Pair Correlation Theories

Abstract

In the simplest possible description of an n-electron system, one one-electron function (spin-orbital) is associated with each electron and the n -electron wave function is a Slater determinant built up from these spin-orbitals. The one-to-one correspondence between electrons and spin-orbitals gives an acceptable first-order description only for closed-shell and certain open-shell states. A one-electron theory that is applicable in general to open-shell states as well is characterized by assigning sets of electrons to sets of degenerate spin-orbitals, where the number of electrons within one set can be equal to or smaller than the dimension of the irreducible representation spanned by the degenerate set of spin-orbitals. An example is the well-known characterization of an atomic state by its configuration,(1) e.g., for the carbon ground state 1s22s22p2, without specifying the ms and ml values. (For a general discussion of closed- and open-shell states in the framework of rigorous quantum mechanics, see Refs. 2 and 3.)