Local-density approach and quasiparticle levels for generalized Hubbard Hamiltonians

Abstract

This paper presents a general method to describe and analyze electron correlation effects in local-orbital electronic structure calculations using a generalized Hubbard Hamiltonian. In our approach, we first introduce a local density formalism where the total energy of the system is obtained as a function of the orbital occupancies ͕n i ͖ associated with each local orbital; in particular, exchange and correlation local potentials are presented for a multilevel case. In parallel, using the dynamical mean field approximation, a many-body solution is obtained by means of a local self-energy that appropriately interpolates between the low and high correlation limits. We also show that the local density and the many-body solutions are linked through charge consistency conditions. These two solutions are applied to a multilevel Anderson impurity and to a multiband Hubbard lattice, our results showing the high accuracy of the approach presented in this paper. Further on, we discuss how to apply our previous analysis to the case of crystals and molecules and analyze several examples: bulk Si, and HF and H 2 O molecules. The good results obtained for these cases show that our approach for the description of correlation effects offers an interesting alternative to the well-established density functional methods based on the calculation of the electron density (r ជ ).

Orbital-selective insulator-metal transition inV2O3under external pressure

“…In contrast to the one-band case, however, the exact atomic limit for the multi-orbital case contains the local, interorbital correlation function, D ab [n] =< n a n b >. 34 We are aware of only one earlier work 35 where D ab [n] is computed using the coherent potential approximation (CPA). Strictly speaking, this is an approximation to the Hubbard model(s) which is qualitatively valid in the Mott insulating state, but is known to fail in the correlated PM phase(s).…”

Multicenter approach to the exchange-correlation interactions inab initiotight-binding methods

“…One possibility is to use non-standard DFT and introduce the exchange-correlation energy and potential as a function of the orbital occupancies [9,20,21]. In this paper, however, we opt for the more traditional approach in which exchange-correlation contributions are calculated as a functional of the electron density ρ( r).…”

Charging energy and barrier height of pentacene on Au(111): A local-orbital hybrid-functional density functional theory approach

“…44 The problem of underestimation of the gap in local density theories (like standard LDA or the one presented above) can be avoided by using a Hartree-Fock approximation for the treatment of the exchange energy. In our particular case, the idea is to use for the exchange energy the expression 44…”

“…(2), U i,αβ and (J iα,jβ ) are intra-atomic (interatomic) electron-electron integrals which represent the most important contributions to the two body interaction (other small contributions are neglected in this argument). 14,44 The exchange energy associated with Hamiltonian (2) can be written as follows:…”