The existence of Dirac cones in the band structure of two-dimensional materials accompanied by unprecedented electronic properties is considered to be a unique feature of graphene related to its hexagonal symmetry. Here, we present other two-dimensional carbon materials, graphynes, that also possess Dirac cones according to first-principles electronic structure calculations. One of these materials, 6,6,12-graphyne, does not have hexagonal symmetry and features two self-doped nonequivalent distorted Dirac cones suggesting electronic properties even more amazing than that of graphene.

Systematic evaluation of the accuracy of exchange-correlation functionals is essential to guide scientists in their choice of an optimal method for a given problem when using density functional theory. In this work, accuracy of one Generalized Gradient Approximation (GGA) functional, three meta-GGA functionals, one Nonseparable Gradient Approximation (NGA) functional, one meta-NGA, and three hybrid GGA functionals was evaluated for calculations of the closest interatomic distances, cohesive energies, and bulk moduli of all 3d, 4d, and 5d bulk transition metals that have face centered cubic (fcc), hexagonal closed packed (hcp), or body centered cubic (bcc) structures (a total of 27 cases). Our results show that including the extra elements of kinetic energy density and Hartree–Fock exchange energy density into gradient approximation density functionals does not usually improve them. Nevertheless, the accuracies of the Tao–Perdew–Staroverov–Scuseria (TPSS) and M06-L meta-GGAs and the MN12-L meta-NGA approach the accuracy of the Perdew−Burke−Ernzerhof (PBE) GGA, so usage of these functionals may be advisable for systems containing both solid-state transition metals and molecular species. The N12 NGA functional is also shown to be almost as accurate as PBE for bulk transition metals, and thus it could be a good choice for studies of catalysis given its proven good performance for molecular species.

Metal nanoparticles (NPs) are ubiquitous in many fields, from nanotechnology to heterogeneous catalysis, with properties differing from those of single-crystal surfaces and bulks. A key aspect is the size-dependent evolution of NP properties toward the bulk limit, including the adoption of different NP shapes, which may bias the NP stability based on the NP size. Herein, the stability of different Pd_n NPs (n = 10–1504 atoms) considering a myriad of shapes is investigated by first-principles energy optimisation, leading to the determination that icosahedron shapes are the most stable up to a size of ca. 4 nm. In NPs larger than that size, truncated octahedron shapes become more stable, yet a presence of larger {001} facets than the Wulff construction is forecasted due to their increased stability, compared with (001) single-crystal surfaces, and the lower stability of {111} facets, compared with (111) single-crystal surfaces. The NP cohesive energy breakdown in terms of coordination numbers is found to be an excellent quantitative tool of the stability assessment, with mean absolute errors of solely 0.01 eV·atom⁻¹, while a geometry breakdown allows only for a qualitative stability screening.

The geometric and electronic structure of catalytically relevant molybdenum carbide phases (cubic δ-MoC, hexagonal α-MoC, and orthorhombic β-Mo₂C) and their low Miller-index surfaces have been investigated by means of periodic density functional theory (DFT) based calculations with the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional. Comparison to available experimental data indicates that this functional is particularly well suited to study these materials. The calculations reveal that β-Mo₂C has a stronger metallic character than the other two polymorphs, both β-Mo₂C and δ-MoC have a large ionic contribution, and δ- and α-MoC exhibit the strongest covalent character. Among the various surfaces explored, the calculations reveal the high stability of the δ-MoC(001) nonpolar surface, Mo- and C-terminated (001) polar surfaces of α-MoC, and the nonpolar (011) surface of β-Mo₂C. A substantially low work function of only 3.4 eV is predicted for β-Mo₂C(011), suggesting that this system is particularly well suited for (electro)catalytic processes where surface → adsorbate electron transfer is essential. The overall implications for heterogeneously catalysed reactions by these molybdenum carbide nanoparticles are also discussed.

The adsorption and activation of a CO₂molecule on cubic δ-MoC(001) and orthorhombic β-Mo₂C(001) surfaces have been investigated by means of periodic density functional theory based calculations using the Perdew–Burke–Ernzerhof exchange–correlation functional and explicitly accounting for (or neglecting) the dispersive force term description as proposed by Grimme.