Tackling excited states: Koopmans functionals now available as an open-source software package

This was published on September 26, 2023

A 10-year effort has led to a theoretical framework and a software package, called koopmans, that allows to obtain reliable spectral properties of molecules and materials with density functional theory. The framework is described in a new article by MARVEL researchers at EPFL, and last month a week-long school co-organised by MARVEL in Pavia saw students learning about Koopmans functionals and trying out the code.

By Nicola Nosengo, NCCR MARVEL

Density functional theory (DFT) is a cornerstone of materials simulation, but it has well known limitations. It allows scientists to calculate the behaviour of electrons inside a material in their lowest energy configuration, but it fails to accurately describe excited states, and thus cannot be used to describe the spectral properties of molecules and materials – such as the energy of light required to eject an electron from a material in a solar cell. Scientists use other computational techniques to study these processes, such as the GW method, but they are computationally more expensive, require a lot of fine-tuning, and are not easy to deploy on a large scale.

That is why, about a decade ago, researchers in Nicola Marzari’s group at EPFL embarked on an effort to devise a new set of functionals that would enable DFT to reliably calculate spectral properties.  They named their new functionals “Koopmans” functionals, after the Dutch mathematician and economist Tjalling Koopmans, author of a foundational theorem on the ionization energy of molecular systems (and a Nobel laureate in economics to boot)

These Koopmans functionals showed excellent promise; they predicted excited state properties well, and the researchers continued to develop them, but there was one major problem.“The very early implementations of these functionals were very inaccessible, private codes” recalls Edward Linscott, a scientist in Nicola Marzari’s laboratory at EPFL and lead author of the new study. “After all, the theory was very novel, there was a lot of unexplored territory, and the formulas were quite different to what existing codes implemented. But over time, we refined our computational techniques and our code base matured, culminating in the release of a code that now can be used also by non-experts”. 

J. Chem. Theory Comput. 2023.

The result of that effort, described in a study published in Journal of Chemical Theory and Computation in August, is now a theoretical framework and an open-source software package called simply koopmans, that contains all the code and workflows needed to perform Koopmans functional calculations and obtain reliable spectral properties of molecules and materials. The newly released package builds upon standard open source tools such as Quantum ESPRESSO.

This effort was over 10 years in the making, but it’s not the end of the story. The team has several developments in sight. “We’ll continue to streamline the workflows and we will be introducing innovations to make them more robust, requiring less intervention and fine- tuning from the user” explains Linscott. “This can open up the door to high throughput studies on large databases of materials, where you can’t babysit each calculation”. To this end, the team will also explore the integration of the koopmans package with the AiiDA ecosystem. The authors of the paper are also eager to apply their new tool to a new set of problems. “For example, we are now investigating the thermal behaviour of some perovskites. These calculations involve large cells with lots of disordered atoms” says Linscott. “By combining Koopmans functionals with machine learning, you can start to tackle very complicated, interesting systems”.

And now with the release of the koopmans package, the authors hope that other scientists will find these functionals useful in their own research. Last month, Koopmans functionals were one of the main topics of a week-long school which was co-organised by MARVEL in Pavia, that saw students learning about Koopmans functionals and trying out the code for themselves.

“We hope that koopmans will be used by people who use DFT for their own research but find themselves limited by DFT’s inability to predict spectral properties,” says Linscott. “Previously, they might have used GW which is more systematic but has much harder calculations to perform and is much more difficult to apply to larger systems, because calculations become prohibitively expensive. We provide these people with a new middle path, without the cost of GW but also without the shortcomings of standard DFT”.

Reference

E. B. Linscott, N. Colonna, R. De Gennaro, N. Linh Nguyen, G. Borghi, A. Ferretti, I. Dabo, and N. Marzari, "koopmans: An Open-Source Package for Accurately and Efficiently Predicting Spectral Properties with Koopmans Functionals". Journal of Chemical Theory and Computation (2023). DOI: 10.1021/acs.jctc.3c00652

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