Reaction field energy

In Section 1.2.3 an integral representation of the reaction potential is derived, under the assumption that the molecular charge distribution is entirely supported inside the cavity C. This representation is then used to reformulate the reaction field energy... 

Continuum Solvation Models in Chemical Physics 1.2.3 Reaction Field Energies of Interior Charges... 

The reaction field energy ER(p,p ) can then, as announced, be written as an integral over T ... 

As underlined above, there is no approximation in the integral representation (1.31) of the reaction field energy, provided (i) the charge distribution p is entirely supported inside the cavity C and (ii) [Pg.37]

If Qs/Q exceeds a few percent, it is likely that the calculation will not be very reliable. A more elaborate procedure consists in establishing error estimates. For instance, it is proved in ref. [14] that the exact reaction field energy ER(p, p) and the IEFPCM estimate of it, denoted by ,]sEFPCM(p, p), satisfy... 

For molecular systems in the vacuum, exact analytical derivatives of the total energy with respect to the nuclear coordinates are available [22] and lead to very efficient local optimization methods [23], The situation is more involved for solvated systems modelled within the implicit solvent framework. The total energy indeed contains reaction field contributions of the form ER(p,p ), which are not calculated analytically, but are replaced by numerical approximations Efp(p,p ), as described in Section 1.2.5. We assume from now on that both the interface Y and the charge distributions p and p depend on n real parameters (A, , A ). In the geometry optimization problem, the A, are the cartesian coordinates of the nuclei. There are several nonequivalent ways to construct approximations of the derivatives of the reaction field energy with respect to the parameters (A1 , A ) ... 

Rocchia W, Sridharan S, Nicholls A et al (2002) Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies applications to the molecular systems and geometric objects. J Comput Chem 23(1) 128-137... 

Since the CM3 charges reproduce the dipole moments very well, they can reproduce also other electrostatic properties. These charges can, in particular, be used in the PB and GB models (see next sections). These models provide electrostatic reaction field energies of the molecular environment, in particular, giving electrostatic contributions to solvation energies. 

The reaction field energy, AG , is the sum over all the atomic charges qj multiplied by the electrostatic potential at charge i caused by the solvent and mobile ions, ... 

The last term, is the reaction potential generated by the solvent and the mobile ions at the charge i. This is the potential used in Eq. [9] to calculate the reaction field energy. Typically, to isolate this quantity, two calculations are done. The first, as described above, is of the molecule surrounded by a continuum with a dielectric Cj, which yields the potential given by Eq. [10] at each charge. The energy for this system, AG "°... 

As an example of the calculation of the reaction field energy, we consider the small molecule acetic acid (CH3COOH) in its uncharged form, surrounded... 

The reaction field energy can then be calculated using the input file ... 

We again consider the Coulombic energy and reaction field energy separately ... 

AfjBorn jg jjjg electronic part of the reaction-field energy... 

After convergence, the reaction field energy is calculated as... 

Chem., 23,128 (2002). Rapid Grid-based Construction of the Molecular Surface and the use of Induced Surface Charge to Calculate Reaction Field Energies Applications to the Molecular Systems and Geometric Objects. 

Most coordination complexes are not well modeled as spheres of uniform charge (e.g., metallo-protein active sites are an extreme example). Therefore, more sophisticated dielectric continuum reaction field models are generally employed to take into account the shape of the complex and even account for the dielectric properties of the ligands themselves. Furthermore, the charge distribution and/or polarity of the complex can be used to model discretely the reaction field energies at various points on the exterior surface of the solute. There are many variations of such solvent models, some of which are available in standard quantum chemistry programs. 

Recently, Sharma has proposed some extension of the Maier-Meier approach to the case of nematogens with antiparallel dipole-dipole correlations of the molecules. He treated a polar LC material as a mixture of unpaired molecules with a finite dipole moment /u. and antiparallel pairs with zero dipole moment. The molecules interact with each other through a combination of the generalized Maier-Saupe pseudopotential for nematic mixtures and a reaction field energy term calculated from an extension of the Maier-Meier theory. Additionally, it was assumed that a dipole with dipole moment fi is embedded in a spherical cavity of dielectric permittivity n, which is surrounded by a medium of average dielectric permittivity e. In that case the expressions for the cavity field factor h and the reaction field factor / are given by h + n ), /= (e - rt")/[2rre a (2e-i-n )] and the left sides of... 

The SGB method has been shown to compare well with the exact solution of the Poisson-Boltzmann (PB) equation. The SGB implementation used in this work includes further correction terms that bring the SGB reaction field energy even closer in agreement with exact PB results [40]. 

If a simple relationship between the reaction field energy calculated via the SGB model and the Coulomb energy as in Eq. (11) could be found, there would be no need to employ more complicated continuum models. Although the bulk of the correlation between these two terms can be explained by a screened Coulomb interaction, the discrimination between native and non-native states is degraded by such an approximation. The dispersion in the reaction field energy versus the Coulomb energy, which is not contained in the screened Coulomb model, provides a more detailed description of solvation effects which aids the discrimination of native-like conformations from misfolded ones. 

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