“…D.01) using the Becke-3eLeeeYangeParr (B3LYP) functional and 6-31G(d) basis set including a zero point vibrational energy correction. Prior to the calculation for (all-E)-lycopene, the structures of the conjugated all-E-polyenes, C n H nþ2 (n ¼ 4e22, even number) were optimized at the ground singlet states, and followed by the methylated undecaenes (2Z,4E 16,20,5,7,9,11,13,15,17,19,21,. The structure of HMHU was estimated using initial conformers at 30 intervals of the dihedral angles of the free rotation in a stepwise manner for two ethyl groups, and (all-E)-lycopene was then estimated in the same way.…”