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Updated: Apr 27, 2026

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Published on: April 8, 2020
Interval prediction of molecular properties in parametrized quantum chemistry
David E Edwards1, Dmitry Yu Zubarev2, Andrew Packard3
1Department of Mechanical Engineering, University of California at Berkeley, Berkeley, California 94720-1740, USA and Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
Abstract:
The accurate evaluation of molecular properties lies at the core of predictive physical models. Most reliable quantum-chemical calculations are limited to smaller molecular systems while purely empirical approaches are limited in accuracy and reliability. A promising approach is to employ a quantum-mechanical formalism with simplifications and to compensate for the latter with parametrization. We propose a strategy of directly predicting the uncertainty interval for a property of interest, based on training-data uncertainties, which sidesteps the need for an optimum set of parameters.
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Prediction Intervals
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.