Exchange-correlation functional based on the density matrix

I present an exchange-correlation functional which incorporates the off-diagonal components of the one-electron density matrix. The functional is derived within tight-binding theory from interpolation between well-established limits, using a rigorous inequality. The functional, unlike the local-density approximation, obtains charge quantization for isolated atoms, fluctuating-dipole interactions, and Hubbard-gap effects. The results should greatly expand the range of problems treatable by ab initio simulations.