Accurate calculations of geometries and singlet-triplet energy differences for active-site models of [NiFe] hydrogenase

We have studied the geometry and singlet-triplet energy difference of two mono-nuclear Ni2+ models related to the active site in [NiFe] hydrogenase. Multiconfigurational second-order perturbation theory based on a complete active-space wavefunction with an active space of 12 electrons in 12 orbitals, CASPT2(12,12), reproduces experimental bond lengths to within 1 pm. Calculated singlet-triplet energy differences agree with those obtained from coupled-cluster calculations with single, double and (perturbatively treated) triple excitations (CCSD(T)) to within 12 kJ mol(-1). For a bimetallic model of the active site of [NiFe] hydrogenase, the CASPT2(12,12) results were compared with the results obtained with an extended active space of 22 electrons in 22 orbitals. This is so large that we need to use restricted active-space theory (RASPT2). The calculations predict that the singlet state is 48-57 kJ mol(-1) more stable than the triplet state for this model of the Ni-Sl(a) state. However, in the [NiFe] hydrogenase protein, the structure around the Ni ion is far from the square-planar structure preferred by the singlet state. This destabilises the singlet state so that it is only similar to 24 kJ mol(-1) more stable than the triplet state. Finally, we have studied how various density functional theory methods compare to the experimental, CCSD(T), CASPT2, and RASPT2 results. Semi-local functionals predict the best singlet-triplet energy differences, with BP86, TPSS, and PBE giving mean unsigned errors of 12-13 kJ mol(-1) (maximum errors of 25-31 kJ mol(-1)) compared to CCSD(T). For bond lengths, several methods give good results, e. g. TPSS, BP86, and M06, with mean unsigned errors of 2 pm for the bond lengths if relativistic effects are considered