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88 ture characterized by a µ-CO group. The gas-phase geometry optimization of the [(CH3 S)4 (Fe4 S4 )(PDT)(Fe2 )(µ-CO)(CO)2 (CN)2 ]–5 isomer 5a1 , reveals that this species is unstable. However, the same complex is stable when the optimization is carried out in presence of a polarizable continuum medium 5a4 and 5a40 . In this case the electronic structure of the [Fe4 S4 ] cluster is very similar to that calculated for 5b4 , being still compatible with a formal Fe(III)Fe(II)Fe(II)Fe(II) redox state and with the Fe(I)Fe(I) redox state of the [2Fe]H cluster.
6 Conclusions and Perspectives The application of quantum chemical methods to the investigation of hydrogenases and related biomimetic models has nicely complemented experimental studies, allowing us to disclose key factors related to the catalytic properties of the enzymes. In particular, the possibility to use theoretical methods to study intermediate and transition state structures, reaction energies and activation barriers, as well as spectroscopic properties, has allowed us to dissect the molecular mechanism of several reaction paths relevant to hydrogenase chemistry.
Among GGA functionals, the Becke–Perdew (BP86) exchange-correlation functional is one of the most used. This functional is composed by the Becke88 exchange  and the Perdew GGA correlation  terms. Another important approach to built DFT functionals is the so-called hybrid method based on the adiabatic connection formula . According to the latter, the exact Exc functional is given by the following integral: 1 ψλ |vxc (λ)|ψλ dλ , Exc = (35) 0 where λ is the parameter deﬁned in the Hamiltonian operator in Eq.