Kohn-Sham Band Gaps Research Articles

Ab initio structural, electronic and optical properties of orthorhombic [formula omitted

Orthorhombic CaGeO 3 is studied using density-functional theory (DFT) considering both the local density and generalized gradient approximations, LDA and GGA, respectively. The electronic band structure, density of states, dielectric function and optical absorption are calculated. Two very close indirect ( S → Γ ) and direct ( Γ → Γ ) band gap energies of 1.68 eV (2.31 eV) and 1.75 eV (2.41 eV) were obtained within the GGA (LDA) approximation, as well as the effective masses for electrons and holes. Comparing with orthorhombic CaCO 3 (aragonite), the substitution of carbon by germanium changes the localization of the valence band maximum of the indirect transition, and decreases by almost 2.0 eV the Kohn–Sham band gap energies.

An Efficient Linear-Scaling Electrostatic Coupling for Treating Periodic Boundary Conditions in QM/MM Simulations.

A new linear-scaling method based on a multigrid approach to treat long-range electrostatic interactions in hybrid quantum mechanics/molecular mechanics (QM/MM) simulations is described. The scheme has been implemented in the context of a QM calculation based on density functional theory (DFT). The method is tested on an analytical model to validate the new algorithm. Two realistic problems in α-quartz crystals and a zwitterionic dipeptide (GLY-ALA) in water have been chosen as further tests. Results from QM/MM calculations with periodic boundary conditions (PBC) show that the use of PBC is essential when studying highly ordered crystal structures, unless a carefully designed MM crystal is used for the calculation. With a general shaped MM subsystem, the absence of PBC leads to an incorrect description of Kohn-Sham band gaps and charge density. The present method allows periodic boundary conditions to be used in molecular simulations of biological and material science systems.

Density functionals from many-body perturbation theory: The band gap for semiconductors and insulators

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical (random phase approximation) screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively [R. W. Godby et al., Phys. Rev. B 36, 6497 (1987)] and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid.

Band-gap energy in the random-phase approximation to density-functional theory

We calculate the interacting bandgap energy of a solid within the random-phase approximation (RPA) to density functional theory (DFT). The interacting bandgap energy is defined as ${E}_{g}={E}^{\mathrm{RPA}}(N+1)+{E}^{\mathrm{RPA}}(N\ensuremath{-}1)\ensuremath{-}2{E}^{\mathrm{RPA}}(N)$, where ${E}^{\mathrm{RPA}}(N)$ is the total DFT-RPA energy of the $N$-electron system. We compare the interacting bandgap energy with the Kohn-Sham bandgap energy, which is the difference between the conduction and valence band edges in the Kohn-Sham band structure. We show that they differ by an unrenormalized ``${G}_{0}{W}_{0}$'' self-energy correction (i.e., a $GW$ self-energy correction computed using Kohn-Sham orbitals and energies as input). This provides a well-defined and meaningful interpretation to ${G}_{0}{W}_{0}$ quasiparticle bandgap calculations, but questions the physics behind the renormalization factors in the expression of the bandgap energy. We also separate the kinetic from the Coulomb contributions to the DFT-RPA bandgap energy, and discuss the related problem of the derivative discontinuity in the DFT-RPA functional. Last we discuss the applicability of our results to other functionals based on many-body perturbation theory.

Orbital dependent exchange-only methods for periodic systems

Various orbital-dependent exchange-only potentials are studied which exhibit correct long-range asymptotic behavior. We present the application of these potentials for polymers and by one of these potentials for molecules. Kohn-Sham type periodic calculations have been carried out for polyethylene in order to make valuable comparison of these potentials with each other as well as with Hartree-Fock and exchange-only LDA (Xa) methods. The difference between total energies and highest occupied orbital energies obtained with Hartree-Fock methods and with localized exchange potentials is larger for this polymer than for atoms or molecules. Various properties of the band structure are also calculated. The band gap strongly depends on the basis set. The larger basis set makes the Kohn-Sham eigenvalue gap too low at about 4.4 eV while the minimal basis set results in value close to the experimental gap ( ;8.8 eV!. For the total energy and the exchange energy, the various orbital-dependent exchange-only and Hartree-Fock results differ only slightly, but for the highest occupied orbital energy the difference is more pronounced. The Kohn-Sham band gap obtained with the optimized effective potential method is corrected with the exchange contribution to the derivative discontinuity of the exchange-correlation potential. The corrected band gap obtained with the Slater’s exchange potential is 9.7 eV. @S0163-1829~99!07731-0#

Density-functional theory on a lattice: Comparison with exact numerical results for a model with strongly correlated electrons.

Most of the basic ideas of the density-functional theory (DFT) are shown to be unrelated to the fact that the particle density is used as the basic variable. After presenting the general formalism and a simple example unrelated to densities, we discuss various approaches to density-functional theory on a lattice. One has proven useful for the understanding of various fundamental issues of the DFT. The exact Kohn-Sham band gap and the band gap in the local-density approximation (LDA) are compared to the exact results for a one-dimensional model. As the interacting homogeneous system can be solved exactly no further approximation is needed to formulate the LDA.