  Characterizing the electronic structure of the iron--sulfur clusters in
nitrogenase is necessary to understand their role in the nitrogen fixation
process. One challenging task is to determine the protonation state of the
intermediates in the nitrogen fixing cycle. Here, we use a dimeric iron--sulfur
model to study relative energies of protonation at C, S or Fe. Using a
composite method based on coupled cluster and density matrix renormalization
group energetics, we converge the relative energies of four protonated
configurations with respect to basis set and correlation level. We find that
accurate relative energies require large basis sets, as well as a proper
treatment of multireference and relativistic effects. We have also tested ten
density functional approximations for these systems. Most of them give large
errors in the relative energies. The best performing functional in this system
is B3LYP, which gives mean absolute and maximum errors of only 10 and 13 kJ/mol
with respect to our correlated wavefunction estimates, respectively. Our work
provides benchmark results for the calibration of new approximate electronic
structure methods and density functionals for these problems.
