By Hector J. de Vega, Norma Sanchez

The current quantity *Field idea, Quantum Gravity and * *Strings, II* includes for the lectures added in 1985/86 at a joint seminar of the DAPHE observatory at Meudon and the LPTHE college Paris VI. This set of lectures includes chosen issues of present curiosity in box and particle conception, cosmology and statistical mechanics. simple difficulties of string and superstring idea are handled in a latest viewpoint, and quantum box theoretical in addition to string ways to cosmology are provided. contemporary growth on integrable theories and comparable matters in , 4 and extra dimensions is reviewed. This seminar on present advancements in mathematical physics addresses researchers in addition to graduate scholars.

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**Field Theory, Quantum Gravity and Strings II**

The current quantity box idea, Quantum Gravity and Strings, II contains for the lectures introduced in 1985/86 at a joint seminar of the DAPHE observatory at Meudon and the LPTHE college Paris VI. This set of lectures includes chosen themes of present curiosity in box and particle thought, cosmology and statistical mechanics.

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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 [23] and the Perdew GGA correlation [24] terms. Another important approach to built DFT functionals is the so-called hybrid method based on the adiabatic connection formula [186]. 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.