Essential factor for DFT predictions of relative energies in FePc: A Diffusion Monte Carlo study

The ground state of the isolated iron phthalocyanine (FePc) with $D_{4h}$ symmetry is still unclear because the previous DFT works gave different predictions owing to their XC functionals. We applied CASSCF+DMC to evaluate the relative energies of the electric configurations reliably without XC functionals. $A_{2g}$ configuration is predicted as the ground state, which is, we found, able to be justified by the recent spectroscopy for FePc gas. Furthermore, we considered why the DFTs give the different predictions. We compared several DFTs with DMC, which include different percentages of exact exchange, and we revealed short-range exchange is essential for the prediction. We identified the discrepancies being due to the assumptions made in the superposition model, which has also been employed in literature to explain the ground state of FePc molecule. Our orbital analysis shows that the assumptions are too simple to describe the proper stabilizing mechanism explained by the orbital shapes: Oversimplified symmetry assumptions as well as the ignorance of outer ligand structures cannot capture the stabilization [destabilization] of $b_{2g}$ [$e_g$] orbitals, those actually realizes $A_{2g}$ as the most stable state.