Nonlinear correlations between ν1 Raman band and global scalar properties for different length carotenoids

The Raman ν1 band corresponding to the polarization of various length carotenoid (Car) and polyene molecules was theoretically analysed using the density functional theory (DFT) approach. The polarization and other properties of Car and polyene monomers were estimated by using global scalar properties. The results demonstrate a linear dependence between the frequency of the so-called ν 1 Raman band corresponding to the C=C stretching modes, and the global hardness (and global softness) for all molecules of different conjugation lengths. Linear correlations between all global scalar properties and the conjugation length were for polyene structures only. From these calculations an additional relationship was also identified: upon s-cis-isomerisation the effective conjugation length and global softness increased for polyenes, while the effective conjugation length and global softness decreased for carotenoids containing β -rings at their ends. According to the electrophilicity index study, charge transfer processes (CT) should be favourable in longer carotenoid and polyene structures. A linear dependence of electronegativity was found for polyene and particular Cars subgroups. The electrophilicity index was very sensitive to special groups bonded to the polyene chain of Cars. Finally, the conjugation length of the Cars did not have a linear dependence on the electronegativity, chemical potential and electrophilicity index, but almost a linear dependence was seen on the global hardness while the polyene models had a linear dependence in all cases.