Natural Expansion of the First-Order Density Matrix for a Spin-Projected Single Determinant

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Abstract
The first‐order density matrix is obtained for the state corresponding to a spin projection of a general different orbitals for different spins single determinental function. Explicit expressions are given for the natural orbitals and occupation numbers in terms of parameters characteristic of the unprojected state. The spin density and the charge density matrices are found to have the same natural orbitals in the projected state as in the unprojected state. A number of special and limiting cases are considered, including that of slightly different orbitals for different spins.