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Local spin

In many cases the spin properties of a molecular system can properly be characterized by the spin density. There are, however, systems for which the description by using the spin density is not sufficient: binuclear complexes, diradicals or antiferromagnets. In such systems one postulates the existence of some local spins, although the overall system is a singlet and there is no spin density. For such systems Clark and Davidson proposed to calculate the one- and two-center components of the expectation value < S2>. Their scheme--although mathematically correct–-lead to hard to accept results: e.g., each hydrogen atom of the H2 molecule treated at the closed-shell RHF level carries a local spin-square of 3/8---half of the value for a free electron. For that reason, and owing to the fact that the partitioning of a single physical quantity into several components is usually not unique, we have proposed such a decomposition of the expectation value < S2> into atomic and diatomic contributions for both single determinant and correlated wave functions, which satisfies the following---physically quite reasonable---additional requirements: (i) one should get no spins whatever for the covalent systems described by a closed shell RHF wave function using doubly filled orbitals, and (ii) if the wave function is properly dissociating, then the asymptotic values of the atomic spins obtained for the atoms at large distances should coincide with the values pertinent to the respective free atoms. The respective formulae have been derived for both single determinant and correlated wave functions; in the latter case they are in terms of the spin-density, the first order density matrix and the cumulant of the second order density matrix. The results of numerical realization are in conformity with the physical expectations ​
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