ELECTRON CORRELATION, GEOMETRY, AND ENERGY-SPECTRUM OF QUADRUPLY EXCITED-STATES

There is a class of quadruply excited states of 5So symmetry where electronic motion is highly correlated and where the electrons tend to form a tetrahedron as the excitation energy increases toward the four-electron ionization threshold. This conclusion has been reached following ab initio state-specific calculations in Be, for the lowest energy state of each intrashall manifold n, of the energies, the average radii rn, and the average interelectronic angle 12. In order to calculate 12, a general theory is developed, applicable to arbitrary N-electron atomic states. The value of 12 is straightforward to compute, and is given from a prescription transforming the expression for the two-electron interaction energy of the state to a formula for the probability density of cos12. The state-specific calculations for each n, up to n=6, were done by the multiconfigurational Hartree-Fock method where all configurations with n1=n2=n3=n4 are included. For n=3, the main configuration 3s3p3 has a weight of 0.90 while 12=103.3°. As n increases, electron correlation increases relative to the Coulomb nuclear attraction. With increasing degeneracy, many configurations with high orbital angular momenta mix heavily, and 12 increases. For example, for n=6, the 6s6p3 configuration has a weight of only 0.59 and 12=106°. In this case, doubly, triply, as well as quadruply excited configurations with respect to nsnp3 contribute to the wave function significantly. Finally, these four-electron ionization ladder states have a simple energy spectrum, given to a very good approximation by En=-A/n2 (n1/2rn), where A is a constant. In conjunction with our earlier results on the geometry and the spectra of special classes of doubly and triply excited states, this finding leads to the conclusion that for highly correlated electronic motion the spectrum is dictated essentially by one dynamical variable, the average radius from the nucleus. © 1994 The American Physical Society.