Abstract
The theory of wave functions which have the form of a single determinant, but without the restriction to doubly occupied orbitals, is developed in general terms. The unrestricted molecular orbitals, the natural spin orbitals, the natural orbitals and the corresponding orbitals are defined and some of their properties deduced. The use of annihilators and projection operators to produce eigenfunctions of spin is investigated. The role of molecular symmetry and of a truncated set of basic functions in forcing a single determinant to be an eigenfunction of spin is discussed. A theorem on the diagonalization of a rectangular matrix by two unitary matrices is proved and applied to density matrices.
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