Interacting resonances and antiresonances in conjugated hydrocarbons: exceptional points and bound states in the continuum.

Quantum interference dramatically modulates electron transport that provides exciting prospects for molecular electronics. We develop a holistic picture of quantum interference phenomena in molecular conductors based on conjugated hydrocarbons taking into account the interaction of resonances and antiresonances (AR). This interaction can result in the coalescence of resonances and ARs accompanied by a significant quantum transparency change. As such a change results from a small variation of the system parameters, it is essential for reducing power consumption in electronics. We establish that the coalescence of ARs is intimately connected with the exceptional point of an underlying non-Hermitian Hamiltonian. The coalescence of ARs cannot be explained considering only the LUMO and HOMO without orbitals beyond them. Cyclobutadiene is discussed as an example. We show that the interaction of resonances and ARs can also result in the formation of a bound state in the continuum (BIC). Our formalism accounting for separate descriptions of resonances and ARs is especially suitable for describing BICs, which can be considered as either a resonance or an AR with zero width. In particular, we show that benzene in the -configuration possesses BICs, which can be revealed as narrow Fano resonances (FRs) in the transmission spectrum by perturbing the molecule symmetry. Any BIC can be turned into an FR by a proper change of the system parameters, but the reverse is not true. We demonstrate that BICs are related to such chemical concepts as non-bonding orbitals, radicals, and diradicals. Our analytical results within the Hückel formalism are closely reproduced by simulations. Therefore, experimentally revealing these phenomena looks quite probable.