Poisson-Boltzman approach

Thermochemistry. Chen et al.168 combined the Kohn-Sham formalism with finite difference calculations of the reaction field potential. The effect of mobile ions into on the reaction field potential Poisson-Boltzman equation. The authors used the DFT(B88/P86)/SCRF method to study solvation energies, dipole moments of solvated molecules, and absolute pKa values for a variety of small organic molecules. The list of molecules studied with this approach was subsequently extended182. A simplified version, where the reaction field was calculated only at the end of the SCF cycle, was applied to study redox potentials of several iron-sulphur clusters181. 

A similar approach was employed in Hecht et al. (1995) for determining the electrostatic potential near the surface of calf thymus DNA. Spin-spin interaction between an N-nitroxide derivative of 9-aminoacridine attached to DNA and free 15N-labeled nitroxides of different charges was monitored by electron-electron double resonance (ELDOR). The electrostatic potential near the surface of DNA was calculated using a nonlinear Poisson-Boltzman equation. The calculated results agreed with the experimental potentials. 

Proper inclusion of the solvent into the calculations is unfortunately quite difficult [46]. One can use classical molecular dynamics or Monte Carlo simulations, classical continuum models based on the Poisson-Boltzman equation, and quantum-chemical studies using various variants of the Self Consistent Reaction Field (SCRF) approach at the semiempirical or ab initio level. There are serious approximations associated with these methods. Continuous models neglect the specific solute-solvent interactions which are very important for polar solvent. Classical methods neglect the changes in the electronic structure of the solute due to the solvent effects. These uncertainties can be illustrated using the predicted solvation energy of adenine treated by various modem approaches. The calculated values vary from -8 to -20 kcal/mol [68]. 

The volumetric charge density is of interest in the study of ionic solutions, in which one can calculate the charge density around a specific ion. This is done by using the Poisson equation, based on electrostatic electric fields or by Boltzman distribution law of classical statistic mechanics. For the simpler case of dilute solutions this approach yields the expression p =... 

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