Fifty Years of an Understandable Misunderstanding of Density Functional Theory (DFT)

The second DFT theorem states that, for a material, the energy reaches its minimum (the ground state), when the charge density is that of the ground state. As this charge density is not known à priori, one necessarily has to minimize the energy to obtain true DFT results. For 50 years, we understandably believed that this minimization is realized upon the attainment of self-consistency, with a single basis set. Such a solution, however, is only one among an infinite number of stationary solutions. Within the linear combination of atomic orbital (LCAO) formalism, we illustrate, for representative semiconductors, that the full minimization of the energy can be realized with successive, self-consistent calculations with a basis set augmented from one calculation to the next. This process leads to the absolute minima of the occupied energies, i.e., the ground state, and results that possess the full physical content of DFT and agree with experiment. We show such excellent results for several semiconductors, including h-BN, zb-GaAs, zb-BAs, w-BeO, and zb-BeSe.