Models Kihara

Song, Y., and Mason, E. A., Analytical equation of state for molecular fluids Kihara model for rodlike molecules, Phys. Rev. A, 42, 4743-4748 (1990). 

It was easy to show that the intermolecular potential curves for spherical molecules would yield a single family of reduced equations of state. If one takes the Kihara model with spherical cores, then the relative core size can be taken as the third parameter in addition to the energy and distance scale factors in the theoretical equation of state. 

With an adequate understanding of globular molecule behavior, I then showed as far as was feasible that the properties of other nonpolar or weakly polar molecules would fall into the same family. It was practical at that time only to consider the second virial coeffi-cent. The Kihara model was used for nonpolar molecules of all shapes while Rowlinson s work provided the basis for discussion of polar molecules. Figure 2 shows the reduced second virial coefficient for several cases. Curves labeled a/po refer to spherical-core molecules with a indicating the core size, correspondingly JI/Pq indicates a linear molecule of core length Si, while y refers to a dipolar... 

The cavity potential U is usually built up from the intermolecular potentials V using the Kihara model... 

The most frequently used model potentials are Rigid sphere, point center of repulsion, Sutherland s model, Lennard-Jones potential, modified Buckingham potential, Kihara potential, Morse potential. Their advantages and disadvantages are thoroughly discussed elsewhere [39] [28]. 

The intermolecular potential in gases is usually assumed to be additive. It has been pointed out, however, that the effect of potential nonadditivity on the equation of state of gases does not seem to be negligible (Kihara ). The simplest system for which the nonadditivity of the intermolecular potential plays a role is the system composed of three spherically symmetric atoms, which will be treated in Sectipn I. The aim of Sections I. A and I. B is to investigate quantum-mechanically the van der Waals interaction between three distant atoms. By use of the results, a model of nonadditive potential is introduced in Section I. C, which model will be applied, in Part II, to the equation of state of gases. 

When multi-parameter potentials are applied to mixtures, the combination rules for parameters other than e and a often follow from the model underlying the potential. For example, the Kihara spherical-core potential is based on a model in which each molecule has a molecular core of characteristic radius an. The combination rules an = (an + jj)/2 follows directly from the hard-core assumption. ... 

Kihara D, Chen H, Yifeng D Yang YD (2009) Quality assessment of protein structure models. 

There are also many variations of the LJ 12-6 potential. One example is the computationally inexpensive tmncated and shifted Lennard-Jones potential (TSLJ), which is commonly used for molecular simulation studies in which large molecular ensembles are regarded, e.g., for investigating condensation processes [15, 16]. Another version of the LJ potential is the Kihara potential [17], which is a non-spherical generalization of the LJ model. 

If molecules are considered to behave by Kihara s model (Kihara, 1953), the following form of potential function can be apphed... 

Kihara, T. (1953). Virial Coefficients and Models of Molecules in Gases. / Chem. Phys. 25, 831. 

A more recent measurement for N2 gas at 100 bar[5] is shown in Figure 1 with a fit to the intra-molecular scattering superimposed. Figure 2 shows the inter-molecular cross-section with a fit based on the Kihara potential [6]. Since the N2 molecule has a small anisotropy, very precise measurements are required to discriminate between different potential forms and this situation is similar to that reflected in the liquid studies presented in the previous chapter. A similar treatment of neutron measurements [7] on SFe gas, however, does reveal some interesting facts about the parameterization of the potential and discriminates between dif ferent models. It therefore seems that neutron diffraction studies of the gas phase can yield useful supplementary information about angle-averaged interaction potentials. In this sense B2((1,T) can be seen as an extension of the conventional second virial coefficient B2(T). At present, these two molecules (N2 and SFg) are the only ones that have been studied in detail but the method clearly has scope for wider applications. 

The works mentioned were based on molecular models to which the geometry of convex bodies could be applied. Besides these geometrical treatments thermodynamic and transport properties of nonspherical molecules were investigated by Comer, by Pople, by Castle, Jansen and Dawson, by Kihara, Midzuno and Kaneko, by Balescu, and by Curtiss. Comer said in his paper, "I have tried to find an intermolecular potential which satisfies the three conditions of accuracy, generality, and integra-bility. It is the purpose of the present article to show that the three conditions of accuracy, generality, and integrability are satisfied in a harmonious manner by the convex-core model of intermolecular potential. 

The most important test of our bimolecular potential is its use in statistical thermodynamic models for the prediction of phase equilibria. Monovariant, three-phase pressure-temperature measurements and invariant point determinations of various gas hydrates are available and are typically used to fit parameters in molecular computations. The key component needed for phase equilibrium calculations is a model of the intermolecular potential between guest and host molecules for use in the configurational integral. Lennard-Jones and Kihara potentials are usually selected to fit the experimental dissociation pressure-temperature data using the LJD approximation (2,4,6), Although this approach is able to reproduce the experimental data well, the fitted parameters do not have any physical connection to the properties of the molecules involved. 

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