Local Noncollinear Spin Analysis

In this work, we generalize the local spin analysis of Clark and Davidson [J. Chem. Phys. 2001 115 (16), 7382] for the partitioning of the expectation value of the molecular spin square operator, <Ŝ²>, into atomic contributions, <Ŝ_A·Ŝ_B>, to the noncollinear spin case in the framework of density functional theory (DFT). We derive the working equations, and we show applications to the analysis of the noncollinear spin solutions of typical spin-frustrated systems and to the calculation of magnetic exchange couplings. In the former case, we employ the triangular H₃He₃ test molecule and a Mn₃ complex to show that the local spin analysis provides additional information that complements the standard one-particle spin population analysis. For the calculation of magnetic exchange couplings, J_AB, we employ the local spin partitioning to extract <Ŝ_A·Ŝ_B> as a function of the interatomic spin orientation given by the angle θ. This, combined with the dependence of the electronic energy with θ, provides a methodology to extract J_AB from DFT calculations that, in contrast to conventional energy differences based methods, does not require the use of ad hoc S_A and S_B values.