The energy of interaction

Because the wavefunction in eqn 10.1 is built from two His orbitals we can expect the overall distribution of the electrons in the molecule to be sausage shaped 

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No more than one particle may occupy a cell, and only nearest-neighbour cells that are both occupied mteract with energy -c. Otherwise the energy of interactions between cells is zero. The total energy for a given set of occupation numbers ] = (n, of the cells is then... 

The parameter J.j is a measure of the energy of interaction between sites and j while h is an external potential or field common to the whole system. The tenn ll, 4s a generalized work temi (i.e. -pV, p N, VB M, etc), so is a kind of generalized enthalpy. If the interactions J are zero for all but nearest-neighbour sites, there is a single nonzero value for J, and then... 

In the reaction field method, a sphere is constructed around the molecule with a radius equal to the cutoff distance. The interaction with molecules that are within the sphere is calculated explicitly. To this is added the energy of interaction with the medium beyond the sphere, which is rnodelled as a homogeneous medium of dielectric constant g (Figure 6.23). The electrostatic field due to the surrounding dielectric is given by ... 

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. 

The effect of polarity in enhancing the energy of interaction has been discussed by Kiselev and his associates who distinguish between non-specific adsorption, where only dispersion and repulsive forces are involved 4>d and and specific adsorption, where coulombic contributions (some or all of (p, [Pg.11]

The energy of interaction between a pair of solvent molecules, a pair of solute molecules, and a solvent-solute pair must be the same so that the criterion that = 0 is met. Such a mixing process is said to be athermal. The solvent and solute molecules must be the same size so that the criterion... 

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. 

Surface Coating. A dense surface coating (encapsulation) that contains no occluded solvent decreases interparticle attraction provided that the coating has a Hamaker constant intermediate between the particle and the Hquid. This is called semisteric stabilization (ST). The energy of interaction between coated spheres is as follows (26) ... 

This dispersion interaction must be added to the dipole-dipole interactions between molecules, such as HCl, NH3 and H2O which have a permanent dipole, fi. The magnitude of die dipole moment depends on tire differences in electronegativity of the atoms in the molecule. Here again, the energy of interaction varies as (orientation effect). 

It is seen that despite the contribution of a methyl group to the free energy being much less than that of the methylene group, the energies of interaction of the two... 

It is evident that many solutions fall between these limiting categories, with both energetic and entropic effects contributing to solution non-ideality. For example, if the energy of interaction between unlike species in a solution is highly favored over like-like interactions, it is obvious that these interactions will be preferred, a fact which in itself will lead to non-randomness of the packing in the solution. 

Electrostatic potential (Section 1.10) The energy of interaction between a point positive charge and the charge field of a molecule. 

Electrostatic Potential. A function describing the energy of interaction of a point positive charge with the nuclei and fixed electron distribution of a molecule. 

It is often useful to know the energy of interaction (/ of a charge distribution in the presence of an external electrostatic field E. It is... 

In a molecule, a given nucleus will generally experience an electric field gradient due to the surrounding electrons. The energy of interaction U between the nuclear quadrupole and the electric field gradient E is given by... 

E. Hydrated divalent cation approaching a channel with a slightly larger diameter than in D, but the energy of interaction with the divalent cation is sufficient to deform the channel drawing the walls in to make lateral coordination with the divalent cation. Since the channel is too small for a monovalent cation to pass through with its first hydration shell and since the monovalent cation channel interaction is insufficient to make the channel small enough for lateral coordination of the monovalent cation, the channel is selective for divalent cations. (Part E reproduced with permission from Ref. 68 )... 

I At intemuclear distances less than 0.074 nm, the energy of interaction rises rapidly because of repulsion between the hydrogen nuclei. 

For simplicity, let us restrict ourselves to the case when fluctuations of the anisotropic potential are connected only with variation of its direction, determined by the Euler angles X. The energy of interaction of a rotator with the directing held depends only on the difference angle... 

Would you expect the energy of interaction of two rotating polar molecules, as given by Eq. 4, to depend on the temperature If so, should the interaction increase or decrease as the temperature is raised ... 

Quantitative calculations can be made on the basis of the assumption that the density of levels in energy for the conduction band is given by the simple expression for the free electron in a box, and the interaction energy e of a dsp hybrid conduction electron and the atomic moment can be calculated from the spectroscopic values of the energy of interaction of electrons in the isolated atom. The results of this calculation for iron are discussed in the following section. 

Rough quantitative calculations of the energy of interaction of the electron pairs and the phonon can be made with use of the force constants for the bonds19 and the changes in the position of the minimum in the potential functions for a bond, as given by the foregoing values of the change in effective radius. 

There are many occupied and unoccupied molecular orbitals in molecules. Interactions occur between any pair of the molecular orbitals. The strengths of the interactions and the effects on the energies of interacting molecules are different from each other. Some lead to significant stabihzation or destabihzation, others to only slight stabihzation or destabilization. 

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