Derivative-Free Optimization for Quantum Chemistry
Published:Dec 30, 2025 23:15
•1 min read
•ArXiv
Analysis
This paper investigates the application of derivative-free optimization algorithms to minimize Hartree-Fock-Roothaan energy functionals, a crucial problem in quantum chemistry. The study's significance lies in its exploration of methods that don't require analytic derivatives, which are often unavailable for complex orbital types. The use of noninteger Slater-type orbitals and the focus on challenging atomic configurations (He, Be) highlight the practical relevance of the research. The benchmarking against the Powell singular function adds rigor to the evaluation.
Key Takeaways
- •Evaluates derivative-free optimization algorithms for quantum chemistry problems.
- •Focuses on Hartree-Fock-Roothaan energy functionals with noninteger Slater-type orbitals.
- •Compares Powell's method, Nelder-Mead, pattern search, and a model-based algorithm.
- •Applies algorithms to He and Be isoelectronic series.
- •Addresses the challenge of non-convex optimization landscapes.
Reference
“The study focuses on atomic calculations employing noninteger Slater-type orbitals. Analytic derivatives of the energy functional are not readily available for these orbitals.”