Thanks to its valency and the possibility of forming hybrid orbitals, carbon can give rise to many different allotropic forms such as diamond, graphene, carbon nanotubes, fullerenes and many more, each one displaying peculiar physical and chemical properties that can be exploited in many aspects of technological development.

Sp-hybridized allotropes such as carbyne, i.e. infinite linear carbon chains, are particularly interesting since they give rise to one-dimensional systems where electronic correlations and nuclear quantum effects become extremely relevant due to low atomic mass and dimensionality.

## Carbyne

Carbyne, an infinite-length straight chain of carbon atoms, is supposed to undergo a second order phase transition from the metallic bond-symmetric cumulene (=C= C=)_{∞} toward the distorted insulating polyyne chain (−C≡C−)_{∞} displaying bond-length alternation. However, recent synthesis of ultra long carbon chains (∼6000 atoms, [Nat. Mater., 2016, 15, 634]) did not show any phase transition and detected only the polyyne phase, in agreement with previous experiments on capped finite carbon chains.

By performing first-principles calculations, I have show that quantum-anharmonicity reduces the energy gain of the polyyne phase with respect to the cumulene one by 71%. The magnitude of the bond-length alternation increases by increasing temperature, in stark contrast with a second order phase transition, confining the cumulene-to-polyyne transition to extremely high and unphysical temperatures. Finally, I have predicted that a high temperature insulator-to-metal transition occurs in the polyyne phase confined in insulating nanotubes with sufficiently large dielectric constant due to a giant quantum-anharmonic bandgap renormalization.

*References*:

- D. Romanin, L. Monacelli, R. Bianco, I. Errea, F. Mauri and M. Calandra,
*Dominant Role of Quantum Anharmonicity in the Stability and Optical Properties of Infinite Linear Acetylenic Carbon Chains*J. Phys. Chem. Lett.**12**, 10339–10345 (2021) .

## Cyclo[*4n+2*]carbon

Cyclo[4n + 2]carbons are sp-bonded carbon rings in which Hückel rule predicts a fully simmetric structure that is, however, in competition with the second order Jahn-Teller (Peierls) distortion. This picture, however, neglects the crucial role played by nuclear quantum effects. Indeed, since cyclo[*4n+2*]carbon can be seen as a curved linear carbon chain closed on itself (especially in the limit of large n, when the relative curvature between
adjacent C atoms tends to zero), anharmonic effects are expected to be extremely relevant to the stability and optical response of cyclo[4n + 2]carbon as I have shown in the case of carbyne.

I have investigated the magnitude of nuclear quantum effects on the stability, vibrational and optical properties of cyclo[*4n+2*]carbons (n =1,2,3,4) in vacuum. The quantum structural minimization reduces the energy separation between the different isomers and determines that the most stable C_{14}
isomer is the cumulenic one, setting the transition from the acetilitic to the cumulenic form at n = 3 (at odd with the classical structural optimization setting the transition at n = 2). Moreover, the quantum anharmonic effects generate very large frequency shifts, linewidth broadenings and satellites in the phonon spectral weight hindering any possible interpretation based on the non-interacting harmonic spectrum. The optical absorbance is completely reshaped by quantum anharmonic vibrations and, finally, I have also determined the crystal structure of C18 on a NaCl bilayer to be a buckled
polyynic phase in agreement with recent experimental findings.

*References*:

- D. Romanin and M. Calandra,
*Giant quantum anharmonic effects on the stability, vibrational and optical properties of cyclo[4n+2]carbon*, Carbon Trends (2022) ;