Many-body polarization/polarizability

Concluding this section, we are confident that the present treatment of the many-body polarization gives transferable and reliable effective polarizabilities and screening factors. 

Rigid non-polarizable models for water attempt to approximate, via a two-body interaction, the many-body polarization effects which are responsible for a substantial contribution to the properties of the condensed phase of highly polar fluids such as water [58], especially on the dielectric constant [59], by having a large effective dipole moment. While a two-body model might work well in approximating quasi-... 

Numerous polarizable water models have recently been developed [75-82]. At least three types of polarizable models have been used for supercritical water PPC [83], a polarizable TIP-type model [84], and a few variations of SPC-type models with either point or smeared electrostatic charges [78,85,86]. With a few exceptions [87-89] the polarizable models are typically built upon successful non-polarizable counterparts, by scaling the Coulombic charges to match the gas-phase dipole moment, and by including either a polarizable point charge or point dipole to account for the many-body polarization contributions. Moreover, sometimes the permanent dipole moment is set larger than the gas-phase value of 1.85D in order to obtain better agreement with experimental data at ambient conditions [78,82]. 

The choice of the adjustable parameters used in conjunction with classical potentials can result to either effective potentials that implicitly include the nuclear quantization and can therefore be used in conjunction with classical simulations (albeit only for the conditions they were parameterized for) or transferable ones that attempt to best approximate the Born-Oppenheimer PES and should be used in nuclear quantum statistical simulations. Representative examples of effective force fields for water consist of TIP4P (Jorgensen et al. 1983), SPC/E (Berendsen et al. 1987) (pair-wise additive), and Dang-Chang (DC) (Dang and Chang 1997) (polarizable, many-body). The polarizable potentials contain - in addition to the pairwise additive term - a classical induction (polarization) term that explicitly (albeit approximately) accounts for many-body effects to infinite order. These effective potentials are fitted to reproduce bulk-phase experimental data (i.e., the enthalpy at T = 298 K and the radial distribution functions at ambient conditions) in classical molecular dynamics simulations of liquid water. Despite their simplicity, these models describe some experimental properties of liquid... 

The electrostatic energy is calculated using the distributed multipolar expansion introduced by Stone [39,40], with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion points (three at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. The induction or polarization term is represented by the interaction of the induced dipole on one fragment with the static multipolar field on another fragment, expressed in terms of the distributed localized molecular orbital (LMO) dipole polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in the molecule. One can opt to include inner shells as well, but this is usually not useful. The induced dipoles are iterated to self-consistency, so some many body effects are included. 

As noted in Chapter 2, computation of charge-charge (or dipole-dipole) terms is a particularly efficient means to evaluate electrostatic interactions because it is pairwise additive. However, a more realistic picture of an actual physical system is one that takes into account the polarization of the system. Thus, different regions in a simulation (e.g., different functional groups, or different atoms) will be characterized by different local polarizabilities, and the local charge moments, by adjusting in an iterative fashion to their mutual interactions, introduce many-body effects into a simulation. 

It is important to note that the two electric fields that lead to a Raman transition can have different polarizations. Information about how the transition probability is affected by these polarizations is contained within the elements of the many-body polarizability tensor. Since all of the Raman spectroscopies considered here involve two Raman transitions, we must consider the effects of four polarizations overall. In time-domain experiments we are thus interested in the symmetry properties of the third-order response function, R (or equivalently in frequency-domain experiments... 

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... 

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 many-body nature of the interactions between polar and polarizable molecules in the condensed phase can be taken into account using several... 

It is increasingly realized that many-body induction interactions should be included in computer models, especially in inhomogeneous environments. Kohlmeyer et al. [44] therefore investigated the role of molecular polarizability on the density profiles of a slab of water in contact with several different metal surfaces. They employed the polarizable TIP4P model by Rick and Berne [46]. It was found that the density profiles are almost identical near a metallic surface the liquid/gas interface appears to become slightly wider. Earlier studies of polarizable water at a hydro-phobic wall by Wallqvist [141] and near the liquid/gas interface by Motakabbir and Berkowitz [142] also concluded that polarization effects are of secondary importance. 

State-specific response of the polarizable environment, calculated by Eq. 5.15, is several times smaller than the indirect polarization shift, or 0.01-0.02 eV in absolute values. Thus, polarization correction provides only a minor contribution to the solvatochromic shift in pNA-water complexes. However, when the ground (reference) state and excited state signiflcantly differ in character, such as the case in EOM-IP methods, direct polarization contribution might become veiy significant. An overall role of polarization is expected to increase in larger clusters and bulk systems, where the many-body effects become prominent. 

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. 

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