Slater half-occupation technique revisited: the LDA-1/2 and GGA-1/2 approaches for atomic ionization energies and band gaps in semiconductors

The very old and successful density-functional technique of half-occupation is revisited [J. C. Slater, Adv. Quant. Chem. 6, 1 (1972)]. We use it together with the modern exchange-correlation approximations to calculate atomic ionization energies and band gaps in semiconductors [L. G. Ferreira et al., Phys. Rev. B 78, 125116 (2008)]. Here we enlarge the results of the previous paper, add to its understandability, and show when the technique might fail. Even in this latter circumstance, the calculated band gaps are far better than those of simple LDA or GGA. As before, the difference between the Kohn-Sham ground state one-particle eigenvalues and the half-occupation eigenvalues is simply interpreted as the self-energy (not self-interaction) of the particle excitation. In both cases, that of atomic ionization energies and semiconductor band gaps, the technique is proven to be very worthy, because not only the results can be very precise but the calculations are fast and very simple.

[1]  K. Hirao,et al.  An improved long-range corrected hybrid functional with vanishing Hartree-Fock exchange at zero interelectronic distance (LC2gau-BOP). , 2009, The Journal of chemical physics.

[2]  Peter Blaha,et al.  Full-potential, linearized augmented plane wave programs for crystalline systems , 1990 .

[3]  U. Gerstmann,et al.  Validity of the Slater-Janak transition-state model within the LDA + U approach , 2008 .

[4]  W. Schmidt,et al.  Rare-earth defect pairs in GaN: LDA+U calculations , 2009 .

[5]  J. R. Leite,et al.  Effects of the Coulomb Correlation on the Calculated Results for Atoms with and without Spin Polarization , 1971 .

[6]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[7]  S. Kümmel,et al.  Single-particle and quasiparticle interpretation of Kohn-Sham and generalized Kohn-Sham eigenvalues for hybrid functionals , 2010 .

[8]  G. Pacchioni,et al.  Transition levels of defect centers in ZnO by hybrid functionals and localized basis set approach. , 2010, The Journal of chemical physics.

[9]  I. Abrikosov,et al.  Numerical investigation of the validity of the Slater-Janak transition state model in metallic systems , 2005 .

[10]  T. Körzdörfer.  On the relation between orbital-localization and self-interaction errors in the density functional theory treatment of organic semiconductors. , 2011, The Journal of chemical physics.

[11]  D. Tew,et al.  Sub-meV accuracy in first-principles computations of the ionization potentials and electron affinities of the atoms H to Ne , 2010 .

[12]  F. Himpsel,et al.  Communication: Systematic shifts of the lowest unoccupied molecular orbital peak in x-ray absorption for a series of 3d metal porphyrins. , 2010, The Journal of chemical physics.

[13]  D. Sánchez-Portal,et al.  Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids , 2007 .

[14]  M. Schlüter,et al.  Density-Functional Theory of the Energy Gap , 1983 .

[15]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[16]  J. C. Slater.  Statistical Exchange-Correlation in the Self-Consistent Field , 1972 .

[17]  G. Kresse,et al.  Ab initio molecular dynamics for liquid metals. , 1993 .

[18]  L. Reining,et al.  Electronic excitations: density-functional versus many-body Green's-function approaches , 2002 .

[19]  N. Marzari,et al.  Koopmans' condition for density-functional theory , 2010, 1008.1934.

[20]  Yutaka Imamura,et al.  Linearity condition for orbital energies in density functional theory: construction of orbital-specific hybrid functional. , 2011, The Journal of chemical physics.

[21]  M. Pederson,et al.  Optical excitation energies, Stokes shift, and spin-splitting of C24H72Si14. , 2010, The Journal of chemical physics.

[22]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[23]  J. C. Slater,et al.  Self-Consistent-Field X α Cluster Method for Polyatomic Molecules and Solids , 1972 .

[24]  Weitao Yang,et al.  Singlet-triplet energy gaps for diradicals from fractional-spin density-functional theory. , 2011, The journal of physical chemistry. A.

[25]  L. Kronik,et al.  When to trust photoelectron spectra from Kohn-Sham eigenvalues: The case of organic semiconductors , 2009 .

[26]  Trickey.  Approximate electron removal energies in density-functional theory from post-hoc correction of local-spin-density eigenvalues. , 1986, Physical review letters.

[27]  B. Alder,et al.  THE GROUND STATE OF THE ELECTRON GAS BY A STOCHASTIC METHOD , 2010 .

[28]  G. Kresse,et al.  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .

[29]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[30]  John P. Perdew,et al.  Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities , 1983 .

[31]  D. Liberman.  Slater transition-state band-structure calculations , 2000 .

[32]  Lara K. Teles,et al.  Approximation to density functional theory for the calculation of band gaps of semiconductors , 2008, 0808.0729.

[33]  E. Davidson,et al.  Spin-state splittings, highest-occupied-molecular-orbital and lowest-unoccupied-molecular-orbital energies, and chemical hardness. , 2010, The Journal of chemical physics.

[34]  G. Makov,et al.  Ensemble v-representable ab-initio density-functional calculation of energy and spin in atoms: a test of exchange-correlation approximations. , 2010, 1011.4567.