Functions and Correlation Coefficients

The charge distribution function q (1) and the pair distribution function 7t (1, 2) of a N-electron system described by a total wave function W are defined as follows 

To introduce correlation functions, let us consider a completely uncorrelated model, in which the probability of finding two particles at two given positions is simply 

Usually, the electron system under consideration has a well-defined spin state S and the reduced density matrices can be decomposed into 

Thus correlation functions themselves may be delSned for each spin situation by putting 

For an antis5nnmetrized independent-particle model represented by a single-determinant wave function, only the correlation function / (1,2) is identically equal to zero and one has 

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The Fig. 2 intuitively shows that there is a significant correlation between K, and W. This correlation can be expressed by an exponential function as function (2). The functions and correlation coefficients are shown in Table 3. 

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