Energy Coulomb

We also focused [156] on the Coulomb energy between atoms in supermolecules. We proposed an atom-atom partitioning of the Coulomb interaction, which should not be confused with the electrostatic component of the intermolecular interaction, defined within the perturbation approach. Instead, this atom-atom Coulomb interaction energy uses the total molecular (in the case of a single, covalently boimd molecule) or the supermolecular (in 

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Direct ligand-protein interactions. Van der Waals and Coulomb energy of interaction of atoms of ligand with atoms on protein. 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

The total electrostatic free energy G j of a system is given by the sum of the Coulomb energy and the Bom free energy of solvation (Eq. (39)) ... 

The density fitting functions may or may not be the same as those used in expanding the orbitals. The fitting constants a are chosen so that the Coulomb energy arising from the difference between the exact and fitted densities is minimized, subject to the constraint of charge conservation. The J integrals then become... 

Potential (Coulomb) energy operator (general, electron-electron, nuclear-electron, nuclear-nuclear)... 

The overall lattice energies of ionic solids, as treated by the Born-Eande or Kaputin-sldi equations, thus depends on (i) the product of the net ion charges, (ii) ion-ion separation, and (iii) pacldng efficiency of the ions (reflected in the Madelung constant, M, in the Coulombic energy term). Thus, low-melting salts should be most... 

Figure 1. The free energies of mixing of fee disordered alloys. The filled eireles eonneeted with a solid line are the energies ealeulated with the LSMS. The erosses eonneeted with a dotted line are the energies calculated with the CPA-LSMS without the Conlomb energy, while the open circles connected with dotted lines include the Conlomb contribution. The plusses connect with a dashed-dotted line are the energies calculated with the SCF-KKR-CPA without the Coulomb energy, while the squares connected with dashed-dotted lines include the Coulomb contribution.

It can be seen from Fig. 7 that V is a linear function of the qf This qV relation was pointed out and discussed at some length in the papers in ref. 6. It is not simple electrostatics in that it would not exist for an arbitrary set of charges on the sites, even if the potentials are calculated exactly. The charges must be the result of a self-consistent LDA calculation. The linearity of the relation and fie closeness of the points to the line is demonstrated by doing a least squares fit to the points. The sums that define the potentials V do not converge at all rapidly, as can be seen by calculating the Coulomb potential from the standard formula for one nn-shell after another. The qV relation leads to a special form for the interatomic Coulomb energy of the alloy... 

The lowest excited states in molecular crystals are singlet and triplet excitons [3]. Since it costs coulombic energy to transfer an electron that has been excited optically from the HOMO (highest occupied molecular orbital) to the LUMC)... 

Here q represents the coulomb energy of an electron occupying a definite p]h orbital in unsubstituted benzene its value has been estimated to be about —2.7 v. e. = —60 kcal./mole.5 /3 is a resonance integral between adjacent orbitals its value has been estimated to be about —0.85 v. e. = — 20 kcal./mole.6 Sk is a constant, the purpose of which is to allow for the different electron affinities of the different atoms. For Sk > 0, the... 

In this calculation the values qc = 0, qn = 2d and q0 = 4/3 were used for the Coulomb energies of the pi orbitals of carbon, nitrogen and oxygen, respectively. 

The potential energy of an ionic crystal (ions of valence z) may be written = —a(e2z2)/i + R), the first term representing the Coulomb energy, and the second the potential of the repulsive forces. Equation 6 suggests a simple form for [Pg.260]

In deriving theoretical values for inter-ionic distances in ionic crystals the sum of the univalent crystal radii for the two ions should be taken, and corrected by means of Equation 13, with z given a value dependent on the ratio of the Coulomb energy of the crystal to that of a univalent sodium chloride type crystal. Thus, for fluorite the sum of the univalent crystal radii of calcium ion and fluoride ion would be used, corrected by Equation 13 with z placed equal to y/2, for the Coulomb energy of the fluorite crystal (per ion) is just twice that of the univalent sodium chloride structure. This procedure leads to the result 1.34 A. (the experimental distance is 1.36 A.). However, usually it is permissible to use the sodium chloride crystal radius for each ion, that is, to put z = 2 for the calcium... 

Bollnow29 has evaluated the Coulomb energy of the rutile arrangement as a function of the axial ratio c/a, making the assumption that u is given by Equation 16. His results may be given by the equation... 

Bollnow also evaluated the Coulomb energy of anatase, the other tetragonal form of titanium dioxide, by again making the assumption of a constant Ti+4-0= distance in order to fix the value of the parameter. He found this energy to have a minimum value... 

The possibility of the existence of two forms of titanium dioxide, rutile and anatase, is evident from the identity of their Coulomb energies taking the energy of the repulsive forces and of possible deformation into account, it is seen that the choice between the two structures would depend on the thermodynamic environment during crystallization. In... 

The Transition to the Sphalerite Structure.—The oxide, sulfide and selenide of beryllium have neither the sodium chloride nor the cesium chloride structure, but instead the sphalerite or the wurzite structure. The Coulomb energy for the sphalerite arrangement is... 

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