Can a Topological Approach Predict Spin-Symmetry Breaking in Conjugated Hydrocarbons?

Abstract

The closed-shell mean-field single determinants of large alternant hydrocarbons are frequently unstable with respect to a possible spin-symmetry breaking which produces different orbitals for the α and β electrons, either in Hartree-Fock or in Kohn-Sham DFT calculations. The present work shows that one may easily predict whether such a symmetry breaking will take place from the elementary topological Hückel Hamiltonian which introduces a simple hopping integral t. The demonstration makes use of the simplest representation of the bielectronic repulsion, namely, the Hubbard bielectronic operator, reduced to an on-site repulsion U, and takes benefit of the mirror theorem. A recipe is proposed to determine the relevant t/U ratio for a given exchange-correlation potential. The symmetry-breaking phenomenon first concerns the mixing between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), but it may eventually run on other pairs of mirror orbitals. These symmetry breakings may take place while the other molecular orbitals keep a closed-shell character. The spin polarization of these MOs, appearing in typical unrestricted mean-field calculations, is an induced and amplifying effect, which has to be distinguished from the symmetry breaking itself. Special attention is paid to the possible appearance of multiple symmetry breakings, leading to a polyradical character. The model is tested on six series of polycyclic hydrocarbons. This elementary approach sheds new arguments on the debate concerning the di- or polyradical character of polyacenes.

Pushing the Limits of Acene Chemistry: The Recent Surge of Large Acenes

“…A qualitative pictorial description of the polyradical character of acenes was developed by Trinquier et al. based on a spin‐symmetry‐broken B3LYP analysis [101, 142] . Similar to the non‐Kekulé structure invoked by Zugermeier et al.…”

Exchange Rules for Diradical π-Conjugated Hydrocarbons

“…Naively, one could expect that diradicals always had a ground state with S = 1, due to the similitude with the case of open-shell atoms. Whereas this is often the case in a variety of systems 3,[11][12][13][14][15] , in others there is a violation of the Hund's rule 12,[16][17][18][19][20][21] . Therefore, the sign of the exchange interaction in this class of diradicals is not always the same 5 .…”

A Practical General Method for the Preparation of Long Acenes

“…The nature of the electronic structure of long acenes is still actively discussed, in particular with respect to the partial contribution of the open‐shell singlet state to the electronic ground‐state configuration beyond decacene . On the other hand, these compounds are predicted to show attractive electronic and magnetic properties . They have been suggested for use as molecular wires in single‐molecule electronics, for solar‐cells applications, for spintronics and plasmonics, and as semiconducting materials in organic‐field effect transistors and in organic light emitting diodes …”

“…[2][3][4][5] On the other hand, thesec ompounds are predicted to show attractive electronic and magnetic properties. [6] They have been suggested for use as molecular wires in single-molecule electronics, for solar-cells applications, [7] for spintronics [8] andp lasmonics, [9] and as semiconducting materials [10,11] in organic-fielde ffect transistors [12] and in organic light emittingd iodes. [13] To overcome the inherentf ragilityo fl ong acenes and to improve their solubility and processability,i ti sp ossible to attach electron-deficiento rb ulky substituents [14][15][16][17][18][19][20] or to introduce heteroatoms into the acene framework such as sulfur or nitrogen atoms.…”