We propose and evaluate algorithms for the calculation of molecular polarizabilities and hyperpolarizabilities of extended chemical systems. These algorithms are generalizations of the Silberstein-Applequist procedure involving interacting induced classical dipoles through the localized polarizabilities and hyperpolarizabilities. The models are evaluated in terms of interacting molecular units as well as interacting atomic units that result from the atomic decomposition scheme known as the LoProp transformation. We introduce a generalized LoProp scheme which applies to hyperpolarizabilities as well as to polarizabilities. The accuracy of the second-order Applequist method is tested for the first hyperpolarizability for the TIP3P water model using both Hartree-Fock and density functional theory evaluated with different basis sets. Possible applications and ramifications of the scheme are discussed.
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 [small alpha, Greek, macron] is determined with respect to the size of the QM and MM parts of the total system.
The application of localized hyperpolarizabilities to predict a total protein hyperpolarizability is presented for the first time, using rat-tail collagen as a demonstration example. We employ a model comprising the quadratic Applequist point-dipole approach, the so-called LoProp transformation, and a procedure with molecular fractionation using conjugate caps to determine the atomic and bond contributions to the net β tensor of the collagen [(PPG)10]3 triple-helix. By using Tholes exponential damping modification to the dyadic tensor in the Applequist equations, a correct qualitative agreement with experiment is found. The intensity of the βHRS signal and the depolarization ratios are best reproduced by decomposing the LoProp properties into the atomic positions and using Tholes exponential damping with the original damping parameter. Some ramifications of the model for general protein property optimization are briefly discussed.
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