Bounds to average interelectronic angles in Hartree-Fock theory of atoms

The average interelectronic angle <theta(12)> is the expectation value of the angle theta(ij) (0less than or equal totheta(ij)less than or equal topi) subtended by the position vectors r(i) and r(j) of a pair of electrons i and j. In the Hartree-Fock theory of atoms, we point out that the angle <theta(12)> and its subshell-pair components <theta(12)>(')(nl,n)l(') are bounded from above and below, where n and l are the principal and azimuthal quantum numbers. The upper bounds for <theta(12)>(')(nl,n)l(') with 0less than or equal tol, l(')less than or equal to3 are 9pi/16 (=101.25degrees), 135pi/256 (congruent to94.922degrees), 265pi/512 (congruent to93.164degrees), and 129pi/256 (congruent to90.703degrees) for sp, pd, df, and sf pairs, respectively, while they are pi/2 (=90degrees) for the other ll(') pairs, independent of n and n('). A weighted sum of these subshell-pair bounds gives an upper bound to <theta(12)>. The lower bounds are pi/2 in all the cases. (C) 2004 American Institute of Physics.