###### Abstract  
The efficient performance of metal-ion batteries strongly depends on electrode materials characteristics. Two-dimensional (2D) materials are among promising electrode materials for metal-ion battery cells, owing to their excellent structural and electronic properties. Two-dimensional graphdiyne has been recently fabricated and revealed unique storage capacities and fast charging rates. The current study explores the performance of the novel phosphorylated-triphenylene graphdiyne (P-TpG) monolayer as an anode material for Li-, Na-, K-, Mg-, and Ca-ions storage via extensive density functional theory (DFT) simulations. Our results reveal that the stable structure of P-TpG monolayers delivers ultra-high storage capacities of -2148, -1696, -1017, and -2035 mA\(\cdot\)h\(\cdot\)g\({}^{-1}\) for Li-, Na-, K-, and Ca- ions, respectively. Notably, the metallic electronic behavior is illustrated by adsorbing metal-ions on the P-TpG nanosheets, suggesting a good electronic conductivity. The NEB results demonstrate that P-TpG can serve as an outstanding candidate for the optimal charging/discharging process. This theoretical study suggests P-TpG nanosheets as a highly promising candidate for the design of advanced metal-ion batteries with remarkable charge capacities and optimal charging/discharging rates. performances as anode material for Ca- or Na- ions batteries as well. First-principles analysis revealed that VS2 and VSe2 have considerable charge capacities of 257 mA\(\cdot\)h\(\cdot\)g\({}^{-1}\) for Ca- or Na-ion storages, which are very promising as non-Li batteries [21]. [PERSON] et al. [22] investigated hierarchical MoS\({}_{2}\)/Ti\({}_{3}\)C\({}_{2}\)T\({}_{\rm x}\) composites structures. Their results revealed that MoS\({}_{2}\)/Ti\({}_{3}\)C\({}_{2}\)T\({}_{\rm x}\) electrodes have a good cycling stability with 250.9 mA\(\cdot\)h\(\cdot\)g\({}^{-1}\) at 100 mA\(\cdot\)g\({}^{-1}\) after 100 cycles with 88% retention of the initial reversible capacity. Mg-ion batteries have confirmed a high cell performance using a VS\({}_{2}\) nanosheet and with 0.4 M (PhMgCl)\({}_{2}\)-AlCl\({}_{3}\)/tetrahydrofuran (APC/THF) and 50 wt.% 1-butyl-1-methylpiperidinium chloride (PP\({}_{14}\)Cl) as the electrolyte. These batteries exhibited 348 mA\(\cdot\)h\(\cdot\)g\({}^{-1}\) storage capacity at 20 mA\(\cdot\)g\({}^{-1}\) current density and excellent rate capability with a 214 mA\(\cdot\)h\(\cdot\)g\({}^{-1}\) capacity at 2.0 A\(\cdot\)g\({}^{-1}\) current density [23]. Electrodes have an essential role in the performance improvement of metal-ion batteries. Hence, searching for optimal electrode materials is one of the significant research challenges in battery development. 2D monolayers and heterostructures are used in various applications [24; 25] due to their high mechanical strength, electronic, and thermal conductivity [26]. Graphene itself has a high electronic conductivity with moderate charge capacities of 372 mA\(\cdot\)h\(\cdot\)g\({}^{-1}\)[10]. Extensive studies have been conducted for novel 2D materials with high electronic conductivity and charge capacity [27; 28; 29; 30; 31; 32] as the most critical parameters in various applications [28; 33; 34]. [PERSON] et al. [33] experimentally designed and fabricated a novel graphdiyne family structure called triphenylene graphdiyne (TpG). TpG nanosheets were synthesized using hexaethylnyltriphenylene monomers within the modified liquid-liquid interfacial method [34]. This experimental realization was motivated to investigate the intrinsic material properties and conducting novel theoretical predictions [35; 36; 37]. Recent studies of graphdiyne family monolayers demonstrated the semiconducting electronic behavior and high charge capacities for metal ion storage [38; 39; 40; 41]. Graphdiyne belongs to the class of 2D carbon allotropes that have been experimentally synthesized through a cross-coupling reaction using hexaethylnylbenzene [42; 43].