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 parameterized 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 non-fragmented 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 alpha-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 non-fragmented xTB. Parallelization over multiple CPU cores yields significant speed ups, and a complete energy and gradient evaluation of a pentacene supercell containing 23760 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.