Nuclear-electronic orbital method within the fragment molecular orbital approach

The nuclear-electronic orbital (NEO) method, which treats selected nuclei quantum mechanically on the same level as the electrons, is combined with the fragment molecular orbital (FMO) method, which is an approximate scheme for electronic structure calculations of large systems. This FMO-NEO approach is implemented in conjunction with Hartree-Fock theory, density functional theory, and second-order perturbation theory using a variety of fragmentation schemes, including those that fraction covalent bonds. A multilayer FMO method, which limits the NEO calculation to a specified portion of the total system, is also implemented. These approaches are applied to four model systems: a water hexamer, a methyl-capped glycine dimer, a cluster of 32 water molecules, and a phenol molecule solvated by 16 water molecules. The FMO-NEO results are in excellent agreement with full NEO results for the calculation of properties associated with the nuclear quantum effects, such as zero-point energies, isotope effects, and vibrational excitation energies. The multilayer FMO-NEO method also provides reasonable results, and systematic improvements can be achieved by increasing the number of fragments in the NEO layer.