Point-polarizable models

In the first example of applications of the theory in this chapter, we made a point with respect to the polarizability of molecules and showed how the problem could have been handled by the RISM-SCF/MCSCF theory. However, the current level of our method has a serious limitation in this respect. The method can handle the polarizability of molecules in neat liquids or that of a single molecule in solution in a reasonable manner. But in order to be able to treat the polarizability of both solute and solvent molecules in solution, considerable generalization of the RISM side of the theory is required. When solvent molecules are situated within the influence of solute molecules, the solvent molecules are polarized differently depending on the distance from the solute molecules, and the solvent can no longer be neat. Therefore, the polarizable model developed for neat liquids is not valid. In such a case, solvent-solvent PCF should be treated under the solute... 

For a given a the force constant ko can be chosen in a way that the displacement d of the Drude particle remains much smaller than the interatomic distance. This guarantees that the resulting induced dipole jl, is almost equivalent to a point dipole. In the Drude polarizable model the only relevant parameter is the combination q /ko which defines the atomic polarizability, a. It is... 

Results of parameter optimization and MD simulations of small model compounds have been published, including alcohols [63], alkanes [63], aromatic [64] and heteroaromatic [209] compounds and liquid amides [65], Studies of ions in aqueous solution were also performed [61, 88] and results from an MD simulation on a DPPC lipid monolayer have been reported (Harder, MacKerell, Roux, submitted). Notable from the monolayer study was the reproduction of the dipole potential across the monolayer, a value that cannot be reproduced using non-polarizable models. This exciting, unforeseen observation points to the types of results that may be obtained from polarizable macromolecular force fields that are not accessible to the present additive models. 

Chelli R, Barducci A, Bellucci L, Schettino V, Procacci P (2005) Behavior of polarizable models in presence of strong electric fields. I. Origin of nonlinear effects in water point-charge systems. J Chem Phys 123(19) 194109... 

Banks JL, Kaminski GA, Zhou RH, Mainz DT, Berne BJ, Friesner RA (1999) Parametrizing a polarizable force field from ab initio data. I. The fluemating point charge model. J Chem Phys 110(2) 741—754... 

Svishchev IM, Kusalik PG, Wang J, Boyd RJ (1996) Polarizable point-charge model for water results under normal and extreme conditions. J Chem Phys 105(11) 4742 1750... 

Before discussing polarizable models, a useful starting point is to consider nonpolarizable models. A typical nonpolarizable potential for molecular systems is ... 

The polarizable point dipole models have been used in molecular dynamics (MD) simulations since the 1970s." For these simulations, the forces, or spatial derivatives of the potential, are needed. From Eq. [18], the force on atomic site k is... 

The polarizable point dipole model has also been used in Monte Carlo simulations with single particle moves.When using the iterative method, a whole new set of dipoles must be computed after each molecule is moved. These updates can be made more efficient by storing the distances between all the particles, since most of them are unchanged, but this requires a lot of memory. The many-body nature of polarization makes it more amenable to molecular dynamics techniques, in which all particles move at once, compared to Monte Carlo methods where typically only one particle moves at a time. For nonpolarizable, pairwise-additive models, MC methods can be efficient because only the interactions involving the moved particle need to be recalculated [while the other (N - 1) x (]V - 1) interactions are unchanged]. For polarizable models, all N x N interactions are, in principle, altered when one particle moves. Consequently, exact polarizable MC calculations can be... 

Most nonpolarizable water models are actually fragile in this regard they are not transferable to temperatures or densities far from where they were parameterized. Because of the emphasis on transferability, polarizable models are typically held to a higher standard and are expected to reproduce monomer and dimer properties for which nonpolarizable liquid-state models are known to fail. Consequently, several of the early attempts at polarizable models were in fact less successful at ambient conditions than the benchmark nonpolarizable models, (simple point charge) and TIP4P (transfer-... 

Many models fail to capture this behavior, however, so temperature transfer-ability is far from an automatic feature of polarizable models.Indeed, it has been demonstrated by several authors that a point dipole-based model designed specifically to reproduce properties of the gas-phase monomer and the bulk liquid at 298 K is doomed to fail at higher temperatures. This failure could arise from insufficiencies in the Lennard-Jones function typically... 

One important difference between the shell model and polarizable point dipole models is in the former s ability to treat so-called mechanical polarization effects. In this context, mechanical polarization refers to any polarization of the electrostatic charges or dipoles that result from causes other than the electric field of neighboring atoms. In particular, mechanical interactions such as steric overlap with nearby molecules can induce polarization in the shell model, as further described below. These mechanical polarization effects are physically realistic and are quite important in some condensed-phase systems. 

All polarizable models share the ability to polarize, by varying their charge distribution in response to their environment. In addition, shell models and EE models with charge-dependent radii have the ability to modify their polarizability—the magnitude of this polarization response—in response to their local environment. Consequently, it is reasonable to expect that shell models and mechanically coupled EE models may be slightly more transferable to different environments than more standard PPD and EE models. To date, it is not clear whether this expectation has been fully achieved. Although some shell-based models for both ionic and molecular compounds have been demonstrated to be transferable across several phases and wide ranges of phase points, " it is not clear that the transferability displayed by these models is better than that demonstrated in PPD- or EE-based models. And even with an environment-dependent polarizability, it has been demonstrated that the basic shell model cannot fully capture all of the variations in ionic polarizabilities in different crystal environments. ... 

Polarizable Point-Charge Model for Water Results Under Normal and Extreme Conditions. 

Phys., 110, 741-754 (1999). Parametrizing a Polarizable Eorce Eield from Initio Data. I. The Eluctuating Point Charge Model. 

Coexistence Properties for the Polarizable Point Charge Model of Water and the Effects of Applied Electric Field. 

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