Electron correlation, geometry, and energy spectrum of quadruply excited states.

Abstract

There is a class of quadruply excited states of $^{5}$${\mathit{S}}^{\mathit{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 following ab initio state-specific calculations in Be, for the lowest energy state of each intrashall manifold n, of the energies, the average radii ${\mathit{r}}_{\mathit{n}}$, and the average interelectronic angle ${\mathrm{\ensuremath{\theta}}}_{12}$. In order to calculate ${\mathrm{\ensuremath{\theta}}}_{12}$, a general theory is developed, applicable to arbitrary N-electron atomic states. The value of ${\mathrm{\ensuremath{\theta}}}_{12}$ 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 cos${\mathrm{\ensuremath{\theta}}}_{12}$. The state-specific calculations for each n, up to n=6, were done by the multiconfigurational Hartree-Fock method where all configurations with ${\mathit{n}}_{1}$=${\mathit{n}}_{2}$=${\mathit{n}}_{3}$=${\mathit{n}}_{4}$ are included. For n=3, the main configuration 3s3${\mathit{p}}^{3}$ has a weight of 0.90 while ${\mathrm{\ensuremath{\theta}}}_{12}$=103.3\ifmmode^\circ\else\textdegree\fi{}. 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 ${\mathrm{\ensuremath{\theta}}}_{12}$ increases.For example, for n=6, the 6s6${\mathit{p}}^{3}$ configuration has a weight of only 0.59 and ${\mathrm{\ensuremath{\theta}}}_{12}$=106\ifmmode^\circ\else\textdegree\fi{}. In this case, doubly, triply, as well as quadruply excited configurations with respect to ${\mathit{nsnp}}^{3}$ 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 ${\mathit{E}}_{\mathit{n}}$=-A'/${\mathit{n}}^{2}$ (${\mathit{n}}^{1/2}$\ensuremath{\sim}${\mathit{r}}_{\mathit{n}}$), 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.