Relativistic correlating basis sets for actinide atoms from 90Th to 103Lr.

For 14 actinide atoms from (90)Th to (103)Lr, contracted Gaussian-type function sets are developed for the description of correlations of the 5f, 6d, and 7s electrons. Basis sets for the 6d orbitals are also prepared, since the orbitals are important in molecular environments despite their vacancy in the ground state of some actinides. A segmented contraction scheme is employed for the compactness and efficiency.

Bounds to electron-pair relative and center-of-mass radii in many-electron atoms.

When the electron-electron interaction is explicitly considered in many-electron atoms, the average electron radius (r) splits into the inner (r<) and outer (r>) radii. It is shown that the sum and difference of these radii constitute upper and lower bounds, respectively, to the electron-pair relative distance r(12)=(/r1-r2/). An analogous result is also derived for the electron-pair center-of-mass radius (R)=(/r1+r2//2).

Radial subshell splittings and double-zeta functions in many-electron atoms.

When the electron-electron interaction is explicitly considered in many-electron atoms, the average subshell radiusnl splits into two different radii, inner radius nl and outer radius >nl, where n and l are the principal and azimuthal quantum numbers. For the 102 atoms He through Lr in their ground states, the radii nl and nl are systematically examined at the Hartree-Fock limit level. For a subshell nl, two exponents zetanl(est) estimated from these radii have good linear correlations with variationally determined exponents zetanl(var) of double-zeta Slater-type functions.

Interelectronic angle densities of equivalent electrons in Hartree-Fock theory of atoms.

The interelectronic angle density A(theta12) is the probability density function that the angle thetaij (0 < or = thetaij < or = pi) subtended by the vectors ri and rj of any two electrons i and j becomes theta12. For equivalent electrons in atoms, it is shown that the density A(theta12) in the Hartree-Fock theory is given by a simple polynomial of cos theta12. Detailed expressions are reported for all LS terms arising from s2, pN (N = 2-6), dN (N = 2-10), and f(N) (N = 2,12) electron configurations.

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

The average interelectronic 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 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 0 < or = l, l' < or = 3 are 9pi/16 (=101.