Does Your Self-Consistent Field Program Know How Wrong It Is? Introducing Quantum Chemistry Uncertainty Propagation.
- 1Ames National Laboratory , Ames, Iowa50010, United States.
- 2Iowa State University , Ames, Iowa50010, United States.
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.
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BibTeX
@article{farias2026does,
title = {{Does Your Self-Consistent Field Program Know How Wrong It Is? Introducing Quantum Chemistry Uncertainty Propagation.}},
author = {Anna Diaz Farias and Shalith C Jayasekara and Jonathan M Waldrop and Eric Weber and Theresa L Windus and Ryan M Richard},
journal = {The journal of physical chemistry letters},
year = {2026},
month = oct,
doi = {10.1021/acs.jpclett.6c02837},
url = {https://europepmc.org/article/MED/42917746},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - Does Your Self-Consistent Field Program Know How Wrong It Is? Introducing Quantum Chemistry Uncertainty Propagation.
AU - Anna Diaz Farias
AU - Shalith C Jayasekara
AU - Jonathan M Waldrop
AU - Eric Weber
AU - Theresa L Windus
AU - Ryan M Richard
PY - 2026
DA - 2026/10/01
JO - The journal of physical chemistry letters
DO - 10.1021/acs.jpclett.6c02837
UR - https://europepmc.org/article/MED/42917746
AB - 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.
SN - 1948-7185
ER -