MAGPACK1 A Package to Calculate the Energy Levels, Bulk Magnetic Properties, and Inelastic Neutron Scattering Spectra of High Nuclearity Spin Clusters.

M agnetic molecular clusters, i.e., molecular assemblies formed by a finite number of exchange-coupled magnetic moments, are currently receiving much attention in several active areas of research as molecular chemistry, magnetism, and biochemistry. A reason for this interest lies in the possibility to use simple molecular clusters as magnets of nanometer size exhibiting unusual magnetic properties as superparamagnetic like behavior or quantum tunneling of magnetization.2 – 4 Organic molecules of increasing sizes and large number of unpaired electrons are being explored as a means of obtaining building blocks for molecule-based magnets.5 Magnetic clusters of metal ions are also relevant in biochemistry.6 This area between molecule and bulk will require new theoretical concepts and techniques for investigation of their peculiar properties. Still, the theoretical treatment required to understand the magnetic and spectroscopic properties of this wide variety of compounds is a challenging problem in molecular magnetism.7 For a long time, this problem has been mostly restricted to treat comparatively simple clusters comprising a reduced number of exchange-coupled centers and special spin topologies, for which solutions can be obtained either analytically or numerically. However, on increasing the spin nuclearity of the cluster, the problem rapidly becomes unapproachable because the lack of translational symmetry in the clusters. An additional complication is the spin anisotropy of the cluster. Until now only the isotropic-exchange case has been treated, so as to take full advantage of the spin symmetry of the cluster.8 In this article we present a very powerful and efficient computational approach to solve the exchange problem in high nuclearity spin clusters with all kind of exchange interactions (isotropic and anisotropic), including the single-ion anisotropic effects. The clusters are formed by an arbitrary number of exchangecoupled centers that combine different spin values and arbitrary topology. This approach is based on the use of the irreducible tensor operators (ITO) technique.7, 9 – 12 It allows evaluation of both eigenvalues and eigenvectors of the system, and then, calculation of the magnetic susceptibility, magnetization, or heat capacity, and also the inelastic neutron scattering spectra. In the following sections we will present both the theory and the four different implemented FORTRAN programs that integrate a package called MAGPACK . In the last section some examples are presented in order to show the possibilities of the programs.