What’s linear sp-Carbon

Carbon can arrange its valence electrons in different ways to produce a wide variety of molecules and structures. This is clear in organic chemistry where the three possible sp3, sp2, and sp1 hybridizations lead to alkanes (e.g methane), alkenes (e.g. ethylene) and alkynes (e.g. acetylene) molecules, respectively. The different geometry of the hybridized orbitals results in linear (1-dimensional), planar (2-dimensional) or tetrahedral (3-dimensional) spatial organization. Moving to solid state systems, carbon shows only two allotropes: graphite and diamond corresponding to sp2 and sp3 hybridization. Graphite and diamond are known since the ancient time, but it was in 1796 that S. Tennant experimentally demonstrated that diamond and graphite were made of the same substance. The search of a third crystalline form based on sp1 hybridization (linear carbon or carbyne) has attracted the attention of scientist for the last two centuries. The discovery of this new carbon was claimed in mineral samples found in a meteor crater, nevertheless the existence of such a new pure carbon solid has still today to be confirmed. In the last 30 years, the discovery of carbon nanostructures such as fullerenes, nanotubes and graphene have raised a renewed interest in nanoscale carbon systems with linear structures.

The ideal model of carbon atomic wire is an infinite chain of carbon atoms. In this case there are only two ways for carbon atoms to arrange in the wire: a sequence of double bonds (cumulene) and single and triple alternated bonds (polyyne). Cumulenes have one atom per unit cell and each contributes with two electrons, one for each pi-orbital. This results in a half-filled conduction band and the system is a 1-dimensional metal. On the contrary, polyynes have two atoms per unit cell thus filling completely the valence band and leaving an empty conduction band. As a results polyyne is a 1-dimensional semiconductor. The same approach applies also for the vibrational properties (i.e. phonons). Cumulene is an example of a 1-dimensional homo-atomic chain usually used to describe the vibrational properties of more complex systems while polyyne is a homo-atomic chain with different bond lengths (and strength) that is the analogue of a hetero-atomic chain. Simple textbook calculations show that cumulene has only acoustic phonons while polyynes have acoustic and optic phonon branches.

The distinction of  wires in the two discussed configurations, alternated and equalized chains, strictly holds only for ideal infinite systems, while for real finite wires the distinction between cumulenic and polyynic configuration is somehow relaxed since in both cases approaching the ends the bond lengths can change due to a different termination. The termination has usually a different bond length and this affects the entire wire structure so that the shorter the wire the larger is the terminating effect. A distribution of bond lengths along the wire is typically found when simulating the structure of finite and terminated wires. In this case the bond length alternation (BLA, the length difference between two adjacent bonds) is a more correct parameter to describe the wire structure. The ideal cumulene has BLA=0 while simulations of the structure of real and finite cumulene-like systems show that the BLA is small but not zero. In the same way the energy gap and the optical and transport properties depend not only on the type of structure but also on chain length (i.e. the number of carbon atoms) and type of end groups. The electronic bands show a gap, which depends on the BLA value. Although the electronic properties have been theoretically addressed by many authors, the experimental evidences are scarce. Only a few works reported the study of electronic core levels and the valence band properties by electron spectroscopy techniques.