Energy of interaction between the

The two-center two-electron repulsion integrals ( AV Arr) represents the energy of interaction between the charge distributions at atom Aand at atom B. Classically, they are equal to the sum over all interactions between the multipole moments of the two charge contributions, where the subscripts I and m specify the order and orientation of the multipole. MNDO uses the classical model in calculating these two-center two-electron interactions. 

Dispersive Interactions. For pairs of nonpolar polymers, the intermolecular forces are primarily of the dispersive type, and in such cases the energy of interaction between unlike segments is expected to be closely approximated by the geometric mean of the energies of interaction between the two like pairs (98). In this case, the Flory-Huggins interaction energy between this polymer pair can be expressed in terms of the solubiUty parameters 5 of the pure components. 

The configuration of the polymer molecule must depend also on its environment. In a good solvent, where the energy of interaction between a polymer element and a solvent molecule adjacent to it exceeds the mean of the energies of interaction between the polymer-polymer and solvent-solvent pairs, the molecule will tend to expand further so as to reduce the frequency of contacts between pairs of polymer elements. In a poor solvent, on the other hand, where the energy of interaction is unfavorable (endothermic), smaller configurations in which polymer-polymer contacts occur more frequently will be favored. 

In equation (2) Rq is the equivalent capillary radius calculated from the bed hydraulic radius (l7), Rp is the particle radius, and the exponential, fxinction contains, in addition the Boltzman constant and temperature, the total energy of interaction between the particle and capillary wall force fields. The particle streamline velocity Vp(r) contains a correction for the wall effect (l8). A similar expression for results with the exception that for the marker the van der Waals attraction and Born repulsion terms as well as the wall effect are considered to be negligible (3 ). 

It was found in later work that it is precisely the idea of ionic hydration that is able to explain the physical nature of electrolytic dissociation. The energy of interaction between the solvent molecules and the ions that are formed is high enough to break up the lattices of ionophors or the chemical bonds in ionogens (for more details, see Section 7.2). The significance of ionic hydration for the dissociation of electrolytes had first been pointed out by Ivan A. Kablukov in 1891. 

Let J,o be the dipole moment of a solvent molecule and Tq its radius. The electrostatic energy of interaction between the ion and hj solvent molecules in the primary shell when computed per mole of ions can be written as... 

Thus the stability of a colloid is a function of the energy of interaction between the particles. The conventional strategies for the preparation of small precious metal... 

There are several isotherm models for which the isotherm shapes and peak prohles are very similar to that for the anti-Langmuir case. One of these models was devised by Fowler and Guggenheim [2], and it assumes ideal adsorption on a set of localized active sites with weak interactions among the molecules adsorbed on the neighboring active sites. It also assumes that the energy of interactions between the two adsorbed molecules is so small that the principle of random distribution of the adsorbed molecules on the adsorbent surface is not significandy affected. For the liquid-solid equilibria, the Fowler-Guggenheim isotherm has been empirically extended, and it is written as ... 

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. 

Consider a system composed of n identical, but distinguishable, particles. The distinguishability of the particles may result, for example horn positions in space, e.g. their coordinates. It is useful in this simplified mo to assume, furthermore, that the energy of interaction between the partic... 

The spin-orbit Hamiltonian (HB0) requires some explanation. The energy of interaction between the magnetic moment M and the magnetic field caused by the orbital motion of an electron can be derived as(134)... 

If the interaction Hamiltonian in the Coulomb term is expanded in a series about the separation vector, the first term of the expansion is a dipole-dipole interaction, the second a dipole-quadrupole interaction, etc.<4> Again reverting to a classical analog (dipole oscillators), the energy of interaction between the two dipoles is inversely proportional to the third power of the... 

In the presence of a magnetic field, the energy of interaction between the magnetic moment, p, of the electron and the field B is ... 

The energy of interaction between the components is conveniently described by means of three mutually independent Flory Huggins parameters x X ° and xP° Indices refer to the respective component pairs. 

By Hess s Law, these two approaches must yield the same energy of interaction between the two double bonds. The virtue of this latter approach is that enthalpy of formation data for the... 

There are three possible orientations of the spin in the field and hence three energy levels. The energy of interaction between the magnetic dipole and the field (Bz) is izBz. The separation between neighbouring energy levels is... 

Thus the XC energy is the energy of interaction between the electrons and a charge distribution represented by p cM(f, r ). The question we wish to answer now is whether the expression in Equation 7.18 is just the rewriting of the XC energy in a different way or does it have a physical interpretation. We now show that it indeed has a physical interpretation the term represents the deficit in the density of electrons at r when an electron is at r. 

Q is the value of Qe when the free energy of interaction between the N2 defects is zero,... 

In intermolecular perturbation theory one of the major problems concerns electron exchange between molecules. In the method described here exchange is limited to single electrons. This simplification is definitely a good approximation at large intermolecular distances. The energy of interaction between the molecules, AE (R), is obtained as a sum of first order, second order, and higher order contributions ... 

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