Combining Self-Consistent-Charge Density-Functional Tight-Binding (SCC-DFTB) with Molecular Mechanics by the Generalized Hybrid Orbital (GHO) Method

In combined quantum mechanical and molecular mechanical (QM/MM) calculations with the QM/MM boundary at a covalent bond, the generalized hybrid orbital (GHO) method has been shown to provide a well balanced and stable connection between the QM and MM regions. The GHO method has previously been developed for semiempirical molecular orbital methods based on neglect of diatomic differential overlap (GHO-NDDO) and for the ab initio Hartree−Fock level (GHO-AIHF). In the present work, we formulate the GHO algorithm and its analytical gradients for treating the QM subsystem by the self-consistent-charge density-functional tight-binding (SCC-DFTB) theory. To obtain a good description of the bond length at the QM/MM boundary, a parametrized empirical correction term involving the GHO boundary atom and its QM frontier neighbor is added. Geometries and Mulliken charges obtained from GHO-SCC-DFTB calculations are compared to the fully QM results for a set of 18 molecules and ions with various functional groups close to the boundary, and we verified that we reproduced the full C−C stretch potential in ethane and in propanoate. The torsion barrier of n-butane around the central C−C bond is studied with the GHO boundary atom placed at different locations. Finally, the energetics of the method are tested for the proton affinities of a series of 15 alcohols, amines, thiols, and acids. The results indicate that the GHO treatment for combining SCC-DFTB with molecular mechanics is both theoretically robust and satisfactory for practical use. In Supporting Information we present parameters for boundaries that cut through O−C and S−C bonds.