Polarization many-body forces

Let us now consider systems formed by polar molecules, e.g. HF, H20 and HC1. The HF and HC1 crystals contain one-dimensional bent chains of molecules between which the mutual interactions are relatively weak (Fig. 12). In the case of HF we observe a marked decrease of the intermoleeular distance (ARpp 0.3 A) upon the formation of the solid phase. Ice I has a fairly complicated three-dimensional structure (Fig. 12), dipoles appear at different relative orientations, and the infinite chain is no appropriate model. Nevertheless, the contraction of the intermoleeular distance in the solid state is substantial (ARoo 0-24 A). In both cases, the stabilizing contributions have to be attributed to attractive many-body forces since the changes observed exceed by far the effects to be expected in polar systems with pairwise additive potentials. The same is true for the energy of interaction (Table 12) ... 

We may conclude that many-body forces are not important for the structure of solid hydrogen chloride (for further details see Sections 4.3 and 5). The energy of interaction in the dimer and in the solid fit very well into our relations. This is more a test of our assumptions of binary potentials in equations 8 and 18 than a limit on the role of many-body forces because the only available value was derived from cluster calculations based on the assumption of pairwise additivity. From the concepts and data discussed in this section it is obvious that an accurate description of clusters and condensed phases formed from polar molecules like HF and H20 which are both characteristic hydrogen bond donors and acceptors, requires a proper consideration of many-body forces. 

AIMD simulations appear as a promising tool for a first-principles modeling of enzymes. Indeed, they enable in situ simulations of chemical reactions furthermore, they are capable of tEiking crucial thermal effects [53] into account finally, they automatically include many of the physical effects so difficult to model in force-field based simulations, such as polarization effects, many-body forces, resonance stabilization of aromatic rings and hydration phenomena. 

KLEIN - We do indeed use a semi-empirical model for the various interaction potentials. First, we model the ammonia inter molecular potential with an effective pair potential which ignores many body polarization. Models of this type are remarkably successful in explaining the physical properties of polar fluids. Of course, we really should include many body forces, but at this stage we ignore them. The ammonia potential is fitted to the heat of evaporation and the zero-pressure density. The electron-alkali metal (Lithium) potential is represented by the Shaw pseudo potential fitted to the ionization energy. This is the simplest and crudest model possible. We have explored the effect of using (a) Heine-Abarenkov, (b) Ashcroft, and (c) Phillips-Kleinman forms. Our results are not very sensitive to the choice of pseudo potential. (In the case of Cs metal, which I did not discuss, the sensitivity to the potential is crucial). 

KLEIN - You raise an important question. Long-range many body forces are important. Short-range many body forces are also important. Alas, our knowlegde of the latter is very poor. We used the crudest possible model and have neglected both of these effects. Our electron-ammonia solvent potential includes the most important polarization effect namely, that caused by the solvent dipoles on the electron. We have ignored the self-consistent many body polarization of the coupled electron-solvent system. This latter effect has been discussed by Wallqvist, Thirumalai and Berne (J. Chem. Phys., 1987). I refer you to this article for details. 

These limitations, most urgently felt in solid state theory, have stimulated the search for alternative approaches to the many-body problem of an interacting electron system as found in solids, surfaces, interfaces, and molecular systems. Today, local density functional (LDF) theory (3-4) and its generalization to spin polarized systems (5-6) are known to provide accurate descriptions of the electronic and magnetic structures as well as other ground state properties such as bond distances and force constants in bulk solids and surfaces. 

Chemistry-Based Force Fields for Polyethylene oxide) with Many-Body Polarization Interactions. 

Specific polarization effects, beyond those modelled by a continuum dielectric model and the movement of certain atoms, are neglected in MIF calculations. Many-body effects are also neglected by use of a pair-wise additive energy function. Polarizable force fields are, however, becoming more common in the molecular mechanics force fields used for molecular dynamics simulations, and MIFs could be developed to account for polarizability via changes in charge magnitude or the induction of dipoles upon movement of the probe. 

The yield stress can in principle be predicted from the polarization model. Rigorous calculation of the movement of one sphere in a flowing ER fluid under an electric field requires computation of the dielectric and hydrodynamic forces on that sphere. But these forces depend on the location and movement of all surrounding spheres, which are themselves responding to similar forces. Thus, one must solve a many-body problem, and this requires computer simulation. 

Potentials that treat the polarization and ionization are important for modeling a number of metal oxide systems. This is difficult since polarization in solids is a many-body effect with various components and depends strongly upon changes in the electronic structure as a function of structure and forces on the ions. One of the most widely used approaches to simulate polarizability effects is that of the Shell model which uses a massless shell of charge (electron density) I 1. 

Current research in water potentials tends to focus on incorporating explicit many-body polarization terms in the water-water energy. This avoids the pairwise additive approach, i.e., the effective media approximation inherent in pairwise additive water potentials, and allows for a better parameterization of the true water-water interaction. Two main avenues for treating polarization effects have developed in the last decade an explicit treatment of classical polarization and fluctuating charge models. The effort expended to find suitable water models will slowly pay off in an enhanced awareness of how to improve current molecular force fields for interactions of other types (e.g., between organic solutes, biomolecules, etc.). 

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. 

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