Generalized Hybrid Orbital (GHO) Method for Combining Ab Initio Hartree−Fock Wave Functions with Molecular Mechanics

The generalized hybrid orbital (GHO) method provides a way to combine quantum mechanical (QM) and molecular mechanical (MM) calculations on a single molecular system or supramolecular assembly by providing an electrostatically stable connection between the QM portion and the MM portion. The GHO method has previously been developed for semiempirical molecular orbital calculations, on the basis of neglect of diatomic differential overlap (GHO−NDDO); in the present work, it is extended to the ab initio Hartree−Fock (HF) level (GHO−AIHF). First, the theoretical foundation for the GHO−AIHF extension is discussed, and four different approaches are proposed to overcome the nonorthogonality between active molecular orbitals (MOs) and auxiliary MOs. In the first scheme, the auxiliary hybrid basis functions are projected out of the active QM basis. The second scheme neglects the diatomic differential overlap between the auxiliary basis and the active QM basis. In the third scheme, hybrid orbitals are constructed from Löwdin-type symmetric orthogonalized atomic orbitals on the basis of global Löwdin orthogonalization. The fourth procedure involves local Löwdin orthogonalization. The procedures for implementing the four GHO−AIHF schemes are described, and analytical gradient expressions are derived. The unparametrized GHO−AIHF method is tested for hydrocarbons with various basis sets, in particular, the geometries and charges are compared with pure QM calculations for ethane, ethyl radical, and n-octane, and the method is tested for the torsion potential around the central bond in n-butane. Furthermore, a parametrization of the GHO−AIHF method for the MIDI! basis is presented and tested for 16 molecules and ions with various functional groups near the QM/MM boundary. The results show the robustness of the algorithm and illustrate the significant improvement made by introducing several one-electron integral-scaling parameters. Finally, the energetic performance of the method is tested by comparing the proton affinities for a set of small model compounds (alcohols, amines, thiols, and acids) to results obtained from fully QM calculations. We conclude that the GHO−AIHF scheme provides a reasonable fundamental solution to the problem of combining an ab initio quantum mechanical electronic structure calculation with molecular mechanics.