All-Electron, Real-Space Perturbation Theory for Homogeneous Electric Fields: Theory, Implementation, and Application within DFT

TL;DR

This paper develops a real-space perturbation theory approach within density-functional theory, enabling efficient and accurate calculation of response properties like Raman spectra for molecules and solids using all-electron methods.

Contribution

It introduces a novel real-space formulation of perturbation theory implemented in FHI-aims, allowing massively-parallel calculations of response properties with high accuracy.

Findings

Validated the method with extensive tests on molecules and solids.

Successfully computed harmonic and anharmonic Raman spectra in good agreement with experiments.

Demonstrated the method's efficiency and accuracy for complex response property calculations.

Abstract

Within density-functional theory, perturbation theory~(PT) is the state-of-the-art formalism for assessing the response to homogeneous electric fields and the associated material properties, e.g., polarizabilities, dielectric constants, and Raman intensities. Here we derive a real-space formulation of PT and present an implementation within the all-electron, numeric atom-centered orbitals electronic structure code FHI-aims that allows for massively-parallel calculations. As demonstrated by extensive validation, this allows the rapid computation of accurate response properties of molecules and solids. As an application showcase, we present harmonic and anharmonic Raman spectra, the latter obtained by combining hundreds of thousands of PT calculations with \textit{ab initio} molecular dynamics. By using the PBE exchange-correlation functional with many-body van der Waals corrections, we obtain spectra in good agreement with experiment especially with respect to lineshapes for the isolated paracetamol molecule and two polymorphs of the paracetamol crystal.