A posteriori error estimation for the non-self-consistent Kohn-Sham equations.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Numerical solutions of Kohn-Sham equations are essential for electronic structure calculations.
• Errors arise from basis set limitations, iterative convergence, and floating-point arithmetic.
• Rigorous error bounding is critical for reliable computational results.

Purpose of the Study:

• To develop and apply a methodology for rigorously bounding numerical errors in Kohn-Sham equation solutions.
• To quantify errors stemming from basis set finiteness, convergence thresholds, and rounding errors.
• To demonstrate the practical application of error bounding in electronic structure analysis.

Main Methods:

• Development of a rigorous mathematical framework for error analysis.
• Computation of fully-guaranteed bounds for non-self-consistent equations.
• Utilizing pseudopotential approximation within a plane-wave basis set.
• Application to calculate silicon band structures with annotated error bars.

Main Results:

• Successfully computed fully-guaranteed error bounds for the numerical solution.
• Quantified combined errors from basis set, convergence, and rounding.
• Presented silicon band structure diagrams with precise error annotations.
• Validated the methodology for reliable electronic structure predictions.

Conclusions:

• The developed methodology provides reliable error bounds for Kohn-Sham equation solutions.
• Accurate electronic structure calculations are achievable with quantified error control.
• This approach enhances the trustworthiness of computational materials science predictions.