Poisson-Boltzmann continuum

Jang, Y. H. Goddard, W. A. Noyes, K. T. Sowcts, L. C. Hwang, S. Chung, D. S. p 3 values of guanine in wate Density functional theory calculations combined with Poisson-Boltzmann continuum-solvation model, J. Phys. Chem. B 2003, 107, 344-357. 

Bryantsev, V.S., Diallo, M.S., Goddard, W.A. pK(a) calculations of aliphatic amines, diamines, and aminoamides via density functional theory with a Poisson-Boltzmann continuum solvent model. J. Phys. Chem. A 2007,111(20), 4422-30. 

M. J. Schnieders, N. A. Baker, P. Ren, and J. W. Ponder. Polarizable atomic multipole solutes in a Poisson-Boltzmann continuum. / Chem. Phys., 126 124114, 2007. 

Fig. 2 Pourbaix diagram for trani-(bpy)2Ru(OH2)2 showing pKas vertical lines) and oxidation potentials (hold lines) determined by cyclic voltammetry [33] and our calculated pKas and oxidation potentials using DFT(M06) and Poisson-Boltzmann continuum solvation (red). Ru /(OF[)2 denotes, for example, the region of stability of trans-(bpy)2Ru (OH)2 "...

Jang YH, Goddard WA, Noyes KT, et al. pJCa values of guanine in water Density functional tlieory calculations combined witli Poisson-Boltzmann continuum-solvation model. / Phys Chem B. 2003 107 344-357. 

Another way of calculating the electrostatic component of solvation uses the Poisson-Boltzmann equations [22, 23]. This formalism, which is also frequently applied to biological macromolecules, treats the solvent as a high-dielectric continuum, whereas the solute is considered as an array of point charges in a constant, low-dielectric medium. Changes of the potential within a medium with the dielectric constant e can be related to the charge density p according to the Poisson equation (Eq. (41)). 

The final class of methods that we shall consider for calculating the electrostatic compone of the solvation free energy are based upon the Poisson or the Poisson-Boltzmann equatior Ihese methods have been particularly useful for investigating the electrostatic properties biological macromolecules such as proteins and DNA. The solute is treated as a body of co stant low dielectric (usually between 2 and 4), and the solvent is modelled as a continuum high dielectric. The Poisson equation relates the variation in the potential (f> within a mediu of uniform dielectric constant e to the charge density p ... 

The continuum treatment of electrostatics can also model salt effects by generalizing the Poisson equation (12) to the Poisson-Boltzmann equation. The finite difference approach to solving Eq. (12) extends naturally to treating the Poisson-Boltzmann equation [21], and the boundary element method can be extended as well [19]. 

Since electrostatic effects dominate the thermodynamic cycle as shown in Figure 10-2, major development efforts have focused on the calculation of electrostatic energy for transferring the neutral and charged forms of the ionizable group from water with dielectric constant of about 80 to the protein with a low dielectric constant (see later discussions). This led to the development of continuum based models, where water and protein are described as uniform dielectric media, and enter into the linearized Poisson-Boltzmann (PB) electrostatic equation,... 

Sections III. 1-III. 3 have described some basic discrete molecular and continuum treatments of solute-solvent interactions. There are many variants and refinements of these that have not been discussed, such as the use of effective dielectric constants66 or the implementation of dielectric screening.155 156 For ionic solutions, it is sometimes preferred to find the reaction field potential via the Poisson-Boltzmann rather than the Poisson equation,132 157 since the effects of the other ions can readily be incorporated into the former.158... 

Electro-osmotic drag phenomena are closely related to the distribution and mobility of protons in pores. The molecular contribution can be obtained by direct molecular d5mamics simulations of protons and water in single iono-mer pores, as reviewed in Section 6.7.2. The hydrod5mamic contribution to n can be studied, at least qualitatively, using continuum approaches. Solution of the Poisson-Boltzmann (PB) equation. 

These workers also calculated the relative stability of the tautomers lOa-c in the gas phase by ab initio and density functional theory (DFT) methods and in solution using several continuum solvation models such as self-consistent reaction fields (SCRF) and the Poisson-Boltzmann method. These results showed good agreement between the experimental and theoretical approaches. 

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