The all-trans to mono-cis isomerizations of polyenes and two C40H56 carotenes, beta-carotene and lycopene, at the ground singlet (S0) and triplet (T1) states are studied by means of quantum chemistry computations. At the S0 state of polyenes containing n acetylene units (Pn), we find that the energy barrier of the central C=C rotation decreases with n. In contrast, however, at the T 1 state, the rotational barrier increases with n. For the C40H56 carotenes, the rotational barriers of lycopene are lower than those of their beta-carotene counterparts. This difference renders the rotational rates of lycopene to be 1-2 orders of magnitude higher than those of beta-carotene at room temperature. For both these carotenes, the barrier is lowest for the rotation toward the 13-cis isomer. The relative abundances are in the following order: all-trans > 9-cis > 13-cis > 15-cis. Although the 5-cis isomer of lycopene has the lowest energy among the cis isomers, its formation from the all-trans form is restricted, owing to a very large rotational barrier. The possible physiological implications of this study are discussed.

Theoretical study of the enthalpies of formation (DeltaHf) for polyenes up to nine ethylene units and for several C40H56 carotenes including beta-carotene, alpha-carotene, lycopene, and prolycopene is presented. For polyenes and small branched alkenes, we used G2, G3, and G3MP2B3 theories, and the DeltaHf 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 DeltaHf value of C40H56 carotenes is promising.

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