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Calculations were carried out by means of the Gaussian 94 package (ref. 12) using the Hartree-Fock and Density Functional Theory [through the B3LYP hybrid functional (ref. 13)] levels and the 6-31G(d) basis set (ref. 14). B3LYP/6-31G(d) calculations are known to perform well as regards cycloaddition reactions (ref. 15). The nature of all stationary points (reactants, transition structures and adducts) was tested by means of frequency calculations, which also served to calculate the thermodynamic parameters of the reactions considered.
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note
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The transition structure search was performed without any geometrical constraint at the HF/6-31G(d) and B3LYP/6-31G(d) levels, leading to very similar geometries. The nature of the transition structure was fully characterized by the presence of only one imaginary frequency, correponding to the symmetric stretching of the four atoms involved in the formation of the sigma bonds. Frequency calculations were only carried out at the HF/6-31G(d) level, due to the size of the system.
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