Electronic structure of schwarzite

The smallest Schwarzite carbon with only heptagonal carbon rings

Carbon materials with full sp2-hybridized buckling is a major challenge pervading fundamental nanoscience and nanotechnology research. Carbon atoms that are sp2 hybridized prefer to form hexagonal rings, such as in carbon nanotubes and graphene, which are low-dimensional materials. The incorporation of heptagonal, octagonal, and/or larger rings into a hexagonal sp2 carbon meshwork has been identified as a strategy for assembling three-dimensional (3D) sp2 carbon crystals, and one of the typical representatives are Schwarzite carbons, which possess a negative surface Gaussian curvature as well as unique physical properties. Herein, a 3D Schwarzite carbon consisting of only sp2-buckled heptagonal carbon rings, which is referred to as Hepta-carbon, is proposed based on first-principles calculations. Hepta-carbon is mechanically and thermodynamically stable, and energetically more favourable than experimental graphdiyne, fullerene C20 and most Schwarzite carbons under ambient conditions. Molecular dynamics simulations indicate that Hepta-carbon exhibits high-temperature thermostability up to 1500 K. Band structure and mechanical property simulations indicate that Hepta-carbon is a semi-metallic material with electron conduction and exhibits impressive mechanical properties such as high strength with quasi-isotropy, high incompressibility similar to diamonds, elastic deformation behaviour under uniaxial stress, and high ductility. Hepta-carbon presents a porous network with a low mass density of 1.84 g cm-3 and connected channels with diameters of 3.3-6.1 Å. Theoretical simulations of gas adsorption energy demonstrate that Hepta-carbon can effectively adsorb and stabilize greenhouse gases, including N2O, CO2, CH4, and SF6.

Schwarz P-surface via isolated sp2 carbon heptagons: Design and properties

Described are the first two molecular designs of the triply periodic Schwarz P surface using merely the Schläfli t{3,7} pattern of sp² -hybridized carbon atoms. Each atom is exactly part of one heptagon and two hexagon rings so that two heptagons do not share the same edge or vertex. Such pattern, called hyperbolic soccer ball obeys the isolated-heptagon rule with the minimum possible number of hexagons between heptagons similar to the isolation of pentagons from hexagons in the C60 fullerene. Both of the designed P surfaces are unbalanced, that is, they have two unequal sides, and belong to space groups P432 of the cubic system, and P4/ncc of the tetragonal system, respectively. Unit cells have a multiple of 24 heptagons similar to the only one previously known in literature Schwarzite with the hyperbolic soccer ball pattern-the D surface of Vanderbilt and Tersoff. The geometry of the periodic structures and unit cell parameters were fully optimized by DFT calculations using CASTEP software with PBE and PBESOL functionals under generalized gradient approximation. The effect of P and D surface dilution by hexagons on the calculated density, elastic and electronic properties is discussed.

Gaussian Curvature Effects on Graphene Quantum Dots

In the last few years, much attention has been paid to the exotic properties that graphene nanostructures exhibit, especially those emerging upon deforming the material. Here we present a study of the mechanical and electronic properties of bent hexagonal graphene quantum dots employing density functional theory. We explore three different kinds of surfaces with Gaussian curvature exhibiting different shapes-spherical, cylindrical, and one-sheet hyperboloid-used to bend the material, and several boundary conditions regarding what atoms are forced to lay on the chosen surface. In each case, we study the curvature energy and two quantum regeneration times (classic and revival) for different values of the curvature radius. A strong correlation between Gaussian curvature and these regeneration times is found, and a special divergence is observed for the revival time for the hyperboloid case, probably related to the pseudo-magnetic field generated by this curvature being capable of causing a phase transition.

Flat corannulene: when a transition state becomes a stable molecule

Flat corannulene has been considered so far only as a transition state of the bowl-to-bowl inversion process. This study was driven by the prediction that substituents with strong steric repulsion could destabilize the bowl-shaped conformation of this molecule to such an extent that the highly unstable planar geometry would become an isolable molecule. To examine the substituents' effect on the corannulene bowl depth, optimized structures for the highly-congested decakis(t-butylsulfido)corannulene were calculated. The computations, performed with both the M06-2X/def2-TZVP and the B3LYP/def2-TZVP methods (the latter with and without Grimme's D3 dispersion correction), predict that this molecule can achieve two minimum structures: a flat carbon framework and a bowl-shaped structure, which are very close in energy. This rather unusual compound was easily synthesized from decachlorocorannulene under mild reaction conditions, and X-ray crystallographic studies gave similar results to the theoretical predictions. This compound crystallized in two different polymorphs, one exhibiting a completely flat corannulene core and the other having a bowl-shaped conformation.

