2023/07/18 by Sohei Ashida, Ashida, Sohei
Chemistry · Physics and Astronomy · #49M15 #81V55 #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #FOS: Physical sciences #History and advancements in chemistry #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2307.09374
openalex publication_date 2023/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper a method to obtain a critical point of the discretized Hartree-Fock functional from an approximate critical point is given. The method is based on Newton's method on the Grassmann manifold. We apply Newton's method regarding the discretized Hartree-Fock functional as a function of a density matrix. The density matrix is an orthogonal projection in the linear space corresponding to the discretization onto a subspace whose dimension is equal to the number of electrons. The set of all such matrices are regarded as a Grassmann manifold. We develop a differential calculus on the Grassmann manifold introducing a new retraction (a mapping from the tangent bundle to the manifold itself) that enables us to calculate all derivatives. In order to obtain reasonable estimates, we assume that the basis functions of the discretization are localized functions in a certain sense. As an application we construct a critical point of a molecule composed connecting several molecules using critical points of the Hartree-Fock functional corresponding to the molecules as the basis functions under several assumptions. By the error estimate of Newton's method we can see that the electronic structures of the molecular fragments are preserved.