Band Gap Problem Caused by Widespread Errors in Calculations and not by Density Functional Theory (DFT)

The second theorem of Density functional theory (DFT) is clear: To obtain results that possess the full, physical content of DFT, an electronic structure calculation must utilize the ground state charge density in order to reach the ground state energy. This three-dimensional charge density is à priori unknown. Consequently, electronic structure calculations must perform a generalized minimization of the energy functional, using successive, self-consistent calculations with augmented basis sets, to reach the absolute minima of the occupied energies, i.e., the ground state. Then, first or smallest of the basis sets that lead to the ground state produces the ground state charge density upon reaching self-consistency. The mainstream practice of selecting a single basis set and of performing iterations to reach a stationary state mistakenly consider that state to be the ground state. We prove, with the Rayleigh theorem for eigenvalues and the second DFT theorem, that it is not. In doing so, we show that the widespread disagreement between the results of “DFT calculations” and corresponding experimental ones cannot be ascribed to DFT. With the correct, computational method, we have described and predicted electronic and related properties of 25 semiconductors, including their band gaps that were underestimated by 359 previous DFT calculations.