g-xTB: A General-Purpose Extended Tight-Binding Electronic Structure Method For the Elements H to Lr (Z=1–103)

We present g-xTB, a next-generation semi-empirical electronic structure method derived from tight-binding (TB) approximations to Kohn–Sham density functional theory (KS-DFT). Designed to bridge the gap between semi-empirical quantum mechanical (SQM) approaches and DFT in terms of accuracy, robustness, and general applicability, g-xTB targets the performance of the ωB97M-V range-separated hybrid density functional with large basis sets while maintaining TB speed. Key innovations include an atom-in-molecule adaptive atomic orbital basis, a refined Hamiltonian incorporating range-separated approximate Fock exchange, up to fourth-order charge-fluctuation terms with a novel first-order electronic contribution, and atomic correction potentials (ACPs), as well as a charge-dependent semi-classical repulsion function. Parameterized on extended and extremely diverse molecular training sets – including “mindless molecules” – g-xTB achieves excellent accuracy across a broad chemical space, including the actinide elements. Benchmarking against around 32k relative energies across thermochemistry, conformational energetics, non-covalent interactions, and reaction barriers shows that g-xTB consistently outperforms GFN2-xTB, often reducing mean absolute errors by half. Notably, it achieves a WTMAD-2 of 9.3 kcal mol−1 on the full GMTKN55 benchmark, comparable to low-cost DFT methods. It also shows substantial improvements for transition-metal complexes, relative spin state energies, and orbital energy gaps – areas where many SQM and even DFT methods often struggle. In summary, g-xTB offers DFT-like accuracy with minimal computational overhead compared to its predecessor, GFN2-xTB, making it a robust, minimally empirical, transferable, and efficient alternative to machine learning interatomic potentials for a wide range of molecular simulations. It is proposed as a general replacement for the GFNn-xTB family and, in many practical cases, a viable substitute for low- and mid-level DFT methods.