Generation of Helical states -- breaking of symmetries, Curie's principle, and excited states

TL;DR

This paper investigates the generation of helical molecular orbitals in linear atomic chains, exploring symmetry breaking and excited states as methods to induce helicity, with applications to cumulene and Möbius systems.

Contribution

It introduces a new index for measuring helical states and proposes symmetry-breaking and excited state methods to generate helical MOs in molecules.

Findings

Structural properties of helical MOs in cumulene and Möbius systems.

Symmetry breaking can induce helical states in molecules.

Excited conformations can also generate helical MOs.

Abstract

Following previous work of M.H. Garner, R. Hoffmann, S. Rettrup and G.C. Solomon, we discuss 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 $[n]$-cumulene and cumulene version of M\"obius 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. Several examples are given.