Potential energy of interaction

Our discussion of solids and alloys is mainly confined to the Ising model and to systems that are isomorphic to it. This model considers a periodic lattice of N sites of any given symmetry in which a spin variable. S j = 1 is associated with each site and interactions between sites are confined only to those between nearest neighbours. The total potential energy of interaction... 

Adsorption Forces. Coulomb s law allows calculations of the electrostatic potential resulting from a charge distribution, and of the potential energy of interaction between different charge distributions. Various elaborate computations are possible to calculate the potential energy of interaction between point charges, distributed charges, etc. See reference 2 for a detailed introduction. 

Fig. 1. Potential energies of interaction between two coUoidal particles as a function of their surface-surface separation, for electrical double layers due...

In a solution of a solute in a solvent there can exist noncovalent intermolecular interactions of solvent-solvent, solvent-solute, and solute—solute pairs. The noncovalent attractive forces are of three types, namely, electrostatic, induction, and dispersion forces. We speak of forces, but physical theories make use of intermolecular energies. Let V(r) be the potential energy of interaction of two particles and F(r) be the force of interaction, where r is the interparticle distance of separation. Then these quantities are related by... 

The correlation of electron motion in molecular systems is responsible for many important effects, but its theoretical treatment has proved to be very difficult. Thus many quantum valence calculations use wave functions which are adjusted to optimize kinetic energy effects and the potential energy of interaction of nuclei and electrons but which do not adequately allow for electron correlation and hence yield excessive electron repulsion energy. This problem may be subdivided into cases of overlapping and nonoverlapping electron distributions. Both are very important but we shall concern ourselves here with only the nonoverlapping case. 

We have been using intermolecular interaction and intermolecular force almost interchangeably. However, it is important to distinguish the force from the potential energy of interaction. In classical mechanics, the magnitude of the force,... 

Show explicitly for a hydrogen atom in the Is state that the total energy is equal to one-half the expectation value of the potential energy of interaction between the electron and the nucleus. This result is an example of the quantum-mechanical virial theorem. 

Vq is the potential energy of interaction between nuclear pairs... 

The DLVO theory, with the addition of hydration forces, may be used as a first approximation to explain the preceding experimental results. The potential energy of interaction between spherical particles and a plane surface may be plotted as a function of particle-surface separation distance. The total potential energy, Vt, includes contributions from Van der Waals energy of interaction, the Born repulsion, the electrostatic potential, and the hydration force potential. [Israelachvili (13)]. 

The potential energy of interaction between point charges q and q2 is given by... 

The Debye-FIuckel theory for association of spherical ions in a medium of dielectric constant Dr posits that the electrostatic potential energy of interaction between oppositely charged ions is... 

AU their resulting (mutual) potential energy of interaction (J) ... 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

Coulombic contributions to the potential energy of interaction Moments of inertia of transition-state complex... 

The "force of interaction , F, between two spherical non-polar molecules is a function of the intermolecular separation , r. For most purposes, however, it is more convenient to use the "potential energy of interaction , 0(r), rather than the force of interaction F(r). These two functions are simply related ... 

The Madelung constant,. 4=-3,99. There are seven ions in the structure in Figure 1.61 six cations and one anion. First, calculate the contribution to the potential energy of interactions of the six cations with the central anion. Each cation is... 

In the kinetic and statistical mechanical formulas for the bulk properties it is the potential energy of interaction >(r) which appears rather than the force of interaction F(r) between the molecules in the fluid. For two spherical nonpolar molecules separated by a distance r the force of interaction is obtained by... 

Intermolecular potential energy of interaction A Mass flux of A with respect to molar-average velocity (see Table III) I a Molar flux of A with respect to molar-average velocity (see Table III) (38)... 

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