Electrostatic potential Gaussian distribution

Fig. 2.2. Average electrostatic potential mc at the position of the methane-like Lennard-Jones particle Me as a function of its charge q. mc contains corrections for the finite system size. Results are shown from Monte Carlo simulations using Ewald summation with N = 256 (plus) and N = 128 (cross) as well as GRF calculations with N = 256 water molecules (square). Statistical errors are smaller than the size of the symbols. Also included are linear tits to the data with q < 0 and q > 0 (solid lines). The fit to the tanh-weighted model of two Gaussian distributions is shown with a dashed line. Reproduced with permission of the American Chemical Society...

Most commonly used is certainly the molecular electrostatic potential. It can be derived from any kind of charge distribution. Usually, the MEP is first calculated on a grid and subsequently transformed to the sphere or Gaussian representation. Quite important is the electron density distribution, which closely models the steric occupancy by a molecule. Other approaches utilize artificial fields for physicochemical properties commonly associated with binding, like a field for the hydrophobicity [193] or H-bonding potential [133,194]. 

To evaluate the electrostatic potential 4> (r) [see Eq. (6.11)] from the periodic Gaussian charge distribution p (r) [see Eq. (6.10a)], it is most convenient to start from Laplace s equation [242], which says that... 

The term weak adsorption implies that the entropic free energy of a chain is comparable to its electrostatic attraction energy to the interface. The chain is assumed to be Gaussian and its conformations are only weakly perturbed by interactions with the surface. This is the most severe approximation of the current model. We also assume that the polyelectrolyte-density profile is built up near the adsorbing surface without disturbing the electrostatic potential and ionic distribution near the interface prescribed by the Poisson-Boltzmann theory. A more general... 

There are a variety of applications where it is necessary to quantify the electrostatic potential outside the volume filled by atoms in a material. The NACs defined by the DDEC approach are well suited to this task because they were specifically derived to reproduce the electrostatic potential defined by a material s full electron distribution. In this section, we describe how the quality of the electrostatic potential defined by DDEC NACs can be assessed for calculations with periodic materials using VASP and localized molecules using GAUSSIAN. 

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