Central force model

More realistic treatment of the electrostatic interactions of the solvent can be made. The dipolar hard-sphere model is a simple representation of the polar nature of the solvent and has been adopted in studies of bulk electrolyte and electrolyte interfaces [35-39], Recently, it was found that this model gives rise to phase behavior that does not exist in experiments [40,41] and that the Stockmeyer potential [41,42] with soft cores should be better to avoid artifacts. Representation of higher-order multipoles are given in several popular models of water, namely, the simple point charge (SPC) model [43] and its extension (SPC/E) [44], the transferable interaction potential (T1PS)[45], and other central force models [46-48], Models have also been proposed to treat the polarizability of water [49],... 

The results of calculations based on the central force model are very satisfying. As shown in Figs. C, D and E the pair correlation functions gHH(R), g(m(R)... 

A very sensitive test of the model is the comparison of calculated and observed structure functions this is shown in Figs. F and G. Note that the central force model yields the characteristic double peak in sh(s) near 2.5 A-1. That the theoretical curve oscillates with greater amplitude than the experimental data indicates that the predicted distribution of near neighbor 00 separations is too narrow. The comparison with neutron diffraction data shows that the theoretical... 

Fig. D. The pair correlation function g0H and the running coordination number oh predicted by the central force model...

Fig. F. The structure function for X-ray diffraction predicted by the central force model O. and the experimental data of Narten ...

Lemberg HL, Stillinger FH (1975) Central force model for liquid water. J Chem Phys 62 1677-1690... 

To extend the usefulness of the model to permit a description of chemical reactions, we must introduce another parameter, the effective duration of a collision. The rectangular well or central force models do this automatically by permitting molecular interaction over a range of distances. However, they are both more complex than the hard sphere model. We can rescue the hard sphere model by specifying a parameter era, the effective diameter for chemical interaction, while keeping hard sphere core diameter. When the centers of two identical molecules are a distance effective reaction volume is 7r([Pg.155]

Eor simplicity, however, let s adopt an atomic-level description of the molecular solution. As with the central-force models (Lemberg and Stillinger, 1975), the interactions treated could be sufficiently complicated as to form complex molecules, but we will focus on the interaction contributions to the chemical potentials of atoms. In that case, all = 1, and any quantum mechanical effects on the internal structures of molecules that may be formed will have to be described by the quantum mechanical approximations that are the target here. 

For central force models of water, the bridge function is essential for accurate solutions of the integral equations. Thuraisingham and Friedman found that at room temperature the HNC [Bab T) = 0] approximation for the CF model was in very poor agreement with... 

Vossen, M., Forstmann, F. (1994). The structure of water at a planar wall An integral equation approach with the central force model, J. Chem. Phys., 101 2379. 

A number of functional forms for the short-range potentials have been used. In the earliest work[7, 8], only pair potentials were employed, but it was quickly realised that the covalent character of silica was too strong to be neglected. Central force models could not reproduce the tetrahedral geometry closely enough, so three-body terms were introduced to provide a measure of the direetional nature of the covalent bonding[9]. These have taken a number of different forms as well. 

Duh DM, Perera DN, Haymet ADJ (1995) Structure and properties of the CFl central force model of water - integral-equation theory. J Chem Phys 102(9) 3736-3746... 

The use of the HNC approximation to study the equilibrium properties of electrolytes and polar fluids is now widespread. Recent examples are the investigations of multipolar fluids by Fries and Patey (1985), the study of the TIPS (transferable intermolecular potentials) model for water and alkali halides in water by Pettitt and Rossky (1982, 1986), and a central-force model for water by Thuraisingham and Friedman (1983). Studies of the rod-like polyelectrolytes (Bacquet and Rossky, 1984) using the HNC approximation have shown qualitative agreement with Manning s (1969, 1978) counter-ion condensation theory, but some quantitative predictions of the theory are not borne out. In the section on WEAK ELECTROLYTES AND DIPOLAR DUMBBELLS, we discuss the sticky electrolyte model for weak electrolytes and acids, which has also been solved numerically in the HNC approximation (Rasaiah and Lee, 1985a). 

In this section we discuss some early examples of rigid models, a flexible model, central force models, and some explicit attempts to include many-body terms into the interaction subsequent sections expand on these descriptions. The models listed in Table 5 date from the 1970s. 

Central force models represent an alternative approach to representing the interactions of water molecules. Here each atom interacts with all other atoms, even on the same molecule, via pairwise additive, central potentials. i83-i85 This is clearly a flexible model because stretch and bend motions are controlled by the potentials. The interactions contain a local minimum for intramolecular interactions this minimum maintains the geometry of the molecule. One advantage of the central force model is that integral equation methods can be applied to the determination of liquid state properties. This is computationally much less demanding than molecular dynamics or Monte Carlo simulations, although the integral equation methods are restricted in practice to central force models. 

H. L. Lemberg and F. H. Stillinger,/. Chem. Phys., 62,1677 (1975). Central-Force Model for Liquid Water. 

Rahman A, Stillinger EH, Lemberg HL (1975) Study of a central force model ftn liquid water by molecular dynamics. J Chem Phys 63 5223... 

Solutes in Water Computer Simulations Using the CFl Central Force Model. 

The central force model does not suffer from the frozen geometry defect of previous electrostatic models. The molecule vibrates properly, and even dissociates. Jtowever, it is internally unaffected by external electrostatic fields, and therefore does not fully mimic real water. 

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