Gaussian charge distributions

As one might expect, the Frost model gives rather poor bond quadrupole moments owing to the diffuse nature of spherical gaussian charge distributions. Amos et al, have additionally extended the calculations to second-order bond properties.64... 

There are other parameterizations possible. Thole noted, in his original paper, that it would be more elegant to describe the interaction—between induced dipoles—in terms of two interacting charge distributions instead of his one-particle ansatz. Jensen et al. [35] took up this suggestion in order to arrive at traceless interaction tensors. He started from the interaction between two isotropic Gaussian charge distributions on a distance r ... 

The damping depends on the width of the Gaussian charge distribution, which in this work was taken to be unit (a.u.). However, both a slightly smaller width [125] and a slightly larger width [126] have been suggested. 

PROBLEM 8.10.1. Derive Shockley s 91 proof of the Ewald formulas [65]. At each lattice point, superpose a fictitious spherically symmetric Gaussian charge distribution at each lattice point, and subtract it out again ... 

The separation of the density in its radial and angular part makes it possible to compute the Coulomb potential generated by the local densities through the multiple expansion of a Gaussian charge distribution... 

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... 

For a point charge, the Fourier transform of the charge density is p(k) = Ze, the charge itself. The Fourier transform of a Gaussian charge distribution is... 

The exact shape and extension of the nucleus may be a matter of debate, and the preceding chapter has discussed possible models. For the derivation of basis sets, the choice is not critical, and the commonly used model is the Gaussian charge distribution... 

By superimposing each charged particle with a Gaussian charge distribution of width and of opposite sign, the total Coulomb interaction can be reformulated according to [59,64]... 

A practical advantage of the finite-nucleus model is that extremely high exponents of the one-particle basis functions are avoided. Since for quantities of chemical interest it is not very important which nuclear model is actually used, the Gaussian charge distribution is often applied, being the most convenient choice. 

Experience has convinced us that some form of control over the induction, particularly in aqueous media is desirable. In our approach this was accomplished by replacing the point charges by Gaussian charge distributions for the polarization sites and for selected permanent charge sites [9,18-20]. The width of these Gaussian charge distributions, was one of the parameters adjusted to obtain... 

Many model potentials (pnuc f) have been used [131] but two have become most important in electronic structure calculations. These are the homogeneous and the Gaussian charge distributions. The homogeneously or uniformly charged sphere is a simple model for the finite size of the nucleus. It is piecewise defined, because the positive charge distribution is confined in a sphere of radius R. The total nuclear charge -f-Ze is uniformly distributed over the nuclear volume 4 rR /3,... 

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