mean-fieldtheory (DMFT) with the quantum Monte Carlo (QMC) method for an effectiveimpurity problem was used to solve this Hamiltonian. We have applied the ODFmethod to the problem of the metal–insulator transition in lanthanum trihydrideLaH3−x. In the LDA calculations for all values of hydrogen nonstoichiometryx the ground state of this material is metallic, while experimentally the system is insulating forx<0.3. The ODF method gave a paramagnetic insulator solution forLaH3 andLaH2.75 but metallicstate for LaH2.5.