Spin state ordering of iron(II) porphyrin
In plain words
An iron atom held flat inside a ring-shaped molecule called a porphyrin can have its electron spins in a low, middle or high configuration. Different high-level methods give different answers for which configuration has the lowest energy.
Precise statement
For the isolated Fe(II) porphine molecule, determine the adiabatic energy differences among the lowest $S = 0, 1 \text{ and } 2$ states (each at its own optimized geometry, zero-point corrected) to 1 kcal/mol, together with the vertical gaps at a stated common $D4h$ geometry, including the sign of the triplet-quintet gap. An answer is agreement among independent wavefunction methods (coupled cluster with high excitations, DMRG plus perturbation theory, quantum Monte Carlo) extrapolated to the complete basis set limit.
What would settle it
Mutually consistent complete-basis extrapolations from at least two unrelated near-exact methods, cross-checked against gas-phase or matrix-isolation spectroscopy.