Frequency-dependent force fields for QMMM calculations

We outline the construction of frequency-dependent polarizable force fields. The force fields are derived from analytic response theory for different frequencies using a generalization of the LoProp algorithm giving a decomposition of a molecular dynamical polarizability to localized atomic dynamical polarizabilities. These force fields can enter in a variety of applications - we focus on two such applications in this work: firstly, they can be incorporated in a physical, straightforward, way for current existing methods that use polarizable embeddings, and we can show, for the first time, the effect of the frequency dispersion within the classical environment of a quantum mechanics-molecular mechanics (QMMM) method. Our methodology is here evaluated for some test cases comprising water clusters and organic residues. Secondly, together with a modified Silberstein-Applequist procedure for interacting inducible point-dipoles, these frequency-dependent polarizable force fields can be used for a classical determination of frequency-dependent cluster polarizabilities. We evaluate this methodology by comparing with the corresponding results obtained from quantum mechanics or QMMM where the absolute mean (alpha) over bar is determined with respect to the size of the QM and MM parts of the total system.