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Herein, we deeply detail for the very first time mathematical concepts behind the generation of helical molecular orbitals (MOs) for linear chains of atoms. We first give a definition of helical MOs and we provide an index measuring how far a given helical states is from a perfect helical distribution. Structural properties of helical distribution for twisted N ${\left[N\right]}$ -cumulene and cumulene version of Möbius systems are given. We then give some simple structural assumptions as well as symmetry requirements ensuring the existence of helical MOs. Considering molecules which do not admit helical MOs, we provide a first way to induce helical states by the breaking of symmetries. We also explore an alternative way using excited conformations of given molecules as well as different electronic multiplicities., (© 2023 Wiley-VCH GmbH.)

Two 2,2'-bipyridines, substituted at the 4,4'-positions by p-dialkylaminophenylazostyryl moieties p-R2N-C6H4-N=N-C6H4-CH=CH-[6 a, R2N=nBu2N; 6 b, R2N=(nBu)(C4H8OTHP)N; 6 c, R2N=(nBu)(C4H8OH)N], were successfully synthesized by using Wadworth-Emmons reactions. The X-ray structure of 6 a has been determined. Esterification of 6 c with 2-bromoisobutyroylbromide afforded 6 d. This ligand was used as an initiator for the living radical polymerization of methylmethacrylate (MMA) and gave rise to macroligand 6 e. Thin films of good optical quality were obtained by the spin-coating technique. Photoisomerization experiments were carried out on 6 a in solution and on 6 e in both solution and film, and the kinetics of photochemical (E/Z) and thermal (Z/E) isomerization were investigated. They were found to show Z-E back isomerization typical of aminoazobenzene-type rather than of push-pull-type molecules. Density functional theoretical (TD-DFT) calculations were performed on model compound 6 a' (R2N=Me2N) to understand the structural and electronic transitions of the corresponding E-E, E-Z and Z-Z isomers. It was found that the E-E isomer is almost planar as observed experimentally by X-ray diffraction, whereas the Z-Z isomer, which is 35.4 kcal mol(-1) less stable than the E-E isomer, is nonplanar. The theoretical studies also reveal that several transitions of pi-pi*, n-pi* and charge-transfer (CT) types, are involved in the long-wavelength transition of 6 a (E-E). The same observations can be made for the (Z-Z) isomer, and the TD-DFT simulated spectrum fits quite nicely to the experimental, reproducing and explaining the apparition of a blue-shifted charge-transfer band at 390 nm.