# Microhartree Precision in Density-Functional-Theory Calculations

## TL;DR

This paper demonstrates that the LAPW+lo method achieves microhartree precision in density-functional-theory calculations, serving as a benchmark for atomic and periodic systems, and compares favorably with other numerical approaches.

## Contribution

The study establishes LAPW+lo as a highly precise benchmark method for DFT calculations, with detailed comparisons to other numerical techniques and applications to atoms, molecules, and periodic solids.

## Key findings

- LAPW+lo yields total energies with 0.9 μHa deviation from other methods.
- Excellent agreement of total and atomization energies for G2-1 molecules.
- LAPW+lo reaches μHa/atom precision for periodic systems like α-iron.

## Abstract

To address ultimate precision in density-functional-theory calculations we employ the full-potential linearized augmented planewave + local-orbital (LAPW+lo) method and justify its usage as a benchmark method. LAPW+lo and two completely unrelated numerical approaches, multi-resolution analysis (MRA) and linear combination of atomic orbitals, yield total energies of atoms with a mean deviation of 0.9~{\mu}Ha and 0.2~{\mu}Ha, respectively. Spectacular agreement with the MRA is reached also for total and atomization energies of the G2-1 set consisting of 55 molecules. With the example of $\alpha$-iron we demonstrate the capability of LAPW+lo of reaching {\mu}Ha/atom precision also for periodic systems, which allows also for distinction between numerical precision and the accuracy of a given functional.