Using first-principles calculations based on density functional theory, the elastic constants and some of the related physical quantities, such as the bulk, shear, and Young’s moduli, Poisson’s ratio, anisotropic factor, acoustic velocity, minimum thermal conductivity, and Debye temperature, are reported in this paper for the hexagonal intermetallic compound Ti ${}_3$ Al. The obtained results are well consistent with the available experimental and theoretical data. The effect of pressure on all studied parameters was investigated. By the mechanical stability criteria under isotropic pressure, it is predicted that the compound is mechanically unstable at pressures above 71.4 GPa. Its ductility, anisotropy, and Debye temperature are enhanced with pressure.

The resource utilization of CO${}_2$ is one of the essential avenues to realize the goal of “double carbon”. The metal–organic framework (MOF) has shown promising applications in CO${}_2$ catalytic reduction reactions due to its sufficient pore structure, abundant active sites and functionalizability. In this paper, we investigated the electrocatalytic carbon dioxide reduction reactions of single-atom catalysts created by MOF two-dimensional coordination network materials constructed from transition metal-tetrahydroxybenzoquinone using density function theory calculations. The results indicate that for 10 transition metals, TM-THQ single levels ranging from Sc to Zn, the metal atom binding energy to the THQ is large enough to allow the metal atoms to be stably dispersed in the THQ monolayer. The Ni-THQ catalyst does not compete with the HER reaction in an electrocatalytic CO${}_2$ reduction. The primary product of reduction for Sc-THQ is HCOOH, but the major product of Co-THQ is HCHO. The main product of Cu-THQ is CO, while the main product of six catalysts, Ti, V, Cr, Mn, Fe, and Zn, is CH${}_4$. The limit potential and overpotential of Ti-THQ are the highest, 1.043 V and 1.212 V, respectively. The overpotentials of the other monolayer catalysts ranged from 0.172 to 0.952 V, and they were all relatively low. Therefore, we forecast that the TM-HQ monolayer will show powerful activity in electrocatalytic carbon dioxide reduction, making it a prospective electrocatalyst for carbon dioxide reduction.

Electrocatalytic reduction of CO₂ to valuable fuels and chemicals can not only alleviate the energy crisis but also improve the atmospheric environment. The key is to develop electrocatalysts that are extremely stable, efficient, selective, and reasonably priced. In this study, spin-polarized density function theory (DFT) calculations were used to comprehensively examine the catalytic efficacy of transition metal-hexaaminobenzene (TM-HAB) monolayers as single-atom catalysts for the electroreduction of CO₂. In the modified two-dimensional TM-HAB monolayer, our findings demonstrate that the binding of individual metal atoms to HAB can be strong enough for the atoms to be evenly disseminated and immobilized. In light of the conflicting hydrogen evolution processes, TM-HAB effectively inhibits hydrogen evolution. CH₄ dominates the reduction byproducts of Sc, Ti, V, Cr, and Cu. HCOOH makes up the majority of Zn’s reduction products. Co’s primary reduction products are CH₃OH and CH₄, whereas Mn and Fe’s primary reduction products are HCHO, CH₃OH, and CH₄. Among these, the Ti-HAB reduction products have a 1.14 eV limiting potential and a 1.31 V overpotential. The other monolayers have relatively low overpotentials between 0.01 V and 0.7 V; therefore, we predict that TM-HAB monolayers will exhibit strong catalytic activity in the electrocatalytic reduction of CO₂, making them promising electrocatalysts for CO₂ reduction.

Carbon dioxide reduction technology can solve the shortage of resources and climate issues like “warming of the planet”. Metal–organic frameworks (MOFs) contain well-defined active sites, a huge specific surface, and a robust porous structure, making them a good candidate for use in CO₂ electrocatalytic reduction. Using the principles of spin-polarization density functional theory, the two-dimensional MOF constructed from transition metal–hexaiminotriphenylene was calculated to reduce CO₂ electrocatalytically. The results show that for ten transition metal (TM-HITP) two-dimensional network structures spanning Sc through Zn, the formation energies E_f are all negative, and they can theoretically be synthesised experimentally, and the metal atoms can be disseminated in the HITP framework steadily because their binding energies to HITP are highly sufficient. Considering the competition with the HER, all catalysts showed CO₂RR selectivity except Co-HITP. Co-HITP catalysts required pH >7.22 to show CO₂RR selectivity. The main products and overpotentials of both Fe and Co catalysts were in agreement with the available literature values, indicating that the calculations were reliable. HCOOH is the primary product for Sc, Ni, and Cu. The principal product of Ti and V is CH₄. CH₃OH is the primary product for Cr, Fe, and Co. The product selectivity of Mn was poor and three products, CH₄, HCHO and HCOOH, were obtained simultaneously at the same limiting potential. The limiting potentials of these ten catalysts for electrocatalytic CO₂ reduction ranged from 0.296 to 0.738 volts and the overpotentials between 0.027 V and 0.754 V, all of which were rather little. Consequently, we forecast that the two-dimensional MOFs constructed with transition metals with hexaiminotriphenylene are potential electrocatalysts for CO₂ reduction because they demonstrate excellent catalytic activity in the electrocatalytic reduction of CO₂.

The complete set of independent second- and third-order elastic constants of rare-earth hexaborides LaB ${}_6$ and CeB ${}_6$ are determined by the combination method of first-principles calculations and homogeneous deformation theory. The ground-state lattice parameters, second-order elastic constants, and bulk modulus are in reasonable agreement with the available experimental data. The third-order elastic constant of longitudinal mode $C_{111}$ has a larger absolute value than other shear modes, showing the contribution to lattice vibrations from longitudinal modes to be greater. The pressure derivatives of the second-order elastic constants related to the third-order elastic constants are calculated to be positive for the two hexaborides, which are consistent with those of their polycrystalline bulk modulus and shear modulus. Furthermore, the effect of pressure on the structural stability, mechanical property, and elastic anisotropy of the two hexaborides are investigated, showing a reduction in mechanical stability and an increase in ductility and anisotropy with increasing pressure.

Metal–organic frameworks have demonstrated great capacity in catalytic CO₂ reduction due to their versatile pore structures, diverse active sites, and functionalization capabilities. In this study, a novel electrocatalytic framework for CO₂ reduction was designed and implemented using 2D coordination network-type transition metal–hexahydroxytricyclic quinazoline (TM–HHTQ) materials. Density functional theory calculations were carried out to examine the binding energies between the HHTQ substrate and 10 single TM atoms, ranging from Sc to Zn, which revealed a stable distribution of metal atoms on the HHTQ substrate. The majority of the catalysts exhibited high selectivity for CO₂ reduction, except for the Mn–HHTQ catalysts, which only exhibited selectivity at pH values above 4.183. Specifically, Ti and Cr primarily produced HCOOH, with corresponding 0.606 V and 0.236 V overpotentials. Vanadium produced CH₄ as the main product with an overpotential of 0.675 V, while Fe formed HCHO with an overpotential of 0.342 V. Therefore, V, Cr, Fe, and Ti exhibit promising potential as electrocatalysts for carbon dioxide reduction due to their favorable product selectivity and low overpotential. Cu mainly produces CH₃OH as the primary product, with an overpotential of 0.96 V. Zn primarily produces CO with a relatively high overpotential of 1.046 V. In contrast, catalysts such as Sc, Mn, Ni, and Co, among others, produce multiple products simultaneously at the same rate-limiting step and potential threshold.