Gaussian fitting, potentials

Fig. 11 Dependence of AGo = Gp - Go on the electrode potential upon adsorption of different anions. Gp is defined by a Gaussian fit to the conductance peak closest to Go in the respective conductance histograms...

In Chapter IX, Liang et al. present an approach, termed as the crude Bom-Oppenheimer approximation, which is based on the Born-Oppen-heimer approximation but employs the straightforward perturbation method. Within their chapter they develop this approximation to become a practical method for computing potential energy surfaces. They show that to carry out different orders of perturbation, the ability to calculate the matrix elements of the derivatives of the Coulomb interaction with respect to nuclear coordinates is essential. For this purpose, they study a diatomic molecule, and by doing that demonstrate the basic skill to compute the relevant matrix elements for the Gaussian basis sets. Finally, they apply this approach to the H2 molecule and show that the calculated equilibrium position and foree constant fit reasonable well those obtained by other approaches. 

Her workers to fit the exchange-correlation potential and the charge density (in the Coulomb potential) to a linear combination of Gaussian-typc functions. 

An even more reliable method of calculation of the atomic charges is the electrostatic potential-derived charge, devised by Kollman. This method, available in the Gaussian-92 program, assigns point charges to fit the computed electrostatic potential at a number of points on or near the van der Waals surface. 

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...

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