A Peierls Transition in Long Polymethine Molecular Wires: Evolution of Molecular Geometry and Single-Molecule Conductance

Abstract

Molecules capable of mediating charge transport over several nanometers with minimal decay in conductance have fundamental and technological implications. Polymethine cyanine dyes are fascinating molecular wires because up to a critical length, they have no bond-length alternation (BLA) and their electronic structure resembles a one-dimensional free-electron gas. Beyond this threshold, they undergo a symmetry-breaking Peierls transition, which increases the HOMO−LUMO gap. We have investigated cationic cyanines with central polymethine chains of 5−13 carbon atoms (Cy3 + −Cy11 + ). The absorption spectra and crystal structures show that symmetry breaking is sensitive to the polarity of the medium and the size of the counterion. X-ray crystallography reveals that Cy9•PF 6 and Cy11•B(C 6 F 5 ) 4 are Peierls distorted, with high BLA at one end of the π-system, away from the partially delocalized positive charge. This pattern of BLA distribution resembles that of solitons in polyacetylene. The single-molecule conductance is essentially independent of molecular length for the polymethine salts of Cy3 + − Cy11 + with the large B(C 6 F 5 ) 4− counterion, but with the PF 6 − counterion, the conductance decreases for the longer molecules, Cy7 + −Cy11 + , because this smaller anion polarizes the π-system, inducing a symmetry-breaking transition. At higher bias (0.9 V), the conductance of the shorter chains, Cy3 + −Cy7 + , increases with length (negative attenuation factor, β = −1.6 nm −1 ), but the conductance still drops in Cy9 + and Cy11 + with the small polarizing PF 6 − counteranion.

Reversed Conductance Decay of 1D Topological Insulators by Tight-Binding Analysis

“…Eventually a longchain regime is reached where the conductance-length relationship reverts to exponential decay (equation 1), as indicated by the complex band theory [21][22][23] . This transition between the two conductance-length regimes has recently been shown in experiments 13,24 . Here, we examine systems of molecular wires terminated by radicals in molecular junctions and use a tight-binding approach 25 to investigate the full evolution of the conductance with length.…”

“…This makes it challenging to build long and highly conducting molecular wires. However, researchers have proposed [6][7][8][9][10][11] and experimentally realized [12][13][14][15][16] a reversed conductance-length decay in mixedvalence or diradical molecular systems, where the conductance increases exponentially with molecular length. Diradical molecules have also been identified as one-dimensional analogs of topological insulators 17 , which suggests that this anomalous conductance-length relationship for diradicals is a consequence of their nontrivial topology.…”

Supramolecular Mitigation of the Cyanine Limit Problem

“…Cyanine dyes with more than seven methines (i.e., beyond Cy7) are known to cross over the "cyanine limit" and undergo a symmetry breaking Peierls transition that favors a ground state with an unsymmetric distribution of π-electron density, localized positive charge, and substantial bond length alternation along the polymethine chain. 22,23 A spectral characteristic of this polar, unsymmetric cyanine state is a broad charge-transfer type absorption band in polar solvents like water, 11,24 or when there is tight ion pairing with small counter-anions. 25,26 The Peierls transition explains why unsymmetric cyanine chromophores exhibit broader absorption bands and lower fluorescence quantum yields compared to symmetrical counterparts.…”

“…Cyanines are popular fluorescent dyes with a cationic polymethine chromophore and tunable wavelengths . The most common cyanine dyes are known commercially and informally as Cy3, Cy5, or Cy7, and there is considerable understanding of the structural factors that control the distribution of π-electrons in the molecular orbital ground and excited states. , In nonpolar solvents, a nonpolar ground state is favored with a symmetric distribution of π-electron density, delocalized positive charge, and close to zero bond length alternation along the polymethine chain (Scheme ). This nonpolar state favors sharp absorption bands (the transition involves low vibronic coupling) and relatively bright fluorescence.…”

Two-step thermotropic phase transition and dielectric relaxation in 1D supramolecular lead iodide perovskite [NH4@18-crown ether]PbI3

“…Thus, the phase transition of metal-to-insulator or paramagnetism to diamagnetism will commonly occur at a certain temperature. This is the so-called Peierls or spin-Peierls transition, which has been observed in various low-dimensional electron [5][6][7] / spin [8][9][10][11][12] systems. It is known that the molecular crystals with 'globular-shaped' components frequently undergo a thermotropic disorder-order phase transition because the globularshaped molecule/ion has the internal rotation degrees of freedom.…”