Journal of Chemical Physics, Vol.121, No.5, 2016-2019, 2004
Bounds to average interelectronic angles in Hartree-Fock theory of atoms
The average interelectronic angle 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 and its subshell-pair components (')(nl,n)l(') are bounded from above and below, where n and l are the principal and azimuthal quantum numbers. The upper bounds for (')(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 . The lower bounds are pi/2 in all the cases. (C) 2004 American Institute of Physics.