Riemannian gradient descent for Hartree-Fock theory

Quantum Physics [Submitted on 16 Mar 2026] Riemannian gradient descent for Hartree-Fock theory Evgueni Dinvay We present a Riemannian optimization framework for Hartree-Fock theory formulated directly in the Sobolev space H^1. The orthonormality constraints are interpreted geometrically via infinite-dimensional Stiefel and Grassmann manifolds endowed with the embedded H^1 metric. Explicit expressions for Euclidean and Riemannian gradients, tangent-space projections, and retractions are derived using resolvent operators, avoiding distributional formulations. The resulting algorithms include Riemannian steepest descent and a preconditioned nonlinear conjugate gradient method equipped with Armijo backtracking and Powell-type restarts. Particular attention is given to physically motivated preconditioning based on inversion of the kinetic energy operator. The framework is naturally compatible with adaptive multiwavelet discretizations, where Coulomb-type convolutions can be evaluated efficiently. Numerical experiments demonstrate robust convergence and competitive performance compared to conventional SCF-DIIS schemes. In addition, for small molecules the gradient descent method converges from random initial guesses. The proposed formulation provides a geometrically consistent and discretization-independent perspective on electronic structure optimization and offers a foundation for further developments in infinite-dimensional Riemannian methods for quantum chemistry. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.15870 [quant-ph]   (or arXiv:2603.15870v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.15870 Focus to learn more Submission history From: Evgueni Dinvay [view email] [v1] Mon, 16 Mar 2026 19:58:42 UTC (147 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)