Hiickels electrostatic model

D is the relative permittivity or dielectrie eonstant of the medium it is a dimensionless property whose value is aroimd 80, for example, in the case of water at ambient temperature, is the electrical permittivity of a vacuum. Its value is 8.85 x lO SI, which equates to arormd 10 / 36 r. 

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Because of the electrostatic model employed (Debye-Hiickel) these formulae apply only in solutions having an ionic strength less than 0.02 M and for non-associated ions. 

The hole correction of the electrostatic energy is a nonlocal mechanism just like the excluded volume effect in the GvdW theory of simple fluids. We shall now consider the charge density around a hard sphere ion in an electrolyte solution still represented in the symmetrical primitive model. In order to account for this fact in the simplest way we shall assume that the charge density p,(r) around an ion of type i maintains its simple exponential form as obtained in the usual Debye-Hiickel theory, i.e.,... 

A more detailed view of the dynamies of a ehromatin chain was achieved in a recent Brownian dynamics simulation by Beard and Schlick [65]. Like in previous work, the DNA is treated as a segmented elastic chain however, the nueleosomes are modeled as flat cylinders with the DNA attached to the cylinder surface at the positions known from the crystallographic structure of the nucleosome. Moreover, the electrostatic interactions are treated in a very detailed manner the charge distribution on the nucleosome core particle is obtained from a solution to the non-linear Poisson-Boltzmann equation in the surrounding solvent, and the total electrostatic energy is computed through the Debye-Hiickel approximation over all charges on the nucleosome and the linker DNA. 

The contribution of electrostatic interactions to fast association was analyzed by applying the classical Debye-Hiickel theory of electrostatic interactions between ions to mutants of bamase and barstar whose ionic side chains had been altered by protein engineering (Chapter 14).16 The association fits a two-step model that is probably general (equation 4.84). 

Debye-Hiickel theory — The interactions between the ions inside an electrolyte solution result in a nonideal behavior as described with the concepts of mixed-phase thermodynamics. Assuming only electrostatic (i.e., coulombic) interactions - Debye and - Hiickel suggested a model describing these interactions resulting in - activity coefficients y suitable for further thermodynamic considerations. Their model is based on several simplifications ... 

Tel. 800-424-9737, fax 415-491-8311 (U.S.A.), tel. 41-38-337633 (U.K.) Model building, display, charge density, electrostatic potential, and molecular orbital plots. Stick, sphere, and dot surface display. 2D to 3D conversion. Protein and DNA fragment libraries. MM+, BIO+ (implementations of MM2 and CHARMM, respectively), OPLS, and AMBER molecular mechanics and dynamics. Solvent box. Semiempirical calculations by Extended Hiickel, CNDO, INDO, MINDO/3, MNDO, AMI, and PM3. Originated at Hypercube, Inc. (Dr. N. Ostlund et al.), of Ontario, Canada. Runs under Windows on a 386 or 486 PC and under Motif on a Silicon Graphics workstation. 

Simplified models may be developed [7,10[ for various limiting cases of thin and thick electrostatic double layers (kR 1 and kR <3C 1, respectively). When the diffuse part of the double layer is thick (kR double layers (k R )./—> 1 producing a form of Eq. (59)... 

The seasoned Debye-Hiickel (D-H) theory, put forth in 1923 [33,34] takes into account the contribution of the ionic electrostatic interactions to the free energy of a solution and provides a quantitative expression for the activity coefficients. The basic concept of the D-H theory is that the long-range Coulomb interaction between two individual ions bathed in a salt solution is mediated by mobile ions from the solution. The effective charges of a certain ion are decreased as the result of charge screening by the mobile counterions it follows that, at sufficient distance, the interaction between two ions decays exponentially. We briefly outline the main considerations and assumptions of the D-H model ... 

Tel. 703-658-4854, fax 703-658-4887, e-mail syazdi presto.ig.com Desktop molecular modeling. NEMESIS SAMPLER for simple modeling. PRO-EXPLORE for sequence analysis and biomolecular modeling. PRO-SIMULATE for molecular simulations with GROMOS, AMBER, and BOSS via a graphical interface. PRO-QUANTUM for semiempirical (MOPAC, extended Hiickel) and ab initio (CADPAC) calculations via a graphical interface. FDCALC and ESCALC for electrostatics calculations. N-DEE for analysis of NMR data. PC-PROT-I- (sequence analysis), PC-TAMMO-I- (protein—lipid modeling), and MASCA (statistics). Macintosh, PCs, and UNIX workstations. 

The difference between the extended Debye-Hiickel equation and the Pitzer equations has to do with how much of the nonideahty of electrostatic interactions is incorporated into mass action expressions and how much into the activity coefficient expression. It is important to remember that the expression for activity coefficients is inexorably bound up with equilibrium constants and they must be consistent with each other in a chemical model. Ion-parr interactions can be quantified in two ways, explicitly through stability constants (lA method) or implicitly through empirical fits with activity coefficient parameters (Pitzer method). Both approaches can be successful with enough effort to achieve consistency. At the present, the Pitzer method works much better for brines, and the lA method works better for... 

The Electrolyte NRTL model " and the Extended UNIQUAC model" are examples of activity coefficient models derived by combining a Debye-Hiickel term with a local composition model. Equation of state models with electrostatic terms for... 

The electrostatic methods just discussed suitable for nonelectrolytic solvent. However, both the GB and Poisson approaches may be extended to salt solutions, the former by introducing a Debye-Huckel parameter and the latter by generalizing the Poisson equation to the Poisson-Boltzmann equation. The Debye-Huckel modification of the GB model is valid to much higher salt concentrations than the original Debye-Hiickel theory because the model includes the finite size of the solute molecules. 

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