Downfolding approaches to electron-ion coupling: Constrained density-functional perturbation theory for molecules

TL;DR

This paper explores downfolding methods, especially constrained density-functional perturbation theory, to understand electron-ion interactions, revealing how screening affects phonon frequencies and the role of dipole selection rules.

Contribution

It provides a detailed analysis of constrained density-functional perturbation theory and its implications for electron-ion coupling, including new insights into phonon behavior and screening effects.

Findings

Electronic screening lowers phonon frequencies.

Dipole selection rules determine Goldstone's theorem compliance.

Validated theory with calculations on molecules and graphene.

Abstract

Constrained electronic-structure theories enable the construction of effective low-energy models consisting of partially dressed particles. However, the interpretation and physical content of these theories is not straightforward. Here, we carefully explore the properties of downfolding theories for electron-ion problems, in particular constrained density-functional perturbation theory (cDFPT). We show that the dipole selection rules determine whether the partially dressed phonons satisfy Goldstone's theorem, and we prove that electronic screening always lowers the phonon frequencies. We illustrate the theory with cDFPT calculations for minimal example systems: the nitrogen and benzene molecule as well as graphene.