  We propose a method for the evaluation of magnetic exchange couplings based
on noncollinear spin-density functional calculations. The method employs the
second derivative of the total Kohn-Sham energy of a single reference state, in
contrast to approximations based on Kohn-Sham total energy differences. The
advantage of our approach is twofold: It provides a physically motivated
picture of the transition from a low-spin to a high-spin state, and it utilizes
a perturbation scheme for the evaluation of magnetic exchange couplings. The
latter simplifies the way these parameters are predicted using
first-principles: It avoids the non-trivial search for different spin-states
that needs to be carried out in energy difference methods and it opens the
possibility of "black-boxifying" the extraction of exchange couplings from
density functional theory calculations. We present proof of concept
calculations of magnetic exchange couplings in the H--He--H model system and in
an oxovanadium bimetallic complex where the results can be intuitively
rationalized.
