Intermolecular potentials energy functions

Tbe results for water are mainly available from computer simulations, although some results of integral equation theories have been reported in recent years. Despite the varied nature of the intermolecular potential energy functions used, most of these studies give a qualitatively similar picture. As an example, we consida in some detail the results obtained for the potential energy function given above (for the interface between water and Pt). 

In principle, it is a simple matter to include solvent water molecules directly in MD simulations, since appropriate intermolecular potential energy functions for water are available (1Z 37,38) one would just surround the solute molecules with a sufficient number of water molecules to approximate a bulk solution. Unfortunately, a "sufficient number of water molecules might be enormous, since many of the effects of aqueous solvation are long range or are due to entropic contributions arising from "structuring of the solvent, which may be cooperative in nature. 

It is customary to split the intermolecular potential energy function p(r) into two parts ... 

Spherical nonpolar molecules obey an interaction potential which has the characteristic shape shown in Fig. 2. At large values of the separation r it is known that the potential curve has the shape — r 6, and at short distances the potential curve rises exponentially the exact shape of the bottom part of the curve is not very well known. Numerous empirical equations of the form of Eq. (78) have been suggested for describing the molecular interaction given pictorially in Fig. 2. The discussion here is restricted to the two most important empirical functions. A rather complete summary of the contributions to intermolecular potential energy and empirical intermolecular potential energy functions used in applied statistical mechanics may be found in (Hll, Sec. 1.3) ... 

Fig. 2. Sketch showing general form of the intermolecular potential energy function.

Finally, the reduced collision integral is usually expressed in terms of a reduced temperature T. If the intermolecular potential energy function can be expressed in the form [178]... 

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,... 

Clark Colton All the comments about molecular simulations have emphasized their power and the computational aspects. Nothing s been said about the intermolecular potential energy functions. What we have is fine for small molecules, but once we get to large, complicated molecules, such as charged proteins in an aqueous electrolyte solution, we have difficulty writing the intermolecular potential energy function. Why hasn t that issue been identified ... 

Within the model represented by equations (1) and (2), the intermolecular potential energy function is fully determined by the set of -1 charges and n n +1) Lennard-Jones parameters, where n is the number of different types of atoms in the system. For example, the water intermolecular potential in this approach requires 5 different parameters. In practice, this is modified in two ways First, one may wish to add additional point charges to provide more flexibility in modeling the molecular charge distribution. In this case, the locations of the point charges are not necessarily identified with the equilibrium positions of the atoms. Second, a major simplification can be achieved if one uses the following approximation[13] ... 

A discussion of Van der Waals molecules is a natural component of a treatise on resonance phenomena, for a variety of reasons. The most obvious of these is simply the fact that transitions involving both compound-state and shape resonance levels figure prominently in the spectra of these species. Indeed, in many cases the metastable nature of the final states of such transitions is a key feature of the manner in which they are observed (1-3). Moreover, observations of structure due to resonances in scattering cross sections can provide detailed information regarding intermolecular potential energy functions ( ). 

In using Eqs. 19 and 34 as starting points for the development of the theory of transport processes, several tasks remain. The first and perhaps simplest is to develop expressions for the transport coefficients in terms of the single and pair densities /(1> and /< >. Next the continuity equations must be solved to give explicit expressions for the densities when the system is perturbed from its equilibrium state by the transport process under consideration. Finally, it is required to obtain the frictional coefficient f in terms of the intermolecular potential energy function according to Eq. 33. 

Coarse-grained chains on the 2nnd lattice, using three (ui, u2, u3) shells for the intermolecular potential energy function employed in the Metropolis criteria during the MC simulation [167] d ui from the first set in Table 4.5 e ui from the second set in Table 4.5... 

A theoretical basis for the law of corresponding states can be demonstrated for substances with the same intermolecular potential energy function but with different parameters for each substance. Conversely, the experimental verification of the law implies that the underlying intermolecular potentials are essentially similar in form and can be transformed from substance to substance by scaling the potential energy parameters. The potentials are then said to be conformal. There are two main assumptions in the derivation ... 

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... 

For direct information on the compression factor, without any assumptions about the form of the intermolecular potential energy function, the differential equations which link the speed of sound and the virial equation of state can be numerically integrated, with known initial conditions. Specifically [96-... 

Forces between polymer-covered surfaces are a subset of the general subject of intermolecular forces, which are more fully discussed elsewhere (Maitland etal. 1981, Israelachvili 1991). Before the SFA and the results obtained from it are discussed, a brief consideration of intersurface forces is needed. If the intermolecular potential energy function between two individual molecules is generated solely by van der Waals forces it is purely attractive and of the form... 

It is useful to focus attention on simple liquids. By simple we mean the intermolecular potential energy function 4>(rj, r2. .. r ) has the special form given by... 

A NEW EMPIRICAL INTERMOLECULAR POTENTIAL ENERGY FUNCTION FOR HYDROGEN BONDING APPLICATION TO THE GAS PHASE AND SOLID STATE OF CARBOXYLIC ACIDS AND ALCOHOLS... 

A NEW EMPIRICAL INTERMOLECULAR POTENTIAL ENERGY FUNCTION FOR HYDROGEN BONDING 439... 

Eqs 3.5 and 3.7 are easily evaluated by numerical quadrature for any assumed intermolecular potential-energy function uy. In a few simple cases, analytical results may be obtained and we consider here the case of the hard-core-square-well potential defined by... 

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