Fixed-charges, polarizable force field

Earlier we mentioned that Voth and co-workers conducted equilibrium MD simulations on [C2mim][N03] at 400 K and computed the self-diffusivity and shear viscosity using both a fixed charge and polarizable force field. They computed the viscosity not from integrating the stress-stress autocorrelation function as is normally done, but rather from integrating the so-called transverse current correlation function, details of which are foimd in a work by Hess. ° They used the standard Einstein formula (Eq. [15]) for the self-diffusivity and were careful to ensure that diffusive behavior was achieved when computing the self-diffusivity. Their calculated values of ca. 1 x 10 m /s for the polarizable model and ca. 5 x 10 m /s are reasonable. The finding that the polarizable model yielded faster dynamics than with the nonpolarizable model... 

We limit the discussion to simple non-polarizable force fields in which the individual atoms carry fixed charges. They capture many-body-effects such as electronic polarization only in an effective way. More sophisticated polarizable force fields have been developed over the past two decades (see for instance Ponder et al. [2010] and references therein) however they are computationally substantially more demanding. 

An important subset of many-body potentials shown to be important for simulating interfacial systems are those referred to as polarizable force fields.Various aspects of polarizable force fields, especially for use in biomolecular modeling, is explained by Ren et al. in Chapter 3 of this volume. If one treats the fixed charges in Eq. [3] as parameters to be fitted to obtain the best agreement of the condensed phase simulations with experiments, in many cases one finds that the optimal values are considerably different from those obtained from a fit to a molecular (gas phase) dipole moment or from quantum calculations on isolated molecules. This is because in a condensed medium, the local electric field E, (at the location of a particle i) is determined by all the fixed charges and by all the induced dipoles in the system ... 

Several approaches for calculating excited states in protein environments were proposed to improve the ordinary QM/MM description. The effect of polarization was included as a classical force field [27], and the excitation energy calculated for bacteriorhodopsin (bR) was 0.34 eV less than that from a fixed-charge non-polarizable QM/MM method [27]. Later, a triple-layer QM1/QM2/MM approach was proposed, and DFT(PBEO) calculations were performed for the QM2 layer, which consisted of the amino acids 4 A from the retinal PSB [28]. The calculated excitation energy of bR was only 0.08 eV smaller than that obtained using the ordinary QM/MM method [28]. In another study, an empirical polarization model combined with the QM/MM calculation produced a red shift of 0.14-0.17 eV [29]. However, these pioneering studies neglected the CT effects between the retinal and the protein environments. 

We finish the discussion of force fields developed for imidazolium-based systems by describing the work of Voth and co-workers who simulated [C2mim][N03] first with traditional fixed-charge models and then with a model that included electronic polarizability. For the fixed-charge system, Del Popolo and Voth used a force field having the AMBER function form, with parameters for the cation and anion taken from existing sources. They... 

The vast majority of CSP has been limited to using intermolecular potentials that lack explicit inclusion of polarization,although its importance has become a topic of interest.Nonpolarizable force fields, based on fixed partial charges or fixed atomic multipoles, must implicitly account for the 20-40% of the lattice energy attributable induction. " On the contrary, polarizable models such as the AMOEBA force field for organic molecules... 

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