Total-energy differences: Sources of error in local-density approximations

A detailed comparison of local-spin-density (LSD), X (exchange-only), and Hartree-Fock calculations with experimental data shows that errors in density-functional calculations using the LSD approximation often arise from an unsatisfactory description of the exchange energy. The exchange energy depends sensitively on the angular characteristics and nodal structure of the orbitals, and these features are not properly incorporated into local-density calculations. Examples of the consequences are provided by errors in the sp and sd transfer energies in first-row and 3d atoms, respectively, since LSD calculations do not distinguish properly between s, p, and d electrons. We identify the main sources of error in these cases. For atoms and small molecules, we show that there is a ``natural'' occupancy of orbitals for which local-density approximations give a satisfactory description of the exchange energy. For other occupancies the relative errors are usually large. The consequences for extended systems and for the development of nonlocal functions are discussed.