Bounds to average interelectronic angles in Hartree-Fock theory of atoms.
The average interelectronic <angle theta12> is the expectation value of the angle thetaij (0 < or = thetaij < or = pi) subtended by the position vectors ri and rj of a pair of electrons i and j. In the Hartree-Fock theory of atoms, we point out that the angle <theta12> and its subshell-pair components <theta12>nl,n'l' are bounded from above and below, where n and l are the principal and azimuthal quantum numbers. The upper bounds for <theta12>nl,n'l' with 0 < or = l, l' < or = 3 are 9pi/16 (=101.25 degrees), 135pi/256 (approximately 94.922 degrees), 265pi/512 (approximately 93.164 degrees), and 129pi/256 (approximately 90.703 degrees) for sp, pd, df, and sf pairs, respectively, while they are pi/2 (=90 degrees ) for the other ll' pairs, independent of n and n'. A weighted sum of these subshell-pair bounds gives an upper bound to <theta12>. The lower bounds are pi/2 in all the cases.
Koga
Toshikatsu
T
Department of Applied Chemistry, Muroran Institute of Technology, Hokkaido 050-8585, Japan.
Matsuyama
Hisashi
H