Representations of the occupation number matrix on the LDA/GGA+ U method

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.