Electrostatics macroscopic

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

In continuum boundary conditions the protein or other macromolecule is treated as a macroscopic body surrounded by a featureless continuum representing the solvent. The internal forces of the protein are described by using the standard force field including the Coulombic interactions in Eq. (6), whereas the forces due to the presence of the continuum solvent are described by solvation tenns derived from macroscopic electrostatics and fluid dynamics. 

SASA), a concept introduced by Lee and Richards [9], and the electrostatic free energy contribution on the basis of the Poisson-Boltzmann (PB) equation of macroscopic electrostatics, an idea that goes back to Born [10], Debye and Htickel [11], Kirkwood [12], and Onsager [13]. The combination of these two approximations forms the SASA/PB implicit solvent model. In the next section we analyze the microscopic significance of the nonpolar and electrostatic free energy contributions and describe the SASA/PB implicit solvent model. 

Bashford D (2004) Macroscopic electrostatic models for protonation states in proteins. Front Bioscience 9 1082-1099. 

PLASMA (Particle). 1 An assembly of ions, electrons, neutral atoms and molecules in which the motion of the particles is dominated by electromagnetic interactions. This condition occurs when the macroscopic electrostatic shielding distance (Debye length) is small compared to the dimensions of the plasma. Because of the large electrostatic potentials... 

Alternatively, there has been a revival of Debye-Hiickel (DH) theory [196-199] which provides an expression for the free energy of the RPM based on macroscopic electrostatics. Ions j are assumed to be distributed around a central ion i according to the Boltzmann factor exp(—/ , - y.(r)), where y(r) is the mean local electrostatic potential at ion j. By linearization of the resulting Poisson-Boltzmann (PB) equation, one finds the Coulombic interaction to be screened by the well-known DH screening factor exp(—r0r). The ion-ion contribution to the excess free energy then reads... 

We call this free energy the total free energy since we suppose it to include the macroscopic electrostatic free energy due to the electrical charge carried by the phase. We then call the quantity... 

Arrhenius theory applies well to solutions of weak acids and bases in water, but fails in the case of strong electrolytes such as ordinary salts. Debye and Hiickel [26] solved this problem assuming complete dissociation, but considering the Coulomb interactions between the ions by a patchwork theory based on both macroscopic electrostatics and statistical mechanics. 

The need for an analytical expressions for the equation of state have led to a revival of the macroscopic electrostatic theory due to Debye, Hiickel and Bjerrum. DH theory becomes exact for large particles. In pilot work by Fisher and Levin (FL) [31], DH-Bj theory is extended by considering the interactions of the pairs with the free ions. Weiss and Schroer (WS) [32] have supplemented this theory accounting for dipole-dipole interactions between pairs and the e-dependence of the association constant. 

The above expression for the long-range part of the electrostatic potential is consistent with a well-known result from macroscopic electrostatics regarding... 

The first attempt to estimate the free energy of hydration of an ion was that of Bom, who in 1920 derived from macroscopic electrostatics the following expression... 

The GC theory is based on macroscopic electrostatics, while much of the present-day work is aimed at a description on a molecular level. There is, however, an elegant alternative based on the methods of statistical field theory, which was developed by Badiali and associates [19, 20]. This leads to a coarse-grained description in terms of the particle-distribution functions. By setting up a suitable model Hamiltonian, a wide variety of phenomena can be described. 

Lorentz-Lorenz equation A relation between the polarizability a of a molecule and the refractive index n of a substance made up of molecules with this polarizability. The Lorentz-Lorenz equation can be written in theforma= (3/4tcA/) [(n -l)/(n + 2)l, where JV is the number of molecules per unit volume. The equation provides a link between a microscopic quantity (the polarizability) and a macroscopic quantity (the refractive index). It was derived using macroscopic electrostatics in 1880 by Hendrik Lorentz and independently by the Danish physicist Ludwig Valentin Lorenz also in 1880. Compare ClAUSIUS-MoSSOTTr EQUATION. 

The energy of reorganization is a molecular concept, and an equation such as (10), which is based on macroscopic electrostatics, can only be a rough approximation. Several other expressions, on the basis... 

Probable configuration surrounding a cation vacancy at the (100) surface of an NaCl type crystal. ]ip and i-iq are the electronic dipoles of the nearest neighbour anions and gp and their fractional radial displacements. For the calculations the polarization of the rest of the crystal was treatedby macroscopic electrostatic formulas-... 

Solvent effects, that is, the macroscopic electrostatic interaction between OF" and a surrounding dielectric, were calculated by an ab initio self-consistent reaction field (SCRF) method [14]. 

Macroscopic Electrostatics Calculation of Solvated Interactions and Macromolecular Titration... 

MEAD = macroscopic electrostatics with atomic detail PMF = potentials of mean force. 

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