Towards an a posteriori error representation to the Hartree-Fock equations

The Hartree-Fock equations are of basic interest in ab initio quantum chemistry. They constitute a nonlinear eigenvalue problem, which has to be solved numerically. This means one has to select an efficient basis for discretizing this problem. In the chemical community, the approximation error commited thereby has hardly been analysed. In the last decade, a posteriori error estimation has grown an important tool for the determination of the approximation space for partial differential equations. Often, one is not interested in the error of the approximate solution with respect to some global norm, but rather to improve the error in the value of some target functional computed from it. This is the aim of the so-called Dual Weighted Residual Method, which we want to apply to the Hartree-Fock equations.