Contracted Gaussian distributions

We first consider a simple case the transition from primitive to contracted Gaussian distributions. To this end, the multipole expressions for primitive charge distributions flap = and flyg = have to be contracted with the contraction coefficients and as... 

Initially, the polyatom program was coded to limit the basis set to 50 elements . By 1966, the ibmol program could (in principle) handle a maximum of 800 Gaussian functions distributed on 50 centers. This program also used contracted Gaussian basis functions which had been introduced earlier by dementi. 

Figure 30. Effect of extreme static disorder in EXAFS analysis. Left Gaussian distributions of equal area but with much different widths. Both the sum of the two functions and the single narrow distribution function are shown. Right Simulated EXAFS functions for the functions at left. It is seen that there is no detectable difference in the EXAFS except at low k-values. This difference would overlap with XANES and be extremely difficult to analyze. Hence physical distributions with a broad tail will have re duced coordination numbers via standard EXAFS analysis, as well as an artificially produced distance contraction . For cases not as severe as this, cumulate analysis can quantify the degree of static disorder and allow more correct results. After Kortright et al. (1983).

Another, even more drastic approximation was proposed by Wilhite and Euwema. In this method, the entire charge distribution function (which is the product of two contracted Gaussians) is replaced by a few s-type Gaussian functions. To minimize the error, coefficients and exponents of the replacement functions are calculated by equating the magnitudes of several multipole moments of the original and approximate charge distributions. 

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