Multilayer Formulation of the Fragment Molecular Orbital Method (FMO)

The fragment molecular orbital method (FMO) has been generalized to allow for multilayer structure. Fragments are assigned to layers, and each layer can be described with a different basis set and/or level of electron correlation. Interlayer boundaries are treated in the general spirit of the FMO method since they also coincide with some interfragment boundaries. The question of the one- and two-layer FMO accuracy dependence upon the fragmentation scheme is also addressed. The new method has been applied to predict the reaction barrier and the reaction heat for the Diels−Alder reaction with a representative set of reactants based on dividing fragments in two layers. The 6-31G* basis set has been used for the active site and the 6-31G*, 6-31G, 3-21G, and STO-3G basis sets have been used for the substituents. Different levels of electron correlation (RHF, B3LYP, and MP2) have been applied to layers in systematic fashion. The one-layer FMO errors in the reaction barrier and the reaction heat were 2.0 kcal/mol or less for all levels applied (RHF, B3LYP, and MP2), relative to full ab initio methods. For the two-layer method the error was found to be several kcal/mol. Benchmark calculations of the activation barrier for the decarboxylation of phenylcyanoacetate by β-cyclodextrin demonstrated that the two-layer calculations are efficient, being 36 times faster than the regular DFT, as well as accurate, with the error being 1.0 kcal/mol.