This review article provides a bird's eye view on how the structural unit changes the funcationalities of materials, a classification of all pentagon-based 2D structures reported so far, highlighting the major breakthroughs that have occurred in this emerging field over the past years and the unexpected physical properties that have enabled these materials to bridge many disciplines in science and technology.

 We demostrate that a large class of superalkalis composed of only simple metal atoms, transition metal complexes as well as organic molecules can be designed by making use of electron counting rules beyond the octet rule. Examples include Al₃⁺, Mn(B₃N₃H₆)²⁺, B₉C3H₁₂⁺, and C₅NH₆⁺ which obey the Jellium shell closure rule, the 18-electron rule, the Wade–Mingos rule, and Hückel’s aromatic rule, respectively. We further show that the ability of superalkalis to transfer an electron easily can be used to activate a CO₂ molecule by transforming it from a linear to a bent structure. These results, based on density functional theory, open the door to a new class of catalysts for CO₂ activation.

A 2D metastable carbon allotrope, penta-graphene, composed entirely of carbon pentagons and resembling the Cairo pentagonal tiling, is proposed. Due to its unique atomic configuration, penta-graphene has an unusual negative Poisson’s ratio and ultrahigh ideal strength that can even outperform graphene. Furthermore, unlike graphene that needs to be functionalized for opening a band gap, penta-graphene possesses an intrinsic quasi-direct band gap as large as 3.25 eV, close to that of ZnO and GaN. Equally important, penta-graphene can be exfoliated from T12-carbon. When rolled up, it can form pentagon-based nanotubes which are semiconducting, regardless of their chirality. 

Design and synthesis of 3D metallic carbon that is stable under ambient conditions has been a long-standing dream. We predict the existence of such phases, T6- and T14-carbon, consisting ofinterlocking hexagons. These studied metallic 3D carbon structures are systems with hybridized sp³ and sp² bonding. They have the uniqye feature that sp³ bonded C atoms guarantee their stability and the sp² bonded C atoms ensure their metallicity. Their dynamic, mechanical, and thermal stabilities are confirmed by carrying out a variety of state-of-theart theoretical calculations. Unlike the previously studied K₄ and the simple cubic high pressure metallic phases, the structures predicted in this work are stable under ambient conditions. Equally important, they may be synthesized chemically by using benzene or polyacenes molecules.

Boron nitride (BN) and carbon are chemical analogues of each other and share similar structures such as one-dimensional nanotubes, two-dimensional nanosheets characterized by sp² bonding, and three-dimensional diamond structures characterized by sp³ bonding.On the basis of state-of-the-art theoretical calculations, we propose a tetragonal phase of BN Analysis of its band structure, density of states, and electron localization function confirms the origin of the metallic behavior to be due to the delocalized B 2p electrons. The metallicity exhibited in the studied three-dimensional BN structures can lead to materials beyond conventional ceramics as well as to materials with potential for applications in electronic devices.

Using semiclassical Boltzmann transport theory and density functional formalism, we have systematically studied the thermoelectric performance of layered GeAs₂. The figure of merit, ZT value, of this layered structure is found to be 2.78 along the out-of-plane direction, with optimal carrier concentration at 800 K. Analysis of the charge density difference and phonon transport properties allows us to attribute such exceptional thermoelectric properties to strong interlayer interaction between the adjacent layers where quasicovalent bonding is responsible for the enhanced electrical conductivity, while the layered structure accounts for the suppressed lattice thermal conductivity. This study highlights the potential of layered crystals for highly efficient thermoelectric materials.

Using state-of-the-art first-principles calculations, we propose a new two- dimensional (2D) carbon allotrope constructed by polymerizing the carbon skeletons of s- indacenes, named PSI (ψ)-graphene. We show that ψ-graphene has the lowest energy among all hitherto reported 2D allotropes of carbon composed of 5−6−7 carbon rings and is dynamically and thermally stable. This structure is metallic with robust metallicity against external strain. In addition, we find that the adsorption of Li atoms on ψ-graphene is exothermic, and the diffusion energy barrier is low and comparable to that of graphene. Furthermore, ψ-graphene can achieve a maximum Li storage capacity equivalent to that of LiC₆, suggesting its potential as an anode material for Li-ion batteries (LIBs). In addition, we show that increasing the number of hexagons in this structure can enhance the thermodynamic stability of the sheet while maintaining its metallicity. This study provides new insights into the design of new metallic carbon for nanostructured anode materials in the next generation of LIBs.

Using first-principles calculations based on density functional theory, we show that when patterned in the form of a kagome lattice, nonmagnetic g-C₃N₄ not only becomes ferromagnetic but also its magnetic properties can be further enhanced by applying external strain. Similarly, the magnetic moment per atom in ferromagnetic g-C4N3 is increased three fold when patterned into a kagome lattice. The Curie temperature of g-C₃N₄ kagome lattice is 100 K, while that of g-C₄N₃ kagomelattice is much higher, namely, 520 K. To date, all of the synthesized twoand three-dimensional magnetic kagome structurescontain metal ions and are toxic.