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

There is a class of quadruply excited states of S-5(o) 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 follo wing ab initio state-specific calculations in Be for the lowest energy state of each intrashell manifold n, of the energies, the average rad ii r(n), and the average interelectronic angle theta(12). In order to calculate theta(12), a general theory is developed, applicable to arbi trary N-electron atomic states. The value of theta(12) is straightforw ard to compute, and is given from a prescription transforming the expr ession for the two-electron interaction energy of the state to a formu la for the probability density of cos theta(12) The state-specific cal culations for each n, up to n = 6, were done by the multiconfiguration al Hartree-Fock method where all configurations with n(1) = n(2) = n(3 ) = n(4) are included. For n = 3, the main configuration 3s3p(3) has a weight of 0.90 while theta(12) = 103.3 degrees. As n increases, elect ron correlation increases relative to the Coulomb nuclear attraction. With increasing degeneracy, many configurations with high orbital angu lar momenta mix heavily, and theta(12) increases. For example, for n = 6, the 6s6p(3) configuration has a weight of only 0.59 and theta(12) = 106 degrees. In this case, doubly, triply, as well as quadruply exci ted configurations with respect to nsnp(3) contribute to the wave func tion significantly. Finally, these four-electron ionization ladder sta tes have a simple energy spectrum, given to a very good approximation by E(n) = -A'/n(2) (n(1/2) similar to r(n)), where A' is a constant. I n 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 t he spectrum is dictated essentially by one dynamical variable, the ave rage radius from the nucleus.