Correlation coefficients for electronic wavefunctions of atoms in S-states and linear molecules

The connection between the correlation coefficients previously discussed by Kutzelnigg. del Re and Berthier and the correlation factors introduced by McWeeny is determined. The correlation coefficients are then discussed for some special cases. It is show that for atoms in S-states the angular correlation coefficient tau is completely determined by tine l = 0 and 1 contributions of the expansion of the pair density pi(r(1). r(2)) in Legendre polynomials, For linear molecules the equatorial correlation coefficient tau(e) can be expressed solely by the lambda = 0 and 1 contributions of the Fourier expansion of pi(r(1). r2) in terms of cos lambda(phi(1) - phi(2)).