Equation-of-motion coupled-cluster protocol for calculating magnetic properties: Theory and applications to single-molecule magnets
We present a new computational protocol for computing macroscopic magnetic properties of transition-metal complexes using equation-of-motion coupled-cluster (EOM-CC) framework. The approach follows a two-step state-interaction scheme: we first compute zero-order states using non-relativistic EOM-CC and then use these states to evaluate matrix elements of the spin-orbit and Zeeman operators. Diagonalization of the resulting Hamiltonian yields spin-orbit- and field-perturbed eigenstates. Temperature- and field-dependent magnetization and susceptibility are computed by numerical differentiation of the partition function. To compare with powder-sample experiments, these quantities are numerically averaged over field orientations. We applied this protocol to several mononuclear Fe(II) and Fe(III) single-molecule magnets (SMMs) trigonal pyramidal, linear, and trigonal bipyramidal coordination environments. The underlying electronic structure was described by the electron-attached (EOM-EA) and spin-flip (EOM-SF) variants of EOM-CC. The computed energy barriers for spin inversion, and macroscopic magnetization and susceptibility agree well with experimental data. Trends of magnetic anisotropy and spin-reversal energy barrier are explained in terms of a molecular orbital picture rigorously distilled from spinless transition density matrices between many-body states. The results illustrate excellent performances of EOM-CC for describing magnetic behavior of mononuclear transition-metal SMMs.