The first flat metal-free corannulene derivative was predicted by computations and achieved by synthesis.

An Isosteric Triaza Analogue of a Polycyclic Aromatic Hydrocarbon Monkey Saddle

Since a few years, the interest in negatively-curved fused polycyclic aromatic hydrocarbons (PAHs) has significantly increased. Recently, the first chiral negatively-curved PAH with the topology of a monkey saddle was introduced. Herein the synthesis of its triaza congener is reported. The influence of this CH↔N exchange on photophysical and electrochemical properties is studied as well as the isomerization process of the enantiomers. The aza analogue has a significantly higher inversion barrier, which makes it easier to handle at room temperature. All experimental results are underpinned by theoretical DFT calculations.

On the structural stability and optical properties of germanium-based schwarzites: a density functional theory investigation

Since graphene was synthesized the interest in building new 2D and 3D structures based on carbon allotropes has been growing every day. One of these 3D structures is know as carbon schwarzites. Schwarzites consist of carbon nanostructures possessing the shape of Triply-Periodic Minimal Surfaces (TPMS), which is characterized by a negative Gaussian curvature introduced by the presence of carbon rings with more than six atoms. Some examples of schwarzite families include: primitive (P), gyroid (G) and diamond (D). Previous studies considering different element species of schwarzites have investigated the mechanical, electrical and thermal properties. In this work, we investigated the stability of germanium (Ge) schwarzites using density functional theory with the GGA exchange-correlation functional. We chose one structure of each family (P8bal), (G688) and (D688). It was observed that regions usually flat in carbon schwarzites acquire buckled configurations as previously observed on silicene and germanene monolayers. The investigated structures presented a semiconducting bandgap ranging from 0.13 to 0.27 eV. We also performed calculations of optical properties within the linear regime, where it was shown that Ge schwarzite structures absorb light from infrared to ultra-violet frequencies. Therefore, our results open new perspectives of materials that can be used in optoelectronics device applications.

Double Negatively Curved C70 Growth through a Heptagon-Involving Pathway

All previously reported C₇₀ isomers have positive curvature and contain 12 pentagons in addition to hexagons. Herein, we report a new C₇₀ species with two negatively curved heptagon moieties and 14 pentagons. This unconventional heptafullerene[70] containing two symmetric heptagons, referred to as dihept-C₇₀ , grows in the carbon arc by a theoretically supported pathway in which the carbon cluster of a previously reported C₆₆ species undergoes successive C₂ insertion via a known heptafullerene[68] intermediate with low energy barriers. As identified by X-ray crystallography, the occurrence of heptagons facilitates a reduction in the angle of the π-orbital axis vector in the fused pentagons to stabilize dihept-C₇₀ . Chlorination at the intersection of a heptagon and two adjacent pentagons can greatly enlarge the HOMO-LUMO gap, which makes dihept-C₇₀ Cl₆ isolable by chromatography. The synthesis of dihept-C₇₀ Cl₆ offers precious clues with respect to the fullerene formation mechanism in the carbon-clustering process.

Low-energy 3D sp2 carbons with versatile properties beyond graphite and graphene

Low-energy sp²-carbons with metallicity, graphene-like Dirac cone, rubber-like ultra-stretchability, and negative Poisson's ratio are theoretically designed from graphene nanoribbons.

BN-schwarzite: novel boron nitride spongy crystals

Novel 3-D BN crystals with a negative curvature, intrinsic porosity and a large specific surface area are proposed for the first time by first-principles study, suggesting that the BN crystals hold great promise in the fields of energy storage, molecular sieving, and environmental remediation.

Designing rigid carbon foams

We use ab initio density functional calculations to study the stability, elastic properties and electronic structure of sp(2) carbon minimal surfaces with negative Gaussian curvature, called schwarzites. We focus on two systems with cubic unit cells containing 152 and 200 carbon atoms, which are metallic and very rigid. The porous schwarzite structure allows for efficient and reversible doping by electron donors and acceptors, making it a promising candidate for the next generation of alkali ion batteries. We identify schwarzite structures that act as arrays of interconnected spin quantum dots or become magnetic when doped. We introduce two interpenetrating schwarzite structures that may find their use as the ultimate super-capacitor.