HUND RULES, THE ALTERNATING RULE, AND SYMMETRY HOLES

We review attempts to explain Hund's first rule, that a triplet state should lie below a singlet state of the same configuration, as a consequence of the ''Fermi hole' in the triplet state electron-electron distribution function. After describing the failure of such attempts, and reviewing the types of exceptions to Hund's first rule, we examine the ''alternating rule'', which accounts for most of the known exceptions. We show that the alternating rule is associated with whether the parity of the two-electron wave function is natural or unnatural. We show that whereas in the case of natural parity the triplet correlation function has a broad Fermi hole and the singlet correlation function does not, in the case of unnatural parity the singlet correlation function has a quartic ''symmetry hole'' that i:s even broader than the quadratic Fermi hole of the triplet correlation function. Thus this more general perspective provides a relationship between the ordering of singlet/triplet energy levels and the breadth of their respective symmetry holes. We argue that although the breadth of symmetry holes cannot be said to cause the ordering of singlet/triplet energy levels, both phenomena are consequences of factors of (-1)S+L+l1+l2 in the construction of the properly antisymmetrized eigenfunctions of spin and angular variables; hence the two phenomena are closely associated, although neither is the cause of the other.