Strain, Anharmonicity and Finite-Size Effects on the Vibrational Properties of Linear Carbon Chains
Linear carbon chains (LCCs) are the ultimate 1D molecular system and they show unique mechanical, optical and electronic properties that can be tuned by altering the number of carbon atoms, strain, encapsulation, and other external parameters. In this work, we probe the effects of quantum anharmonicity, strain and finite size on the structural and vibrational properties of these chains, using high$-$level density functional theory (DFT) calculations. We find strong anharmonicity effects for infinite chains, leading to ground$-$state nuclear wavefunctions that are barely localized at each of the dimerized geometries, i.e. strong tunneling occurs between the two minima of the potential energy surface. This effect is enhanced for compressive strains. In addition, vibrational C$-$band frequencies deviate substantially from experimental measurements in long chains encapsulated in carbon nanotubes. On the other hand, calculations for finite chains suggest that quantum anharmonicity effects are strongly suppressed in finite system, even in the extrapolation to the infinite case. For finite systems, vibrational C$-$band frequencies agree well with experimental values at zero pressure. However, these frequencies increase under compressive strain, in contradiction with recent results. This contradiction is not resolved by adding explicitly the encapsulating carbon nanotubes to our calculations. Our results indicate that LCCs embody an intriguing 1D system in which the behavior of very large finite systems do not reproduce or converge to the behavior of truly infinite ones.