New insights into the 1D carbon chain through the RPA

Sampling the reciprocal Coulomb potential in finite anisotropic cells

We present a robust strategy to numerically sample the Coulomb potential in reciprocal space for periodic Born-von Karman cells of general shape. Our approach tackles two common issues of plane-wave based implementations of Coulomb integrals under periodic boundary conditions: the treatment of the singularity at the Brillouin-zone center and discretization errors, which can cause severe convergence problems in anisotropic cells, necessary for the calculation of low-dimensional systems. We apply our strategy to the Hartree-Fock and coupled cluster (CC) theories and discuss the consequences of different sampling strategies on different theories. We show that sampling the Coulomb potential via the widely used probe-charge Ewald method is unsuitable for CC calculations in anisotropic cells. To demonstrate the applicability of our developed approach, we study two representative, low-dimensional use cases: the infinite carbon chain, for which we report the first periodic CCSD(T) potential energy surface, and a surface slab of lithium hydride, for which we demonstrate the impact of different sampling strategies for calculating surface energies. We find that our Coulomb sampling strategy serves as a vital solution, addressing the critical need for improved accuracy in plane-wave based CC calculations for low-dimensional systems.

One-dimensional carbon chains encapsulated in hollandite

One-dimensional carbon chains are highly reactive allotropes that are stabilized inside the protective environment of carbon nanotubes. Here we show that carbon chains can be encapsulated in metal oxides containing open structural channels, exemplified by hollandite α-MnO2. The α-MnO2 channels stabilize cumulene chains due to their structural commensurability, whereas the triple bonds in polyyne chains exhibit excessive steric repulsion to the oxide ions bordering the channel. Cumulene exhibits an interaction energy of only 0.065 eV per carbon atom, obtained by first-principles calculations, which is significantly more favorable than for encapsulation in a similarly sized carbon nanotube. Encapsulation of carbon chains is associated with lateral expansion of the α-MnO2 channel and polarization of the manganese and oxygen charge densities adjacent to the chains. Accordingly, the interaction energy is governed by a balance between van der Waals attraction and steric repulsion between the materials.

On-Surface Synthesis of sp-Carbon Nanostructures

The on-surface synthesis of carbon nanostructures has attracted tremendous attention owing to their unique properties and numerous applications in various fields. With the extensive development of scanning tunneling microscope (STM) and noncontact atomic force microscope (nc-AFM), the on-surface fabricated nanostructures so far can be characterized on atomic and even single-bond level. Therefore, various novel low-dimensional carbon nanostructures, challenging to traditional solution chemistry, have been widely studied on surfaces, such as polycyclic aromatic hydrocarbons, graphene nanoribbons, nanoporous graphene, and graphyne/graphdiyne-like nanostructures. In particular, nanostructures containing sp-hybridized carbons are of great advantage for their structural linearity and small steric demands as well as intriguing electronic and mechanical properties. Herein, the recent developments of low-dimensional sp-carbon nanostructures fabricated on surfaces will be summarized and discussed.

Dominant Role of Quantum Anharmonicity in the Stability and Optical Properties of Infinite Linear Acetylenic Carbon Chains

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. Here, by performing first-principles calculations, we 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, we predict 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.