Representations of the occupation number matrix on the LDA/GGA+Umethod

Abstract

An analysis of the general representation of the occupation number matrix on density functional theory in conjunction with the generalized Hubbard model is presented. A central fact that will be addressed is that the total charge density cannot be broken down into simple atomic contributions. This fact means that the orbital occupations are not well defined. Different representations of the occupation number matrix, both that it conserves and that it does not conserve the number of electrons of the system, are compared. A localized basis set is used, which is suitable for large-scale electronic structure calculations based on the density functional theory. This methodology is applied to typical and well-analysed transition-metal oxide bulk systems and to Cr-doped zinc chalogenides and chalcopyrites. The bandgap, magnetic moment and detailed electronic structures are investigated and discussed with the different choices of the occupation number matrix. The results are in good agreement with previous theoretical and experimental studies.

Microscopic Optical Absorption, Analysis, and Applications of Famatinite Cu3SbS4

“…Standard functionals used in the local density approximation (LDA) and in the generalized gradient approximation (GGA) underestimate the band gap of a wide range of semiconducting materials. Therefore, a further extension beyond the standard DFT was carried out using the DFT+U method [7][8][9][10][11] including an orbital-dependent one electron potential to account explicitly for the important Coulomb repulsions not dealt with adequately in the standard approaches.…”

“…The value of U depends on the choice of the orbital subspace on which the correction is applied, on the orbital occupations numbers, and the implementation chosen [8][9][10][11] . In this work we applied the orbital-dependent one-electron potential using the DFT+U formalism described in references 8,9 .…”

“…In this work we applied the orbital-dependent one-electron potential using the DFT+U formalism described in references 8,9 . For the exchange-correlation potential, we used the GGA from Perdew, Burke and Ernzerhof 12 .…”

Microscopic Analysis and Applications of the Cu(Sb,Bi)S2 High Optical Absorption

“…We will use the DFT+U method [26][27] . The U value depends on the choice of the orbitals on which the correction is applied, on the way the orbital occupations are computed, and on the DFT+U implementation chosen [27][28][29][30] . In this work we applied the orbital-dependent one-electron potential using the DFT+U formalism described in references [27][28] .…”

Subspace Representations in Ab Initio Methods for Strongly Correlated Systems

“…Thus, for example, its trace is invariant under both unitary rotations and the generalized Löwdin transformations 16 of Ref. 9.…”