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In this paper a method to obtain a critical point of the discretizedHartree-Fock functional from an approximate critical point is given. The methodis based on Newton's method on the Grassmann manifold. We apply Newton's methodregarding the discretized Hartree-Fock functional as a function of a densitymatrix. The density matrix is an orthogonal projection in the linear spacecorresponding to the discretization onto a subspace whose dimension is equal tothe number of electrons. The set of all such matrices are regarded as aGrassmann manifold. We develop a differential calculus on the Grassmannmanifold introducing a new retraction (a mapping from the tangent bundle to themanifold itself) that enables us to calculate all derivatives. In order toobtain reasonable estimates, we assume that the basis functions of thediscretization are localized functions in a certain sense. As an application weconstruct a critical point of a molecule composed connecting several moleculesusing critical points of the Hartree-Fock functional corresponding to themolecules as the basis functions under several assumptions. By the errorestimate of Newton's method we can see that the electronic structures of themolecular fragments are preserved.

Critical points of the discretized Hartree-Fock functional of connected molecules preserving structures of molecular fragments