Reference-state density functional theory definition

The ESR hyperfine coupling is determined by triplet perturbations. Thus, in principle one should use an unrestricted wave function to describe the reference state. However, it is also possible to use a spin-restricted wave function (Fernandez et al. 1992) and take into account the triplet nature of the perturbation in the definition of the response. Within such a (e.g., SCF or MCSCF) restricted-unrestricted approach, first-order properties are given as the sum of the usual expectation value term and a response correction that takes into account the change of the wave function induced by the perturbation (of the type (0 H° 0)). This restricted-unrestricted approach has also been extended to restricted Kohn-Sham density functional theory (Rinkevicius et al. 2004). 

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