FMO-xTB: Fragment Molecular Orbital Method with GFN1-xTB for Large-Scale Quantum-Mechanical Simulations

We present the fragment molecular orbital method (FMO) combined with the GFN1-xTB extended tight-binding approach (FMO-xTB) for efficient quantum-mechanical calculations of large molecular systems. Both the two-body (FMO2) and three-body (FMO3) expansions are formulated, and fully analytic energy gradients including the response contribution from the self-consistent embedding potential are derived and implemented. The FMO-xTB method inherits the broad element coverage of GFN1-xTB, which employs element-specific rather than atom-pair-specific parameters and is parametrized for all spd-block elements up to radon (Z = 86), representing a significant practical advantage over FMO-DFTB approaches. The accuracy of FMO-xTB is systematically benchmarked against nonfragmented xTB calculations for water clusters, anthracene aggregates, and pentacene supercells. FMO3-xTB reproduces the reference energies with deviations on the order of 10–4 hartree for organic semiconductor systems. The covalent bond fragmentation capability using the hybrid orbital projection (HOP) boundary treatment is also implemented with fully analytic gradients and validated for polyalanine α-helices and B-DNA double helices, yielding FMO3-xTB energy deviations on the order of 10–6 hartree for polyalanine and in the millihartree range for B-DNA. Near-linear scaling is achieved with effective scaling exponents between b = 1.06 and b = 1.28, compared to cubic scaling for nonfragmented xTB. Parallelization over multiple CPU cores yields significant speed ups, and a complete energy and gradient evaluation of a pentacene supercell containing 23 760 atoms is feasible within minutes on a single computing node, enabling routine molecular dynamics simulations of systems with tens of thousands of atoms. The method is implemented in the DIALECT software package.