# Unveiling the Low-Lying Spin States of [Fe3S4] Clusters via the Extended Broken-Symmetry Method

## TL;DR

This paper introduces a new method to better understand the magnetic properties of iron-sulfur clusters in hydrogenase enzymes, which are important for clean energy production.

## Contribution

The Extended Broken-Symmetry method is introduced to accurately compute low-lying spin states of [Fe3S4] clusters in hydrogenases.

## Key findings

- The Extended Broken-Symmetry method reduces spin contamination errors in calculations.
- The method provides accurate bond length differences and magnetic coupling constants for [Fe3S4] clusters.
- Geometric arrangement of metal centers significantly affects the magnetic properties of the clusters.

## Abstract

Photosynthetic water splitting, when synergized with hydrogen production catalyzed by hydrogenases, emerges as a promising avenue for clean and renewable energy. However, theoretical calculations have faced challenges in elucidating the low-lying spin states of iron–sulfur clusters, which are integral components of hydrogenases. To address this challenge, we employ the Extended Broken-Symmetry method for the computation of the cubane–[Fe3S4] cluster within the [FeNi] hydrogenase enzyme. This approach rectifies the error caused by spin contamination, allowing us to obtain the magnetic exchange coupling constant and the energy level of the low-lying state. We find that the Extended Broken-Symmetry method provides more accurate results for differences in bond length and the magnetic coupling constant. This accuracy assists in reconstructing the low-spin ground state force and determining the geometric structure of the ground state. By utilizing the Extended Broken-Symmetry method, we further highlight the significance of the geometric arrangement of metal centers in the cluster’s properties and gain deeper insights into the magnetic properties of transition metal iron–sulfur clusters at the reaction centers of hydrogenases. This research illuminates the untapped potential of hydrogenases and their promising role in the future of photosynthesis and sustainable energy production.