Spherical gaussians

I hi additional terms are spherical Gaussian functions with a width determined by the parameter L. It was found that the values of these parameters were not critical and many... 

Comparing the core-core repulsion of the above two equations with those in the MNDO method, it can be seen that the only difference is in the last term. The extra terms in the AMI core-core repulsion define spherical Gaussian functions — the a, b, and c are adjustable parameters. AMI has between two and four Gaussian functions per atom. 

For atoms, the radial part of ( )8i(p) is expressed as a linear combination of spherical gaussians, which, in the case of 2p orbitals writes as ... 

This consideration excludes the free-electron model for example, and the Floating Spherical Gaussian Orbital approach in its simplest form. 

These permutations on coordinates are equivalent to operations on the basis functions. We will use shifted spherical Gaussians for this example (these functions will be discussed in a detailed way below in this chapter) ... 

Model Fitting When experimental variograms reveal the structure and distribution pattern in an ore body then for any further estimation, it is necessary to fit a mathematical model to experimental variograms, which are called theoretical variograms. These mathematical models will be used in Kriging estimation. Several predefined models (Linear, Spherical, Gaussian, etc.). 

H2O we also use the Dunning s contraction of Huzinaga s basis. Polarization exponent for oxygen is 1.2, while for the set of p orbitals of H a = 0.8. Water molecule is stretched symetrically, with the equilibrium geometry defined in [27]. Calculations are made at Re, 1.5 Re and 2.0 R . Spherical Gaussians (5 7-orbitals) were used. 

We define a spherical Gaussian function (SGTF) centred at the origin... 

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... 

Construction of molecular wavefunctions from Lewis basis sets of spherical Gaussian s has been investigated by Frost 42> and co-workers 43>. For ethane, e.g., one Gaussian (at least) would be centered in each of the domains of Fig. 4 or 5. 

Additionally, from Fig. 29 one sees that, if, as proposed by Frost 42), a spherical gaussian function is a fair representation of the distribution of charge within an electride ion, there should he, as found by Slater 97>, a very good correlation, and in many cases practically an equality, between the atomic radii. . . and the calculated radius of maximum radial charge density in the outermost shell of the atom". 

Double Zeta + Polarization functions Extended Hartree-Fock Electron Spectroscopy for Chemical Analysis Floating Ellipsoidal Gaussian Orbital Floating Spherical Gaussian Orbital Generalized Atomic Effective Potential Gaussian Type Orbital... 

Note that the k-means relocation method is really a special case of EM that assumes (1) each cluster is modeled by a spherical Gaussian distribution, (2) each data item is assigned to a single cluster, and (3) the mixture weights... 

An interesting approach for comparison with XPS experiments is a generalization of the Floating Spherical Gaussian Orbital (FSGO) technique. In this method, each electron pair is represented by a single Gaussian basis function whose exponent and position are obtained by a variational procedure or by reference... 

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