Spin projection of single-determinant wavefunctions

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Abstract
Using the method of expansion in terms of the natural orbitals of charge density, we have rederived the components of the one‐ and two‐particle density matrices that result upon spin projection of a single‐determinant wavefunction. We have corrected several errors in the unrestricted two‐particle density matrix elements given by Harriman and co‐workers, pointed out the necessity of correcting the phases of the natural orbitals, and generalized the theory to the extent necessary to treat molecules having unequal numbers of electrons and basis orbitals. The theory has been applied to several of the types of cases for which the use of the projected UHF method is desirable: (a) small hydrocarbon radicals and singly charged ions, (b) hydrocarbon ions with pseudodegenerate ground states, and (c) a postulated photoproduct of dipyridyl, which had previously been predicted to be a triplet. The UHF wavefunctions of several of the small hydrocarbon radicals and monoions have only limited spin contamination by higher multiplicity states and therefore provide good checks on the correctness and internal consistency of the present results by comparison with the results obtained by alternative methods. The results on the ions with pseudodegenerate ground states demonstrate that the projected UHF theory provides a good alternative to extensive configuration interaction treatments. The results for the postulated photoproduct of dipyridyl reverse the earlier prediction of the ground state multiplicity and demonstrate the importance of comparing energies of UHF wavefunctions for both the singlet and triplet states for predicting singlet‐triplet splittings.