Herein, we deeply detail for the very first time mathematical con- cepts 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 heli- cal distribution for twisted [N]-cumulene and cumulene version of Möbius systems are given. We then give some simple structural assumptions as well as symmetry requirements ensuring the exis- tence 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 us- ing excited conformations of given molecules as well as different electronic multiplicities.