Density-functional formalism: Sources of error in local-density approximations

The local spin-density approximation in density-functional calculations of energy differences leads to some poorly understood departures from experiment, including excitation energies in atoms and binding energies in molecules. We show that errors in the exchange energy are a major source of these discrepancies. We identify classes of problems where local spin-density results should be satisfactory and others where they must be treated with caution. The consequences, particularly for the development of nonlocal modifications, are clear.