Estimating the Complete Basis Set Extrapolation Error through Random Walks

Area of Science:

• Computational chemistry
• Quantum chemistry

Background:

• Extrapolation to the complete basis set (CBS) limit is crucial for accurate quantum chemical calculations.
• Estimating the uncertainty associated with CBS extrapolation is challenging but essential for reliable predictions.

Purpose of the Study:

• To propose a novel, parameter-free method for quantifying the uncertainty in results obtained via CBS extrapolation.
• To provide a statistically rigorous framework for predicting error bounds at a desired confidence level.

Main Methods:

• The method employs an ensemble of random walks to simulate all potential extrapolation outcomes.
• Statistical analysis of the ensemble results enables uncertainty prediction.
• The approach is designed to be compatible with any existing CBS extrapolation scheme.

Main Results:

• Numerical trials demonstrate the reliability and tightness of the predicted error bounds.
• The method provides conservative estimates, ensuring a high level of confidence in the uncertainty quantification.
• The approach was validated by comparison with reliable reference data.

Conclusions:

• The proposed random walk ensemble method offers a robust and versatile tool for uncertainty estimation in CBS extrapolation.
• This technique enhances the reliability of computational chemistry results by providing accurate and conservative error bounds.
• The parameter-free nature and compatibility with various schemes make it broadly applicable in scientific research.