Statistical Analysis of Semiclassical Dispersion Corrections.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Semiclassical dispersion corrections (D3-type) are vital for Kohn-Sham density functional theory.
• Understanding their parametrization is key for improving accuracy.

Purpose of the Study:

• To rigorously assess the fit parameters in D3-type dispersion corrections.
• To evaluate the impact of cost function choices and weighting schemes.
• To provide unbiased uncertainty estimates for parameters and predictions.

Main Methods:

• Statistical analysis of D3-type dispersion correction parameters.
• Nonparametric bootstrap analysis for uncertainty estimation.
• Jackknife analysis of the reference dataset.

Main Results:

• Cost function choice has a minor effect on parameters, but weighting schemes significantly impact dispersion energy predictions.
• Bootstrap analysis yields small parameter standard deviations and prediction uncertainties comparable to prior estimates.
• Reference dataset skewness has minimal impact, but error cancellation is not guaranteed, leading to potential deviations in large molecules.

Conclusions:

• Weighting schemes in cost functions critically influence D3-type dispersion correction reliability.
• Uncertainty quantification is essential for accurate dispersion energy calculations.
• A software tool is provided to determine associated uncertainties.