Thole damping

In this section we briefly outline the parametrization protocol for determining the partial atomic charges, atomic polarizabilities, and the atom-based Thole damping factors, as well as the optimization procedure of the force field parameters not dependent of the Drude oscillator positions, namely the bonded and Lennard-Jones terms. While the overall parameter optimization is described linearly in the text, it is important to bear in mind that the bonded and nonbonded parameters are strongly interdependent, such that in practice, an iterative procedure is adopted, with the electrostatic and LJ nonbonded and bonded parameters optimized in turn until a self-consistent solution is reached, offering optimal agreement with all sets of target data. 

Ren and coworkers report a new polarizable development and parameterization of their atomic multipole-based optimized energetics for biomolecular simulation, AMOEBA2013 force field for proteins. It uses atomic multipole-based electrostatics and has explicit treatment of dipole polarization. Based on a mutual induction model with Thole damping it describes both intra- and intermolecular polarization. 

Both the induced dipole and Drude oscillator approaches benefit from short-range Thole damping to avoid a polarization catastrophe and to produce an anisotropic molecular polarization response." ... 

Thole s polarizability parameters were selected to optimize the molecular polarizabilities for a set of 16 molecules. The method was later expanded to fit 52 molecules [146], It must be emphasized that this electric-field damping method is totally independent of the polarization scheme used. For the Drude and fluctuating charge methods only /i(r) is required, whereas for methods based on induced dipoles both /i(r) and /2(r) are necessary. In the context of the induced dipole model other models were proposed since the formula of Thole does not provide enough attenuation. For example, in Ref. [152] the field is evaluated using... 

From Eq. (3-36) we learn that for r approaching (Aapaq)y6, a// goes to infinity and becomes negative for smaller distances. In order to avoid this unphysical situation, Thole [59] introduced a damping scheme by rewriting the interaction tensor in terms of a reduced distance upq=Rpq /(a. paq)1/6 as... 

An important modification of this approach has been the consideration of damping of the internal electric fields due to the dipoles first proposed by Thole [38]. Extension to dynamic polarizabilities has also been arrived at and application to the calculation of absorption spectra has been reported. The dipole model has also been extended to include atomic charges induced by external field along with the internal field due to other charges and dipoles. 

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