Accuracy and Precision in Electronic Structure Computation: Wien2k and FPLO

Electronic structure calculations in the framework of density functional theory are based on complex numerical codes which are used in a multitude of applications. Frequently, existing experimental information is used as a gauge for the reliability of such codes. However, their results depend both on the chosen exchange-correlation energy functional and on the specific numerical implementation of the Kohn-Sham equations. The only way to disentangle these two items is a direct comparison of two or more electronic structure codes. Here, we address the achievable numerical accuracy and numerical precision in the total energy computation of the two all-electron density-functional codes Wien2k and FPLO. Both codes are based on almost independent numerical implementations and largely differ in the representation of the Bloch wave function. Thus, it is a highly encouraging result that the total energy data obtained with both codes agree within less than 10-6. We here relate the term numerical accuracy to the value of the total energy E, while the term numerical precision is related to the numerical noise of E as observed in total energy derivatives. We find that Wien2k achieves a slightly higher accuracy than FPLO at the price of a larger numerical effort. Further, we demonstrate that the FPLO code shows somewhat higher precision, i.e., less numerical noise in E than Wien2k, which is useful for the evaluation of physical properties based on derivatives of E.

Automated summary

This study compares the numerical accuracy and numerical precision of two electronic structure codes, Wien2k and FPLO, in calculating the total energy. The results show that the total energy data obtained from both codes agree within a difference of less than 10^-6. Wien2k achieves slightly higher accuracy at the cost of larger numerical effort, while FPLO shows higher precision, i.e., less numerical noise in the total energy derivatives, which is useful for evaluating physical properties.