koopmans: an open-source package for accurately and efficiently predicting spectral properties with Koopmans functionals

TL;DR

This paper introduces koopmans, an open-source software package that implements Koopmans functionals, providing a computationally efficient and accurate method for predicting spectral properties of molecules and materials, addressing limitations of traditional DFT.

Contribution

The paper presents the theory, algorithms, and implementation of Koopmans functionals in an open-source package, enabling reliable spectral property predictions with reduced computational cost.

Findings

Koopmans functionals match electron removal/addition energies.

Achieves accuracy comparable to many-body perturbation theory.

Provides an efficient, open-source tool for spectral property calculations.

Abstract

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise linearity condition to the entire electronic manifold, ensuring that orbital energies match the corresponding electron removal/addition energy differences (in contrast to semi-local DFT, where a mismatch between the two lies at the heart of the band gap problem and, more generally, the unreliability of Kohn-Sham orbital energies). This strategy has proven to be very powerful, yielding molecular orbital energies and solid-state band structures with comparable accuracy to many-body perturbation theory but at greatly reduced computational cost while preserving a functional formulation. This paper reviews the theory of Koopmans functionals, discusses the algorithms necessary for their implementation, and introduces koopmans, an open-source package that contains all of the code and workflows needed to perform Koopmans functional calculations and obtain reliable spectral properties of molecules and materials.