Reverse Bond-Length Alternation in Cumulenes: Candidates for Increasing Electronic Transmission with Length

Abstract

Single-molecule conductance generally decays exponentially with the length of the molecule when the transport mechanism is a coherent tunneling process. However, it was recently found that this length dependence can be reversed in linear conjugated molecules if the bond-length alternation is reversed. In this work we show that even-carbon cumulenes show this behavior as the bond lengths are reversed for the dominant π-system compared to the equivalent polyenes and polyynes. We explore the electronic origins of the reversed bond-length alternation in cumulenes and its relation to the length dependence of the electronic transmission. Through density functional theory and nonequilibrium Greens function calculations we predict that cumulenic wires have reverse decay of transmission with length; that is, the decay constant β is found to be negative. As a direct consequence of the reversed bondlength alternation, the electronic transmission increases with length as the highest occupied molecular orbital−lowest unoccupied molecular orbital gap rapidly narrows. On the basis of recent progress in cumulene synthesis, we discuss substituent strategies that may increase reverse bond-length alternation. Cumulenes stand out as promising candidates for a series of molecules that may show reverse decay of single-molecule conductance with increasing length.

Unusual Length Dependence of the Conductance in Cumulene Molecular Wires

“…Fort he alkene, [ 3]cumulene, and [5]cumulene,t he energetically preferred conformations have two terminal thioanisole rings that are not coplanar (see Section S2.2 for details), in agreement with crystallographic studies. [15,21] Theconformations of relaxed molecules embedded in Au-Aujunctions are shown in Figure 4a.T he frontier molecular orbitals ( Figure S3) show that the HOMO of the alkene as well as the HOMO and LUMO of [3]cumulene and [5]cumulene form extended p-conjugated transport paths through the whole molecules.I nc ontrast, the molecular orbitals of the allene and [4]cumulene are formed from p z and p x orbitals and follow chiral paths through the molecules, leading to terminal thioanisole rings that are orthogonal to each other, and the absence of an extended p-system in the HOMO and LUMO.Asshown in Figure 4b,these differences between the even-and odd-numbered cumulenes are reflected in their transmission functions.O ver ar ange of E F within the HOMO-LUMO gap,i ndicated by the shaded region in Figure 4b,t he conductances of the allene and the [4]cumulene are expected to be lower than those of the other three molecules.M ore interestingly,t he conductances of the [3]cumulene and the [5]cumulene are predicted to be about the same,d espite the substantial change in length. This prediction is consistent with previous computational studies of charge transport through cumulene molecular wires.…”

“…[15,21] Theconformations of relaxed molecules embedded in Au-Aujunctions are shown in Figure 4a.T he frontier molecular orbitals ( Figure S3) show that the HOMO of the alkene as well as the HOMO and LUMO of [3]cumulene and [5]cumulene form extended p-conjugated transport paths through the whole molecules.I nc ontrast, the molecular orbitals of the allene and [4]cumulene are formed from p z and p x orbitals and follow chiral paths through the molecules, leading to terminal thioanisole rings that are orthogonal to each other, and the absence of an extended p-system in the HOMO and LUMO.Asshown in Figure 4b,these differences between the even-and odd-numbered cumulenes are reflected in their transmission functions.O ver ar ange of E F within the HOMO-LUMO gap,i ndicated by the shaded region in Figure 4b,t he conductances of the allene and the [4]cumulene are expected to be lower than those of the other three molecules.M ore interestingly,t he conductances of the [3]cumulene and the [5]cumulene are predicted to be about the same,d espite the substantial change in length. [4,9] Thel ocal density of states (LDOS) of the alkene and allene (Figure 4c)r eveals ac lear transport path for the alkene (magenta surface), while there is no such LDOS path on the allene molecule.T he alkene is predicted to have as lightly lower conductance than both the [3]-and [5]cumulenes because of the larger angle between the two thioanisole rings [3]cumulene, and [5]cumulene attached to two gold leads, where the gray,white, and pale-yellow balls represent carbon, hydrogen, and sulfur,respectively.The yellow balls at both ends represent gold leads. [4,9] Thel ocal density of states (LDOS) of the alkene and allene (Figure 4c)r eveals ac lear transport path for the alkene (magenta surface), while there is no such LDOS path on the allene molecule.T he alkene is predicted to have as lightly lower conductance than both the [3]-and [5]cumulenes because of the larger angle between the two thioanisole rings [3]cumulene, and [5]cumulene attached to two gold leads, where the gray,white, and pale-yellow balls represent carbon, hydrogen, and sulfur,respectively.The yellow balls at both ends represen...…”

“…[5][6][7] Herein, we report an experimental and computational investigation of the length dependence of charge transport through these linear carbon chains.Recently,near length-independent conductances were reported for as et of cyanine dyes,w hich constitute aclass of cationic p-systems with BLA % 0. [5,6] Cumulenes are said to have a" metallic" electronic structure, [4][5][6][7][9][10][11] because an infinitely long cumulene would have ab and structure characteristic of am etal, with ap artially occupied band derived from the p and p*orbitals.Incontrast polyynes have a p-p*g ap that persists even in long chains, and an infinite polyyne is expected to be asemiconductor. Cumulenes and polyynes have fascinated chemists for many years as models for carbyne,t he infinite 1D form of carbon.…”

How to Bend a Cumulene

“…These linear molecules have several interesting properties. For example, they can be used as molecular wires [31][32][33][34] as their conductivity is significantly better than the other possible form of linear carbon chains,p olyynes. [32,35,36] Strong s donors as end-capping groups of the cumulene chain give their radical speciesaremarkable stability, [26,32,[37][38][39][40] with someo ft hese radicals stable even to air.…”

“…For example, they can be used as molecular wires [31][32][33][34] as their conductivity is significantly better than the other possible form of linear carbon chains,p olyynes. [32,35,36] Strong s donors as end-capping groups of the cumulene chain give their radical speciesaremarkable stability, [26,32,[37][38][39][40] with someo ft hese radicals stable even to air. [39,40] Cumulenes have been known for around100 years, [41] however, [3]cumulenes that have strong s donors as terminal groups, such as N-heterocyclic or cyclic (alkyl)(amino) carbenes (NHCs or CAACs, respectively), have only recently been studied.…”