Coulomb contribution

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]

Both entropic and coulombic contributions are bounded from below and it can be verified that the second variation of is positive definite so that the above equations correspond to a minimum [27]. Using conditions in the bulk we can eliminate //, from the equations. Then we get the Boltzmann equation in which the electric potential verifies the Poisson equation by construction. Hence is equivalent within MFA to the... 

To conclude this section let us note that already, with this very simple model, we find a variety of behaviors. There is a clear effect of the asymmetry of the ions. We have obtained a simple description of the role of the major constituents of the phenomena—coulombic interaction, ideal entropy, and specific interaction. In the Lie group invariant (78) Coulombic attraction leads to the term -cr /2. Ideal entropy yields a contribution proportional to the kinetic pressure 2 g +g ) and the specific part yields a contribution which retains the bilinear form a g +a g g + a g. At high charge densities the asymptotic behavior is determined by the opposition of the coulombic and specific non-coulombic contributions. At low charge densities the entropic contribution is important and, in the case of a totally symmetric electrolyte, the effect of the specific non-coulombic interaction is cancelled so that the behavior of the system is determined by coulombic and entropic contributions. 

Consider the following Coulomb contribution to the element of the Fock matrix (eq. (3.51)) similar considerations hold for the exchange contribution. 

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.

Thus, we can alternatively express the Coulomb contribution in equation (7-12) solely in terms of the basis functions as the following four-center-two-electron integrals (since the four basis functions qfl, r v, q/ r a can be attached to a maximum of four different atoms)... 

Another advantage of PB based pKa calculations is that effects of electrolytes are readily accounted for in the PB equation. The Coulombic contribution in conjunction with salt dependence to the abnormally depressed pAVs of histidine in staphylococcal nuclease has been experimentally tested [56], Recently, the methodology used in the PB calculations (Eqs. 10-11 and 10-12) has been combined with the generalized Born (GB) implicit solvent model [94] to offer pKa predictions at a reduced computational cost [52],... 

For the two-component mixed phases the surface and Coulomb contributions can be estimated along the lines of the analysis performed in Ref. [47] for the interface between nuclear and CFL matter. We find a gain in bulk energy of at most 6 MeV/fm3 which is already weight out by Coulomb and surface energy for relatively small values of the surface tension a 10 MeV/fm2. Note... 

TLM Activity Coefficients. In the version of the TLM as discussed by Davis et al. (11), mass action equations representing surface complexation reactions were written to include "chemical" and "coulombic" contributions to the overall free energy of reaction, e.g., the equilibrium constant for the deprotonation reaction represented by Equation 2 has been given as... 

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

Corrections of lower orders in Za are generated by the simplified Coulomb-Coulomb and Coulomb-transverse entries in (4.13). The main part of the Coulomb-Coulomb contribution in Eq. (4.13) may be written in the form... 

Frequently, simple potentials such as Lennard-Jones potentials must be complicated by the inclusion of coulombic contribution parameters, as used for CO2 and C3H8 by Klauda, requiring other fitting parameters. 

The electronic coupling is the driving force of EET processes, and accounts for the dependence of the rates on the interchromophoric separation and mutual orientation. In the last decade, there has been a lot of research effort aimed at the development of theoretical methods able to accurately estimate this quantity. [1] We shall start by noting that the electronic coupling can be partitioned into a long-range Coulombic contribution, VCoul, and a short-range term which depends on the orbital overlap between D and A, Vshort ... 

In Forster theory, [76] the short-range term Vshort is neglected, and the Coulomb contribution is approximated as a dipole-dipole interaction between the transition dipole moments of D and A ... 

Combined with the electron-electron and electron-core interaction terms allows one, in this setting, to rewrite the Coulomb contribution to the molecular energy in the form ... 

Now we turn to an analysis of the two-center Coulomb contributions to the energy. They can be written as follows ... 

Analysis of the general energy expression eq. (3.69) shows that for the MINDO/3 Hamiltonian the only HO orientation dependent contribution to the energy is the resonance energy of the two center bonds. In the NDDO approximation there are the orientation-dependent Coulomb contributions, but they are much less important and we consider them separately later. 

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