A variety of powerful theoretical tools are in use within the Ames Laboratory magnetic molecules collaboration. For many magnetic molecules the theoretical analysis can proceed via diagonalization of the Heisenberg Hamiltonian matrix followed by the application of standard methods of statistical mechanics. However, this approach is usually impractical if the dimensionality, D = (2s + 1)^N, of the underlying Hilbert space exceeds about 10⁷, a situation that can occur even for relatively small numbers, N, of identical spins s. For these difficult situations we are finding that thermal equilibrium properties can in many cases be successfully determined by employing the quantum Monte Carlo method. Important progress can also be achieved for magnetic molecules when s = 5/2 or larger, by using computer simulational methods of classical spin dynamics and the classical Monte Carlo method to determine the dependence of physical quantities on external variables, including both thermodynamic functions and equilibrium time correlation functions. The latter are of great importance for the analysis of neutron scattering and magnetic resonance measurements. Moreover, by comparing results obtained by invoking both classical and quantum Monte Carlo methods we are able to establish guidelines for when the classical methods, which are relatively easy to implement, can provide useful predictions for finite quantum Heisenberg spin systems.

Electronic structure and exchange interactions in single magnetic molecules