Near-exact correlation energy of benzene in a standard basis
In plain words
Benzene with 30 active electrons in 108 orbitals has a unique exact answer but is too large for brute-force solution. When the best approximate methods were run on it blind in 2020 they did not all agree.
Precise statement
For benzene at the reference geometry in the cc-pVDZ basis with frozen $1s$ cores (30 electrons in 108 orbitals), determine the full configuration interaction correlation energy to $0.1\,\mathrm{m}E_h$ ($E_h$ = Hartree unit, about $627.5\,\mathrm{kcal}/\mathrm{mol}$) and establish which near-exact methods (selected configuration interaction, DMRG, FCIQMC, many-body expanded FCI, high-order coupled cluster) converge to it. An answer is a value with a defensible error bar confirmed by at least two independent methods.
What would settle it
Two or more independent near-exact methods with controlled extrapolation agreeing within $0.1\,\mathrm{mE}_h$.
Status in the literature
A 2020 blind comparison (Eriksen et al., J. Phys. Chem. Lett., https://doi.org/10.1021/acs.jpclett.0c02621) gave estimates from the leading methods spread over about $1\,\mathrm{m}E_{\mathrm{h}}$, larger than the $0.1\,\mathrm{m}E_{\mathrm{h}}$ target; later work narrowed the spread, but agreement at $0.1\,\mathrm{m}E_{\mathrm{h}}$ is not established in the literature checked.