The fragment molecular orbital method combined with density-functional tight-binding and the polarizable continuum model.

The energy and its analytic gradient are formulated for the fragment molecular orbital (FMO) method combined with density-functional tight-binding (DFTB) and the polarizable continuum model (PCM). The accuracy is demonstrated in comparison with unfragmented calculations and numerical gradients. The instability in the description of proteins using density functional theory (DFT) and DFTB is analyzed for both unfragmented and FMO methods. The cause of the instability is shown to be charged residues, and the problem is particularly severe in the gas phase when long-range functionals are not used. Adding solvent effects considerably increases the gap between occupied and virtual orbitals and stabilizes convergence. The pair interaction energies calculated using FMO-DFT and FMO-DFTB in solution are shown to correlate, whereas the latter method is 4840 times faster than the former for a protein consisting of 1961 atoms. The structures of five proteins (containing up to 3578 atoms) optimized using FMO-DFTB/PCM agree reasonably well with experiment.