Mn₂ Dimers Encapsulated in Silicon Cages: A Complex Challenge to MC-SCF Theory

MC-SCF wavefunctions for three endohedral Mn/Si clusters, Mn₂Si₁₀, Mn₂Si₁₂, and [Mn₂Si₁₃]⁺, show evidence for strong static correlation, both in the Mn-Si bonds ('in-out correlation') and between the two Mn centers ('up-down correlation'). We use both Restricted and Generalized Active Spaces (RAS and GAS) to place constraints on the configurations included in the trial wavefunction, showing that, particularly in the high-symmetry cases, the GAS approach captures more of the static correlation. The important correlating pairs are similar across the series, indicating that the electronic structure of the endohedral Mn₂ unit is, to a first approximation, independent of the size of the silicon cage in which it is embedded.