Fluctuating Charges Model

The polarizable fluctuating charge model in CHARMM results from the work of Patel, Brooks and co-workers [92, 214], The water model is based on the TIP4P-FQ model of Rick, Stuart and Berne [17], In the development of the force field the electronegativities and hardnesses were treated as empirical parameters and do not have any association with experimental or QM values, for example, from ionization energies and electron affinities of single atoms. 

The fitting of electronegativities and hardnesses is done independently of each other with the help of a reformulation of the fluctuating charge model in terms of a linear response model [117, 120, 210], In the presence of an external potential the electrostatic energy defined in Eq. (9-35) is  

Taking the difference of Eqs. (9-68) and (9-69) yields an expression for the response of the molecular charge distribution to the external field 

An objective function measuring the deviation from the parameterized model and the target response, determined, for example, from density functional theory based methods can be defined as 

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The total electric field, E, is composed of the external electric field from the permanent charges E° and the contribution from other induced dipoles. This is the basis of most polarizable force fields currently being developed for biomolecular simulations. In the present chapter an overview of the formalisms most commonly used for MM force fields will be presented. It should be emphasized that this chapter is not meant to provide a broad overview of the field but rather focuses on the formalisms of the induced dipole, classical Drude oscillator and fluctuating charge models and their development in the context of providing a practical polarization model for molecular simulations of biological macromolecules [12-21], While references to works in which the different methods have been developed and applied are included throughout the text, the major discussion of the implementation of these models focuses... 

Applications of the fluctuating charge model have relied on iterative methods to determine the converged charges [52, 159, 164, 196] and for very large-scale systems, multilevel methods have also been developed [197, 198], MC methods have also been used with fluctuating-charge models [116, 194],... 

Brodersen S, Wilke S, Leusen FJJ, Engel GE (2005) Comparison of static and fluctuating charge models for force-field methods applied to organic crystals. Cryst Growth Des 5(3) 925—933... 

Medeiros M, Costas ME (1997) Gibbs ensemble Monte Carlo simulation of the properties of water with a fluctuating charges model. J Chem Phys 107(6) 2012-2019... 

Patel S, Brooks CL (2005) A nonadditive methanol force field bulk liquid and liquid-vapor interfacial properties via molecular dynamics simulations using a fluctuating charge model. J Chem Phys... 

One feature of the semiempirical models is that because the polarization is described by a set of coefficients that have a normalization condition, for example, Eq. [69], there will be no polarization catastrophe like there can be with dipole polarizable or fluctuating charge models. With a finite basis set, the polarization response is limited and can become only as large as the state with the largest dipole moment. 

Monte Carlo Simulation of the Properties of Water with a Fluctuating Charges Model. 

M.J. Field, Hybrid quantum mechanical molecular mechanical fluctuating charge models for condensed phase simulations. Mol. Phys., 91 (1997), 835-845. 

Very recently, the above mentioned fluctuating charge model of Rick et al [100] has been parametrized using ab initio calculations on dimers and trimers by Liu et al [147]. The main reason behind this new approach is the need of enhancing transferability with respect to empirical potentials, that, as already noted, incorporate parameters optimized to reproduce a few properties at a specified thermodynamic state. 

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