Time-dependent mean-field theory for x-ray near-edge spectroscopy

We derive equations of motion for calculating the near-edge x-ray absorption spectrum in molecules and condensed matter, based on a two-determinant approximation and Dirac's variational principle. The theory provides an exact solution for the linear response when the Hamiltonian or energy functional has only diagonal interactions in some basis. We numerically solve the equations to compare with the Mahan-Nozieres-De Dominicis theory of the edge singularity in metallic conductors. Our extracted power-law exponents are similar to those of the analytic theory, but are not in quantitative agreement. The calculational method can be readily generalized to treat Kohn-Sham Hamiltonians with electron-electron interactions derived from correlation-exchange potentials.