Does Your Self-Consistent Field Program Know How Wrong It Is? Introducing Quantum Chemistry Uncertainty Propagation
Year: 2026
Type: article
Abstract: Quantum chemistry relies on numerical approximations. Establishing the correctness and limits of these approximations traditionally requires laborious benchmarking. We introduce a more direct approach, quantum chemistry uncertainty propagation (QCUP), and apply it to a full iterative self-consistent field (SCF) calculation. QCUP-SCF estimates uncertainty from floating-point arithmetic, primitive-Gaussian screening, and incomplete SCF convergence, and propagates it to the final energy and density. Across all systems tested, predictions are typically within 1 kcal/mol compared to analytic error bars and within an order of magnitude of the true error ─ enough to establish significant figures and support runtime decision making. We also show how thresholded-affine forms improve on interval bounds by exploiting guaranteed error cancellation. This is, to our knowledge, the first end-to-end forward uncertainty quantification demonstration for an iterative ab initio method, and the first applied to both energy and wave function.
Institutions: Ames National Laboratory, Iowa State University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,500
OpenAlex ID: W7214017471