Accurate density functional theory prediction of low-dimensional yttrium nitride: From 2D hexagonal and square monolayers to 1D zizag single walled nanotubes

Through this contribution, we aim to highlight the structural stability of low dimensional YN structures ranging from the 3D bulk to the 2D square and hexagonal monolayers and their corresponding 1D zigzag single walled nanotubes. For all arrangements, geometry optimization is achieved at the DFT/B3LYP level of theory using a Gaussian basis set. Then, the coupled perturbed Kohn-Sham and Hartree-Fock (CPKS/HF) computational approach is used to simulate Raman and IR spectrum. Rolling, cohesive and relaxation energies, electronic and vibrational contributions to the polarizability and equilibrium lattice parameters are also reported. Insights into their structural stability are provided by combining optimized parameters and vibrational phonon spectra. For the optimized 3D bulks, 2D monolayers and 1D square nanotubes, no imaginary frequency has been recorded in their vibrational spectra which reveals a dynamic stability. Likewise, imaginary frequencies appeared only for relatively large YN (n,0) single walled hexagonal nanotubes (n > 6) indicating that the optimized structures are not a real global minimum and implying a dynamic instability. A scaning mode procedure along the largest imaginary vibrational mode has been adopted to obtain the equilibrium geometry of (22,0) YN hexagonal nanotube. Therefore, it must be emphasized that the obtained potential energy surface presents two minima between a saddle point. These minima corresponds to a stable structures slightly distorted compared to the initial one. The absence of imaginary phonon frequencies in the Raman and IR spectra of the optimized (22,0) YN hexagonal nanotube confirms its structural stability.

Stability and electronic properties of gallenene

Two-dimensional metals offer intriguing possibilities to explore the metallic and other related properties in systems with reduced dimensionality. Here, following recent experimental reports of synthesis of two-dimensional metallic gallium (gallenene) on insulating substrates, we conduct a computational search of gallenene structures using the Particle Swarm Optimization algorithm, and identify stable low energy structures. Our calculations of the critical temperature for conventional superconductivity yield values of ∼7 K for gallenene. We also emulate the presence of the substrate by introducing the external confining potential and test its effect on the structures with unstable phonons.

Periodicity of Two-Dimensional Bonding of Main Group Elements

In the periodic table the position of each atom follows the 'aufbau' principle of the individual electron shells. The resulting intrinsic periodicity of atomic properties determines the overall behavior of atoms in two-dimensional (2D) bonding and structure formation. Insight into the type and strength of bonding is the key in the discovery of innovative 2D materials. The primary features of 2D bonding and the ensuing monolayer structures of the main-group II-VI elements result from the number of valence electrons and the change of atom size, which determine the type of hybridization. The results reveal the tight connection between strength of bonding and bond length in 2D networks. The predictive power of the periodic table reveals general rules of bonding, the bonding-structure relationship, and allows an assessment of published data of 2D materials.

Bonding, structure, and mechanical stability of 2D materials: the predictive power of the periodic table

This tutorial review describes the ongoing effort to convert main-group elements of the periodic table and their combinations into stable 2D materials, which is sometimes called modern 'alchemy'. Theory is successfully approaching this goal, whereas experimental verification is lagging far behind in the synergistic interplay between theory and experiment. The data collected here gives a clear picture of the bonding, structure, and mechanical performance of the main-group elements and their binary compounds. This ranges from group II elements, with two valence electrons, to group VI elements with six valence electrons, which form not only 1D structures but also, owing to their variable oxidation states, low-symmetry 2D networks. Outside of these main groups reviewed here, predominantly ionic bonding may be observed, for example in group II-VII compounds. Besides high-symmetry graphene with its shortest and strongest bonds and outstanding mechanical properties, low-symmetry 2D structures such as various borophene and tellurene phases with intriguing properties are receiving increasing attention. The comprehensive discussion of data also includes bonding and structure of few-layer assemblies, because the electronic properties, e.g., the band gap, of these heterostructures vary with interlayer layer separation and interaction energy. The available data allows the identification of general relationships between bonding, structure, and mechanical stability. This enables the extraction of periodic trends and fundamental rules governing the 2D world, which help to clear up deviating results and to estimate unknown properties. For example, the observed change of the bond length by a factor of two alters the cohesive energy by a factor of four and the extremely sensitive Young's modulus and ultimate strength by more than a factor of 60. Since the stiffness and strength decrease with increasing atom size on going down the columns of the periodic table, it is important to look for suitable allotropes of elements and binaries in the upper rows of the periodic table when mechanical stability and robustness are issues. On the other hand, the heavy compounds are of particular interest because of their low-symmetry structures with exotic electronic properties.