Long-range electrostatic interaction

The variational parameter is the effective free charge, Z in a more refined treatment, the distance X can also be varied and the assumption of uniform density can be relaxed. 

We consider the limit of a dilute dispersion of spheres so that a. In addition, we consider the high charge density limit, X a. Using the variational ansatz for the charge density, the free energy per charge, F/Z (see Chapter 5) is written in these limits as 

The fraction of delocalized or free charge is approximately a constant with a logarithmic increase as the volume fraction of spheres is decreased. This occurs because the entropy of the counterions becomes more important for small j , thus stabilizing the free charge. The fraction of charge that is free or unbound is much larger than that of the one-dimensional case where the entropy is much more restricted and either another variational calculation 

This relation does not hold exactly for an array of spheres. However, heuris-tically, one might expect that for dilute arrays, the force per unit area between two of the spheres may be related to Tn(rb) where ri, represents the Wigner-Seitz cell boundary. This simple form for the pressure arises because the electric field vanishes on the boundary one is thus left only with the osmotic pressure of the counterions. From the previous discussion, n R) Z R Z p a and can still be sufficient to stabilize the crystal, even though the effective charge may be small compared to Z. 

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Belhadj,M., Alper, H.A., Levy, R.M. Molecular dynamics simulations of wa ter with Ewald summation for the long-range electrostatic interactions. Chem. Phys. Lett. 179 (1991) 13-20. 

A very simple — and in fact quite widely used — approximation completely neglects long range electrostatic interactions beyond a certain cut-off distance [43] of typic ally 8 — 15 A. For systems which are significantly larger... 

The first modification is to simply scale the dielectric permittivity of free space (8 ) by a scale factor D to mediate or dampen the long range electrostatic interactions. Its value was often set to be between 1.0 and 78.0, the macroscopic value for water. A value of D=2.5, so that 8 =2.58q, was often used in early CHARMM calculations. 

Further simphfication of the SPM and RPM is to assume the ions are point charges with no hard-core correlations, i.e., du = 0. This is called the Debye-Huckel (DH) level of treatment, and an early Nobel prize was awarded to the theory of electrolytes in the infinite-dilution limit [31]. This model can capture the long-range electrostatic interactions and is expected to be valid only for dilute solutions. An analytical solution is available by solving the Pois-son-Boltzmann (PB) equation for the distribution of ions (charges). The PB equation is... 

From conformational analysis it appears that there is no signifiant influence of the methoxyl group on the conformational behaviour [31,32] only the role of the carboxylic group on the long range electrostatic interaction must be important... 

In the present non-Bornian theory it should be noted again that the long-range electrostatic interactions of an ion with solvents in the second and further solvation shells are ignored. However, the electrostatic energies should contribute to a considerable extent to the solvation energies of ions in each phase. Nevertheless, the proposed equations for... 

When looking at the reaction mechanisms of glutathione peroxidase and isopenicillin N synthase, we did not find any reaction step where the transition state is significantly stabilized by long-range electrostatic interactions (i.e. electrostatic interactions outside the active-site model). However, it is should be added that most transition states have been calculated using ONIOM-ME. 

All nt are determined, in principle, by the equations of statistical mechanics, since they are one-particle distributions.4 As such, each n, depends on the interactions between particles of species i and all other particles in the system, whether belonging to the metal or to the other phase. If there is a geographical separation of particles of species i from, say, particles of species k (as when i and k belong to different phases), the interaction between particles k and a particle of species i near the surface may be averaged over positions of particles /c, i.e., no correlation is assumed between the particles of the two species, so that the particles k become a source of external field for particles i. For a particle i far from the surface, the interaction is probably unimportant (unless it is a long-range electrostatic interaction). 

Water-soluble polymers in general, and especially polyelectrolytes, are often difficult due to their specific and long range electrostatic interactions, which complicate all analytical techniques that rely on single particle properties that are usually realized by high dilution. In most cases the ionic strength of the solution must be increased by the addition of salt in order to screen electrostatic forces. Ideally, SEC separation is predominantly governed by entropic interactions,... 

Thompson, Damien Plateau, Pierre Simonson, Thomas, Free-energy simulations and experiments reveal long-range electrostatic interactions and substrate-assisted specificity in an aminoacyl-tRNA synthetase., ChemBioChem Feb 2006, 7, 337-344. 

Lee, F. S. Warshel, A., A local reaction held method for fast evaluation of long-range electrostatic interactions in molecular simulations, J. Chem. Phys. 1992, 97, 3100-3107. 

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