A Universal Power Law Governing the Accuracy of Wave Function-Based Electronic Structure Calculations

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Physics

Background:

• Wave function-based electronic structure calculations are fundamental in chemistry and physics.
• Accurate prediction of electronic energy is crucial for understanding molecular properties and reactions.
• Estimating the error in these calculations is often challenging.

Purpose of the Study:

• To derive a universal power law for the accuracy of wave function-based electronic structure calculations.
• To provide a method for facile estimation of the error in electronic energy.
• To present approaches for estimating a key system-specific factor.

Main Methods:

• Derivation of a universal power law from first principles.
• Development of an expression relating error to system size and basis set.
• Investigation of methods to estimate the on-top two-electron density-dependent factor.

Main Results:

• A universal power law, $$, governing calculation accuracy was established.
• The formula allows estimation of the error $$ in electronic energy for N-electron systems.
• Approaches for estimating the system-specific factor $$ were presented.

Conclusions:

• The derived power law offers a new tool for assessing the reliability of electronic structure calculations.
• This work facilitates the prediction of computational accuracy, aiding in the selection of appropriate methods and basis sets.
• Understanding the dependence on the on-top two-electron density provides insights into error sources.