Pair potential energy function

E.B. Smith, The intermolecular pair-potential energy functions of the inert gases, Physica, 73 (1974) 211-225. 

Fig 1. Potential energy curve of the Au2- Circles represent the relativistic density functional theory (RDFT) results, full line represents the fitted empirical pair potential energy function (PEF). 

We have expressed the pair potential energy function (PEF) of the dimer with in the form of the recently developed empirical function, which works well for transition metals [14]. It s form is... 

Over the past 15 years, a large number of papers have appeared dealing with computer simulations of water structure, thanks to the increased capacity and availability of fast computers. Simulations are based on accepting a reasonable expression for the pairwise interaction of water molecules, namely, the pair potential (energy) function. Much has been learned from simulation studies, and the results are valuable hints as to what the structure of liquid water may be, but not necessarily as to what the structure must be. Because of computational limitations, the typical sample of water molecules used in such analyses is about 500. If these molecules formed a small droplet, the radius would be five molecules, half of which would be from the outside layer. Thus, one must expect some dramatic surface effects. Furthermore, as discussed below, the calculations are based on a pairwise potential energy function this is probably a most serious limitation, as also discussed below. 

Values for the virial coefficients are derived from experimental measurements which can be conveniently classified as follows low pressnre p-V-T measnrements high pressnre p-V-T measnrements speed of sonnd measurements vaponr pressnre and enthalpy of vaporization measnrements refractive index/dielectric constant measurements and Jonle-Thomson experiments. These will be discussed in Chapter 1.2, and methods of data evalnation described in Chapter 1.5. Much attention has been paid to the correlation of virial coefficient data and the more satisfactory methods are considered in Chapter 1.3, together with a brief discussion of the theoretical calculation of the second virial coefficient from pair potential energy functions which have been derived a priori or by consideration of other dilute gas properties. So far, this calculation is only applicable to molecules with a spherically symmetric intermolecular potential energy function, for which... 

The most satisfactory methods of data correlation are based on sound theory. In the case of the second virial coefficient, this depends on accurate knowledge of the intermolecular pair potential energy function, U(R, coi, oi) which, in general, depends on the orientations, Oh and ofe, as well as the separation, R, of the molecules ... 

Sun et al. (2005) have used MD with a pair potential energy function known as the Buckingham potential model to predict the phase transition, lattice constant, thermal expansivity, isothermal bulk modulus and heat capacity for GaN in the isothermal isobaric N, P, T) ensemble for a temperature range of 300 K to 3000 K and for pressures from 0 to 65 GPa. In the isothermal-isobaric ensemble, the number of atoms, N, pressure, P, and temperature, T, are held constant while allowing the volume, V, and internal energy, E, to vary. 

In view of the problems in describing accurately the interactions between water molecules, theoretical predictions of thermophysical properties have not been quantitatively very successful for water and steam. An investigation by Thoen-Hellemans Mason (1973) of the mumal consistency of the thermal conductivity and viscosity data at low density for steam, which does not require detailed knowledge of the inter-molecular pair potential energy function, showed that the thermal conductivity data in the skeleton tables at that time were consistent with the viscosity data within the given tolerances, but it was considered that the thermal conductivities were a few percent too low. However, more recent recommendations for the thermal conductivity data of steam (Sengers et al. 1984) are in fact lower than those earlier values. 

The function u(rij) is called the pair potential energy function of particles i and j. We consider only monatomic gases, for which u depends only on the distance between the centers of particles i and j. The limits on the double sum in Eq. (9.7-4) are chosen so that the contribution of a single pair of particles is counted only once. 

Although the potential energy functions can be made to reproduce thermodynamic solvation data quite well, they are not without problems. In some cases, the structure of the ion solvation shell, and in particular the coordination number, deviates from experimental data. The marked sensitivity of calculated thermodynamic data for ion pairs on the potential parameters is also a problem. Attempts to alleviate these problems by introducing polarizable ion-water potentials (which take into account the induced dipole on the water caused by the ion strong electric field) have been made, and this is still an active area of research. 

In our paper we are concerned with a potential energy function which is somewhat more realistic than one implied by the excluded volume effects. This potential function allows indirectly bonded chain elements which occupy adjacent lattice sites to interact with a finite energy . We call these interactions nearest-neighbor interactions, which should not be confused with interactions between near-neighbor pairs along the chain. 

The pair potential energy between the guest molecule and any water molecule is related to the force (F) each exerts on the other by, F = — d

molecular center distance between the two. The potential, which itself is a function of separation distance, is unique to every molecular type and is given by... 

The double helices thus constructed are tested for geometric acceptability using semiempirical potential energy functions that reflect the extent of intrastrand base stacking and interstrand base pairing in a miniature dinucleoside monophosphate duplex of the same conformation. As described elsewhere (22), the base stacking potential Vs is chosen to display a minimum at a close to ideal base separation distance of 3.3 /( Energies within... 

The potential energy function looks somewhat different for an ionic bond, such as in the molecule 39K 37Cl, which can be approximately written as the ion pair... 

Leland and Co-workers (8-10) have been able to re-derive the van der Waals mixing rules with the use of statistical mechanical theory of radial distribution functions. According to these investigators, for a fluid mixture with a pair intermolecular potential energy function,... 

The potential energy function applied in most force fields is an additive function of pairs of atoms such as ... 

Many adsorption systems can be shown to correspond either to a localized adsorption model or to a two-dimensional gas. However, there must also be a large number of adsorbate-adsorbent pairs for which the potential energy functions will have variations intermediate between the extremes required for the limiting models. The formal equations applicable to these systems are included in the theory presented here, and furthermore, it appears to be feasible to carry out specific computations of the isotherms and heats for such systems up to moderate coverages (11, 24). 

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