# Extensions to Extended Tight‐Binding Methods for Transition‐Metal Containing Systems

## TL;DR

This paper introduces improvements to a quantum chemistry method to better model systems containing transition metals, especially iron complexes.

## Contribution

The paper introduces a geometric direct minimization scheme and a self-consistent Hubbard-U correction to the xTB method for transition-metal systems.

## Key findings

- The +U correction significantly reduces error and improves electronic linearity in iron complexes.
- The +U correction stabilizes SCF convergence by widening the HOMO–LUMO gap.
- Optimized U values are system-dependent and improvements are only partially transferable.

## Abstract

Semi‐empirical quantum‐chemical methods such as extended tight‐binding (xTB) models are widely used for large‐scale simulations. Despite their popularity, their accuracy for transition‐metal containing systems is lower than, for example, closed‐shell organic molecules. In this work, we extend the Q‐Chem‐xTB framework with a geometric direct minimization (GDM) scheme for robust self‐consistent convergence and Hubbard correction (+U) to improve the description of local interactions and reduce self‐interaction errors similar to those characteristic of density‐functional theory calculations for transition‐metal complexes. The Hubbard correction term is integrated self‐consistently within the xTB Hamiltonian, allowing shell‐specific U values for each atom. The performance of Q‐Chem‐xTB+U is assessed for four benchmark sets of iron complexes, focusing on their spin‐state energetics. Sensitivity and optimization analyses of the spin parameters show that parameter tuning alone cannot systematically reduce the error or consistently recover correct spin ground‐state predictions across different datasets. In contrast, introducing the +U correction yields significant error reduction and improved electronic linearity with respect to fractional occupation, demonstrating that the correction fulfills its intended role of reducing self‐interaction error. However, the optimized U values remain system‐dependent, and the resulting improvements are only partially transferable. As a side effect, the +U correction stabilizes the self‐consistent field optimization by widening the HOMO–LUMO gap, thereby overcoming convergence instabilities of the conventional direct inversion of the iterative subspace (DIIS) scheme at low electronic temperatures.

We present a new GFN2‐xTB implementation with a geometric direct minimization scheme and a Hubbard‐U correction. We demonstrate that the Hubbard correction improves linearity of the elctronic energy, stabilizes SCF convergence, and enables more accurate spin‐gap predictions in narrow application domains such as specific iron‐containing complexes.