Authors: Siyavash Moradi | Rebecca Tomann | Martin Head‐Gordon | Christopher J. Stein
Source: Journal of Computational Chemistry (article, 2026-03-10)
Field: Materials Science — Materials Chemistry

Extensions to Extended Tight‐Binding Methods for Transition‐Metal Containing Systems 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 (+ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>U</mml:mi></mml:mrow> <mml:annotation>$$ U $$</mml:annotation></mml:semantics> </mml:math> ) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>U</mml:mi></mml:mrow> <mml:annotation>$$ U $$</mml:annotation></mml:semantics> </mml:math> values for each atom. The performance of Q-Chem-xTB+ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>U</mml:mi></mml:mrow> <mml:annotation>$$ U $$</mml:annotation></mml:semantics> </mml:math> 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 + <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>U</mml:mi></mml:mrow> <mml:annotation>$$ U $$</mml:annotation></mml:semantics> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>U</mml:mi></mml:mrow> <mml:annotation>$$ U $$</mml:annotation></mml:semantics> </mml:math> values remain system-dependent, and the resulting improvements are only partially transferable. As a side effect, the + <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>U</mml:mi></mml:mrow> <mml:annotation>$$ U $$</mml:annotation></mml:semantics> </mml:math> 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. Minification ; Convergence (economics) ; Benchmark (surveying) ; Sensitivity (control systems) ; Reduction (mathematics) ; Linearity ; Error detection and correction ; Field (mathematics) Machine Learning in Materials Science ; Advanced Chemical Physics Studies ; Advanced Physical and Chemical Molecular Interactions