Mixed ab initio/empirical force-field simulation studies, calculations in which one part of the system is treated using a fully ab initio description and another part is treated using an empirical description, are becoming increasingly popular. Here, the ability of the commonly used, plane wave-based generalized gradient approximation to density functional theory is extended to model systems in which the electrons are assumed to be localized in a single small region of space, that is, itself, embedded within a large chemically inert bath. This is accomplished by introducing two length scales, so that the rapidly varying, short range, electron–electron and electron–atom interactions, arising from the region where the electrons are localized, can be treated using an appropriately large plane wave basis, while the corresponding, slowly varying, long range interactions of the electrons with the full system or bath, can be treated using a small basis. Briefly, a novel Cardinal B-spline based formalism is employed to derive a smooth, differentiable, and rapidly convergent (with respect to the small basis) expression for the total electronic energy, which explicitly contains the two length scales. The method allows reciprocal space based techniques designed to treat clusters, wires, surfaces and solids/liquids (open, and 1-D and 2-D periodic boundary conditions, respectively) to be utilized. Other plane wave-based “mixed” methods are restricted to clusters. The new methodology, which scales as N log N at fixed size of the chemically active region, has been implemented for parallel computing platforms and tested through applications to both model and realistic problems including an enzyme, human carbonic anhydrase II solvated in an explicit bath of water molecules.

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