Electrostatic free energy

Levy, R. M., Belhadj, M., Kitchen, D. B. Gaussian fluctuation formula for electrostatic free energy changes. J. Chem. Phys. 95 (1991) 3627-3633... 

Use of a Monte Carlo or a cluster (Hybrid) algorithm to calculate ionization constants of the titratable groups, net average charges, and electrostatic free energies as functions of pH. 

The total electrostatic free energy G j of a system is given by the sum of the Coulomb energy and the Bom free energy of solvation (Eq. (39)) ... 

Combining Eqs. (12)-(14) yields Eq. (7) directly. Although such a free energy decomposition is path-dependent [8], it provides a useful and rigorous framework for understanding the nature of solvation and for constructing suitable approximations to the nonpolar and electrostatic free energy contributions. 

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. 

The electrostatic free energy contribution in Eq. (14) may be expressed as a thennody-namic integration corresponding to a reversible process between two states of the system no solute-solvent electrostatic interactions (X = 0) and full electrostatic solute-solvent interactions (X = 1). The electrostatic free energy has a particularly simple form if the thermodynamic parameter X corresponds to a scaling of the solute charges, i.e., (X,... 

The electrostatic free energy of a macromolecule embedded in a membrane in the presence of a membrane potential V can be expressed as the sum of three separate terms involving the capacitance C of the system, the reaction field Orffr), and the membrane potential field p(r) [73],... 

The quantitative theory of ionic reactions, within the limitations of a continuum model of the solvent, is based on the Bom equation for the electrostatic free energy of transfer of an ion from a medium of e = 1 to the solvent of dielectric constant... 

S. Miertus and J. Tomasi, Approximate Evaluations of the Electrostatic Free Energy and Internal Energy Changes in Solution Processes, Chem. Phys. 65, 239 (1982). 

ELECTROSTATIC FREE ENERGIES AND DIELECTRIC EFFECTS IN MACROMOLECULES... 

The PDLD model described above is quite useful for evaluating electrostatic free energies in proteins. However, with more computer power one can use... 

The electrostatic free energy associated with the separation of the ion pair and the recombination of the neutral pair can be easily calculated with Coulomb s law and a large dielectric constant, (e.g., s = 40, which is the... 

The concept of electrostatic complimentarity is somewhat meaningless without the ability to estimate its contribution to AAg. Thus, it is quite significant that the electrostatic contribution to AAthat should be evaluated by rigorous FEP methods can be estimated with a given enzyme-substrate structure by rather simple electrostatic models (e.g., the PDLD model). It is also significant that calculated electrostatic contributions to A A g seem to account for its observed value (at least for the enzymes studied in this book). This indicates that simple calculations of electrostatic free energy can provide the correlation between structure and catalytic activity (Ref. 10). 

Electrostatic Free-Energies and Dielectric Effects in Macromolecules, 122... 

Tanford, Charles. The electrostatic free energy of globular protein ions in aqueous salt solution. Journal of Physical Chemistry 59 (1955) 788-793. 

Thermodynamic Pathways and Electrostatic Free Energy Components The PBFE Method... 

The most important model parameter in PBFE and MM/PBSA is the dielectric constant used for the solutes. Most studies have taken an empirical approach, viewing the dielectric constant as an adjustable parameter. While this seems plausible, it is prudent to analyze the physical problem in more detail, because, in some cases, the experimental data can be fit by models that are distinctly unphysical, despite some plausible features. We therefore come back to the simplest possible PBFE calculation the important problem of proton binding, or pKa shifts. We discuss a nonem-pirical model that attempts to avoid parameter fitting and that gives insights into the limitations of simplified continuum electrostatic free energy methods. 

Simonson, T., Electrostatic free energy calculations for macromolecules a hybrid molecular dynamics/continuum electrostatics approach, J. Phys. Chem. B 2000, 104, 6509-6513. 

Banavali, N.K. Im, W. Roux, B., Electrostatic free energy calculations using the generalized solvent boundary potential method, J. Chem. Phys. 2002,117,7381-7388. 

One of the most critical technical issues regarding LIE type of calculations seems to be the treatment of electrostatic interactions, at least for charged ligands. These problems were discussed in Ref. 19 using the trypsin-benzamidine complex as an illustration. The starting point was then that one should expect, or require, that the electrostatic free energies calculated with the LIE method have some physical meaning, even in... 

There are several separate problems involved in trying to obtain accurate electrostatic free energies for charged groups from simulations of the type discussed herein. The most important of these can tentatively be summarized... 

Continuum models have a long and honorable tradition in solvation modeling they ultimately have their roots in the classical formulas of Mossotti (1850), Clausius (1879), Lorentz (1880), and Lorenz (1881), based on the polarization fields in condensed media [32, 57], Chemical thermodynamics is based on free energies [58], and the modem theory of free energies in solution is traceable to Bom s derivation (1920) of the electrostatic free energy of insertion of a monatomic ion in a continuum dielectric [59], and Kirkwood and Onsager s... 

F> obtained by solving the equation is consistent with the F> used to calculate the reaction field. Having established an effective nonlinear Hamiltonian, one may solve the Schrodinger equation by any standard (or nonstandard) manner. The common element is that the electrostatic free energy term Gp is combined with the gas-phase Hamiltonian Hq to produce a nonlinear Schrodinger equation... 

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