Energy density in density functional theory: Application to crystalline defects and surfaces

TL;DR

This paper introduces a method to decompose total energies in density functional theory into atomic contributions using energy density formalism, enabling precise calculations of surface and defect energies in crystalline materials.

Contribution

The authors develop and implement a novel energy density decomposition method within DFT, allowing for accurate atomic-level energy analysis of defects and surfaces in supercells.

Findings

Accurate calculation of surface and defect energies using energy density integration.

Method agrees with size-converged total energy difference calculations.

Convergence of defect energies can be analyzed from a single calculation.

Abstract

We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transformation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation.