Theoretical study of the enthalpies of formation for C₄₀H ₅₆ carotenes

Theoretical study of the enthalpies of formation (ΔH_f) for polyenes up to nine ethylene units and for several C₄₀H₅₆ carotenes including β-carotene, α-carotene, lycopene, and prolycopene is presented. For polyenes and small branched alkenes, we used G2, G3, and G3MP2B3 theories, and the ΔH_f values were evaluated with the atomization, isodesmic bond separation, and homodesmic schemes. The applicability of six DFT functionals were evaluated by comparing their predictions with those obtained using G3 theory within the atomization scheme. Additivity approaches, including atom equivalents and group equivalents using DFT and semiempirical theories, were explored. We found that group equivalents associated with isodesmic reactions are able to provide the most accurate predictions within the test set. The predictions from the six functionals are in good agreement with the G3 results. Among them, B3LYP performs the best, with an average absolute deviation of only 0.30 kcal/mol. The application of DFT in the prediction for the ΔH_f value of C₄₀H ₅₆ carotenes is promising.