Intermolecular potential, defined

The pair potential in this equation is the intermolecular potential, defined in Eq. (3), for example. It is now written in terms of displacement coordinates, however. The translational displacements are related to the (instantaneous and equilibrium) vectors R R = R + b vibrational displacements are related... 

Compared witii other direct force measurement teclmiques, a unique aspect of the surface forces apparatus (SFA) is to allow quantitative measurement of surface forces and intermolecular potentials. This is made possible by essentially tliree measures (i) well defined contact geometry, (ii) high-resolution interferometric distance measurement and (iii) precise mechanics to control the separation between the surfaces. 

First, we need to elaborate on the concept of the radius or diameter of the molecules involved in the binding process. Real molecules do not have well-defined boundaries as do geometrical objects such as spheres or cubes. Nevertheless, one can assign to each molecule an effective radius. This assignment depends on the form of the intermolecular potential function between any pair of real particles. 

Spectroscopic measurement. Specifically, if the induced dipole moment and interaction potential are known as functions of the intermolecular separation, molecular orientations, vibrational excitations, etc., an absorption spectrum can in principle be computed potential and dipole surface determine the spectra. With some caution, one may also turn this argument around and argue that the knowledge of the spectra and the interaction potential defines an induced dipole function. While direct inversion procedures for the purpose may be possible, none are presently known and the empirical induced dipole models usually assume an analytical function like Eqs. 4.1 and 4.3, or combinations of Eqs. 4.1 through 4.3, with parameters po, J o, <32, etc., to be chosen such that certain measured spectral moments or profiles are reproduced computationally. 

The one-dimensional potential curves depicted in Figures 1.1-1.3 represent the dissociation of diatomic molecules for which the potential V(Rab) depends only on the internuclear distance between atoms A and B. However, if one or both constituents are molecules, V is a multidimensional object, a so-called potential energy surface which depends on several (at least three) nuclear coordinates denoted by the vector Q = (Ql,Q2,Q3,---) (Margenau and Kestner 1969 Balint-Kurti 1974 Kuntz 1976 Schaefer III 1979 Kuntz 1979 Truhlar 1981 Salem 1982 Murrell et al. 1984 Hirst 1985 Levine and Bernstein 1987 ch.4 Hirst 1990 ch.3). The intramolecular and intermolecular forces, defined by... 

Intermolecular interactions define crucial characteristics of materials for hydrogen storage materials. This topic is discussed in detail in the chapter by Cheng et al. devoted to molecular dynamics simulations of single-walled carbon nanotubes (SWNT) with molecular hydrogen. The properties of modified SWNTs, in the contribution from Politzer et al., are also analyzed from the point of view of potential applications in molecular electronics. 

SA determines the change in a response R as a result of a perturbation in one of the parameters P of the model. Parameters of a model can be any conceivable ones. For example, in a MD simulation, parameters could be all factors appearing in the intermolecular potential. Since the magnitude of various parameters can be very different, it is common to compute a normalized sensitivity coefficient (NSC) defined as... 

First, a complete description of the adsorbent is required this must include details of its solid structure, surface chemical structure, pore size and shape. One starts by assuming that the pores in the model adsorbent are all of the same size and shape and that they are unconnected. Secondly, the nature of the fluid-fluid and fluid-solid interactions must be precisely defined since the validity of the calculations is dependent on the accuracy of the intermolecular potential functions. 

Surface tension is one of the most basic thermodynamic properties of the system, and its calculation has been used as a standard test for the accuracy of the intermolecular potential used in the simulation. It is defined as the derivative of the system s free energy with respect to the area of the interface[30]. It can be expressed using several different statistical mechanical ensemble averages[30], and thus we can use the molecular dynamics simulations to directly compute it. An example for such an expression is ... 

Thus perturbation theory calculations currently suffer from the same disadvantage of supermolecule calculations for defining the intermolecular potential between organic molecules at short range. They are so expensive when used to obtain results of reasonable accuracy that are converged with respect to basis set, even for small molecules, that it is impossible to calculate the energies at a sufficient number of points to define the potential energy surface. Calcula-... 

All intermolecular potentials are anisotropic to a certain extent. We need to consider anisotropy theoretically, first to define numerically the limits of the previously employed spherical approximation and second in an attempt to extend our simple theoretical tools to more complex potentials. 

Three other important equations in the statistical thermodynamics of liquids involve the direct correlation function and provide a connection between the intermolecular potential u(r) for two molecules and the potential of mean force W(r). One way of deriving these equations is by writing an approximate expression for the indirect contribution to the pair correlation function g(r). Keeping in mind that W(r) is defined as — lng(r)/p, and defining gind( ) as the contribution to g(r) from indirect interactions, an approximate expression for c(r) is... 

The concept of an intermolecular potential appears in the Born-Oppen-heimer approximation. The energy of interaction between molecules A and B is defined as,... 

Discussion We conclude that considerable advancement has been made in the understanding of the intermolecular potential of the rare gas pairs. Both the shape and the size parameters appear to be defined to within narrow limits. This development has been made possible by using the results of quite different fields which often provide complementary information for the different parts of the potential function. Specifically, bulk properties of dilute gases give mainly integral information on the potential. The area of the potential is probed by the vibrational levels of the molecule obtained from spectroscopy. Properties of the solid at low temperatures are mainly sensitive to the attractive well and to the minimum distance rm whereas specific scattering features determine very accurately specific parts of the potential, e.g. the rainbow structure determines the region near the inflection point (see Section III). 

Eor real gases, the pV product attains the limiting value RT at zero pressure, where intermo-lecular potential energy vanishes. The extrapolation to zero pressure frees the pVproduct from the effect of intermolecular forces. An ideal gas is defined as one that is free of intermolecular potential energy at finite pressures. For the ideal gas, the pv product equals RT at all pressures, and is called the ideal-gas equation. 

---