We describe a simple and novel method for identifying misconceptions. This approach utilizes the Certainty of Response Index (CRI) in conjunction with answers to multiple choice questions.

We review some salient points in the derivation of density functional theory (DFT) and of the local density approximation (LDA) of it. We then articulate an understanding of DFT and LDA that seems to be ignored in the literature. We note the well-established failures of many DFT and LDA calculations to reproduce the measured energy gaps of finite systems and band gaps of semiconductors and insulators. We then illustrate significant differences between the results from self consistent calculations using single trial basis sets and those from computations following the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). Unlike the former, the latter calculations verifiably attain the absolute minima of the occupied energies, as required by DFT. These minima are one of the reasons for the agreement between their results and corresponding, experimental ones for the band gap and a host of other properties. Further, we note predictions of DFT BZW-EF calculations that have been confirmed by experiment. Our subsequent description of the BZW-EF method ends with the application of the Rayleigh theorem in the selection, among the several calculations the method requires, of the one whose results have a full, physics content ascribed to DFT. This application of the Rayleigh theorem adds to or completes DFT, in practice, to preserve the physical content of unoccupied, low energy levels. Discussions, including implications of the method, and a short conclusion follow the description of the method. The successive augmentation of the basis set in the BZW-EF method, needed for the application of the Rayleigh theorem, is also necessary in the search for the absolute minima of the occupied energies, in practice. C

We present calculated electronic properties of gallium nitride ͑GaN͒, silicon ͑Si͒, diamond ͑C͒, and ruthenium dioxide (RuO 2 ). We implemented a simple computational procedure that avoids a recently identified basis set and variational effect. This effect, inherent to the use of basis sets in variational calculations, is believed to have affected ab initio calculations of electronic properties of semiconductors since their inception. We employed ab initio, density-functional calculations using a local-density-approximation potential and the linear combination of atomic orbital formalism. There is an excellent agreement between our findings and experimental results. In particular, the calculated, direct, minimum band gap of GaN, for low temperatures, is 3.2 eV, while the practical band gap, as per the calculated density of states, is 3.40 eV. Band gaps and excitation energies for silicon and diamond compare favorably with experimental results.

The electronic structure, charge distribution, effective charge, and charge transfer in ferroelectric tetragonal BaTiO 3 are carefully studied using a local density functional potential and a self-consistent ab initio LCAO (linear combination of atomic orbitals) method. It is shown that the band gap and low-energy conduction band can be calculated with a reasonable accuracy when the ab initio LCAO method is used with an optimum basis set of atomic orbitals. The calculated optical spectrum, band gap, and effective mass of BaTiO 3 , obtained from the calculated electronic structure, are in good agreement with experimental results.

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We report self-consistent ab-initio electronic, structural, elastic, and optical properties of cubic SrTiO3 perovskite. Our non-relativistic calculations employed a generalized gradient approximation (GGA) potential and the linear combination of atomic orbitals (LCAO) formalism. The distinctive feature of our computations stem from solving self-consistently the system of equations describing the GGA, using the Bagayoko-Zhao-Williams (BZW) method. Our results are in agreement with experimental ones where the later are available. In particular, our theoretical, indirect band gap of 3.24 eV, at the experimental lattice constant of 3.91 Å, is in excellent agreement with experiment. Our predicted, equilibrium lattice constant is 3.92 Å, with a corresponding indirect band gap of 3.21 eV and bulk modulus of 183 GPa

We report a nonrelativistic self-consistent, all-electron, local-density-functional calculation of the electronic structure of silver. The linear combination of Gaussian orbitals method is used. We present our results for the band structure, density of states, Fermi surface, Compton profiles, and optical conductivity. Our results are compared with experiments and with other calculations where possible.