Orbital hardness

Calculations of the UV spectra of the isomeric thieno-thiophenes " indicate that, as in the case of thiophene,3d and higher sulfur orbitals hardly affect the electronic spectra of sulfur-containing condensed heteroaromatics. In the case of sulfones of thienothiophene 2 and dithienothiophenes 5-10 in which the sulfur... 

Within the concept of orbital electronegativity as outlined above, it is easy to identify the orbital hardness as... 

Low polarisability High electronegativity Vacant, high-energy orbitals Hard to oxidise... 

This approximation fails if the HOMO-LUMO energy difference is close to zero. Moreover, for a more accurate computation of T], the contribution to the hardness of various orbitals should be taken into account. Recently, different approaches, accounting for the orbital hardness values, have been proposed [54-56]. 

Applying the Pearson s principle [70[, that states the more localized. system is less reactive, the orbital hardness can be interpreted as a measure of the degree of electron localization of a given orbital [71 [.Moreover, in such a manner, the two particle interelectronic interaction, that is the most significant contribution in the hardness evaluation, is considered [69[. 

Some general conclusions can be drawn from the reported results. For each scheme orbital hardness values are about two times smaller than the vertical ones in all cases, except when the HF/6-31+G computational protocol is adopted. In this latter case the differences are less pronounced and, on the contrary, the vertical values are smaller than the orbital ones. Results obtained at local VWN and non-local BP86 levels are coincident and in some cases differences are negligible also with respect to the B3LYP values. The HF values are completely different when the orbital operational definition of hardness is used, whereas vertical values are very close to those obtained at all the other levels of theory. 

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