Electronic structure calculations on the nature of electronic states and the magnetic coupling in Mn-acetate $\left[{\mathrm{Mn}}_{12}{\mathrm{O}}_{12}\right(R\mathrm{COO}{)}_{16}\left({\mathrm{H}}_2\mathrm{O}{)}_4\right]$ molecules have been been carried out within the generalized gradient approximation to the density functional formalism. Our studies on this 100-atom molecule illustrate the role of the nonmagnetic carboxyl host in stabilizing the ferrimagnetic ${\mathrm{Mn}}_{12}{\mathrm{O}}_{12}$ core and provide estimates of the local magnetic moment at the various sites. We provide a first density-functional-based prediction of the second-order magnetic anisotropy energy of this system. Results are in excellent agreement with experiment. To perform these calculations we introduce a simplified exact method for spin-orbit coupling and magnetic anisotropy energies in multicenter systems. This method is free of shape approximations and has other advantages as well. First, it is valid for periodic boundary conditions or finite systems and is independent of basis set choice. Second, the method does not require the calculation of electric field. Third, for applications to systems with a finite energy gap between occupied and unoccupied electronic states, a perturbative expansion allows for a simple determination of the magnetic anisotropy energy.

• Received 4 March 1999

DOI:https://doi.org/10.1103/PhysRevB.60.9566