The Effects of Computational Modeling Errors on the Estimation of Statistical Mechanical Variables

Area of Science:

• Computational chemistry
• Statistical mechanics
• Thermodynamics

Background:

• Approximate energy models are crucial for computational chemistry, relying on parameterization and error cancellation.
• Estimating thermodynamic quantities necessitates understanding how errors in energy calculations propagate.

Purpose of the Study:

• To derive and analyze the propagation of energy function errors in statistical mechanics-derived thermodynamic quantities.
• To provide methods for correcting systematic errors and estimating random errors in computed quantities.

Main Methods:

• Derivation of low-order expressions for error propagation in free energy, average energy, and entropy.
• Gedanken experiments and Monte Carlo simulations to validate error propagation formulas.
• Analysis of error propagation based on the magnitude of microstate energy errors.

Main Results:

• Low-order formulas for error propagation were derived for free energy, average energy, and entropy.
• Discrepancies between derived formulas and Monte Carlo simulations were observed for large energy errors, suggesting simulation necessity.
• Systematic errors can be removed, while random errors provide uncertainty estimates.

Conclusions:

• End-point free energy methods amplify random errors and should be avoided.
• Local sampling of potential energy wells significantly reduces random errors.
• The developed techniques will improve free energy calculations for biomolecular processes.