# Magnetic Energy Landscape of Dimolybdenum Tetraacetate on a Bulk Insulator Surface
## 4 Discussion and Conclusions  
We perform a detailed computational study of the magnetic states of the dimolybdenum tetraacetate molecule (MoMo), both in gas-phase and adsorbed on the calcite (10.4) insulating surface. The long-term goal of our investigation is to assess the possibility to use MoMo as a single molecule magnet (SMM), which would open up the possibility to have magnetic molecular networks on a bulk insulating substrate. The work is based on the recent observations that regular MoMo assemblies hold firmly on calcite (10.4) at ambient conditions [48]. MoMo seems particularly interesting for the vertical alignment of the Mo-Mo axis, that favors the symmetry breaking between the two Mo on the surface (a favorable condition for the onset of magnetic states [93]) and the external C-CH\({}_{3}\) linkers that prevent the molecule dissociation, even when all four Mo-Mo bonds are broken.While standard GGA-PBE functionals predict a nonmagnetic (NM) state with quadruple Mo-Mo bond and excited magnetic states at significantly higher energies (growing with the number of broken bonds and ultimately with the magnetization \(M\)), Hubbard corrections stabilize magnetic configurations (FM or AFM) with Mo atoms near their high-spin configurations and atomic magnetizations near their Hund's saturation limit of four. More importantly, the corrections render many FM states metastable. Although the obtained AFM ground state does not seem consistent with available literature on similar systems (but notably missing external linkers between the Mo centers), our calculations show that MoMo might have magnetic states provided that the system is excited to metastable configurations with Mo atoms pulled apart from each other. In the gas-phase, the FM state at the lowest energy (denoted FM8) is about 1 eV above the ground state. It features parallel spins on the Mo atoms (close to maximum atomic magnetization), with a total magnetization of \(M=8\,\upmu_{\text{B}}\). On the surface, the MoMo second lowest-energy state features an antiferrimagnetic (AFiM) order with the atomic moments of the two Mo atoms having opposite direction and different length, still resulting in \(M=2\,\upmu_{\text{B}}\). Importantly, we find that the presence of the insulating surface does not quench the magnetic ordering found in the gas-phase. This is a necessary condition for having stable and regular SMMs arrays on an insulating substrate at room conditions. From this point of view, insulators seem an advantage over metallic surfaces, where the substrate-molecule electronic hybridization could alter or completely quench the magnetic properties of the isolated molecule. For the lowest energy ferromagnetic state (FM8) we calculated the magnetic anisotropy energy (MAE) in the gas-phase, using a noncollinear formalism. We found that the molecule possesses an easy magnetization axis (EMA) that coincides with the Mo-Mo direction and we estimated a MAE barrier around 9.3 meV. This value is compatible with the one found in the [Mn\({}_{12}\)] compound (5.2 meV) [1] although, to the best of our knowledge, no experimental magnetic measurements of MAE exist for our system. The system could also represent a prospect SMM worth of further investigations, if a state with a non-vanishing total \(M\) could be experimentally stabilized on the calcite surface. In this perspective, a first direction of investigation concerns the calculation of the MAE for the molecule adsorbed on the surface, to ascertain that a finite magnetic moment is not too volatile. Other aspects of interest include the assessment of other insulating surfaces (e.g., fluorite) and the characterization of the behavior of molecular systems on metallic surfaces, aimed at verifying the survival of finite magnetic moments [49]. It is also worth extending the present investigation to other TM-based molecules that can be adsorbed firmly on insulating surfaces.