Due to the world's steady rise of energy consumption, the employment of innovative techniques and systems of energy production with high energy efficiency and density as well as low pollution is a priority. As a result, the use of fuel cells (FCs) is highly valued for offering an effective production system [1]. FCs are electrochemical instruments that directly transform chemical energy (usually hydrogen) into electrical energy, allowing us to create power and heat without the usage of carbon fuels [2]. FCs are distinguished by their similarity to batteries and their environmental friendliness [3,4]. They have several benefits over conventional power generators, including high efficiency, no harmful gas emissions, no noise pollution owing to the lack of moving parts, relative ease of the repair system and maintenance, long life, and lower fuel usage. In contrast to the benefits noted, the primary drawbacks of FCs are their expensive price, which is attributable to a number of elements in the manufacturing and production process. Meanwhile, the slow kinetics of the oxygen reduction reaction (ORR) at the cathode heavily influences the FCs performance [5]. The reduction of molecular oxygen (O2) in the ORR can take namely, by a two-electron O2 + 2H+ + 2e−→ H2O2 or a four-electron path O2 + 4H+ + 4e−→ 2H2O.

Platinum and other noble metal-based materials have been frequently employed as possible electrocatalysts in FCs. Nevertheless, the high price, sluggish kinetics, and scarcity of platinum supplies are significant barriers to large-scale research and commercialization of these electrocatalysts. Meanwhile, inexpensive and efficient alternative cathode electrocatalysts must be developed, because their design and engineering are very critical in technology. Carbon-based nanomaterials as metal-free electrocatalysts for the ORR have received a lot of interest due to their high conductivity, low cost, and good durability [[6], [7], [8]].

Many efforts have been devoted in recent decades to find alternative electrocatalysts in ORR, such as non-precious metals, heteroatoms, polymers, and non-metallic carbon nanomaterials [[9], [10], [11]]. Catalyzed processes have a lower activation energy, and reactants may be employed more effectively, resulting in fewer undesired products and impurities [[12], [13], [14]]. Novoselov and Geim discovered graphene, the first two-dimensional (2D) material, in 2004 [15]. It has been the subject of many research activities in recent years due to its unusual features [16,17]. The use of metal dopants has displayed great potential for facilitating the ORR on carbon-based catalysts [18,19]. For example, researchers have been able to improve the ORR process by doping Fe on the surface of porous carbon nanostructures [20]. By means of density functional theory (DFT) calculations, it was already found that FeN4 moiety embedded in graphene can significantly improve its ORR activity compared to precious platinum catalysts [21]. The researchers found that adding active transition metals such as copper to nitrogen-doped graphene can create highly active sites for the oxygen reduction reaction. This could be due to the presence of scattered electrons in these structures, which accelerates electron transfer during the reaction [22]. Intercalation with heteroatoms improves the poor chemical reactivity of pure graphene. Previous studies have also shown that chemical doping of graphene with non-metal elements such as N [23,24], B [[25], [26], [27]] or S [[28], [29], [30]], or P [31] improves its electrical features and catalytic activity. N-doped graphene, for example, has been frequently employed as a potential catalyst in the ORR process [32,33].

When a carbon atom is replaced with a nitrogen impurity in the graphene matrix, some novel electronic properties might be explored. It is well known that the integration of nitrogen atoms into the carbon matrix via sp2 bonding can cause the formation of several forms of nitrogen impurities including graphitic, pyridinium and pyrrolic configurations [34,35]. Each of these arrangements has a distinct effect on the electronic and transport characteristics of functional materials. For instance, three valence electrons of nitrogen in the graphitic configuration contribute to form three chemical bonds with neighbor carbons, one electron enters the π states, while the fifth electron occupies the π∗-states of the conduction band (CB). This generates a significant n-doping effect, and as the surface gets more negative, the transition of electron becomes simpler to perform. Among alternative bonding media, this configuration is thought to be the most efficient n-doping impurity. Because it is in the same group as the nitrogen atom, the phosphorus atom takes a similar role [36,37]. This means that P atoms on defective graphene can be employed as a catalyst in the ORR process of FCs, as evidenced by extensive experimental [38,39] and theoretical [[40], [41], [42]] researches. Yang et al. discovered that the P-doped graphene sheets is thermodynamically stable, and that this structure can be used to create new metal-free catalysts.

In 2015, chemists proposed a chemical process to create a novel 2D layered crystal known as C2N (nitrogenated holey graphene) [43]. This novel graphene-like porous material then attracted the interest of many researchers due to its exceptional properties such as large surface area and good structural stability [[44], [45], [46], [47]]. C2N is also a good material for FCs owning to its low cost, chemical stability, adjustable electrical and thermal structure [48]. As a result of its outstanding adsorption capacity and electrocatalytic activity, C2N can be employed as a highly efficient electrocatalyst [49].

Chemical doping is a helpful technique for improving the electrical structure and surface characteristics, as well as increasing the efficiency and activity of the cathode electrode in FCs [50]. Likewise, the introduction of non-metallic atoms into the electrocatalyst is a useful strategy to improve its activity and performance due to its environmental friendliness and ease of synthesis [51]. Particularly, heteroatoms of comparable size and electronegativity to carbon atoms could alter the distribution of electrons and the electrical properties of the carbon structure, influencing its interaction with oxygen molecules. Furthermore, because the heteroatom often establishes a covalent bond with the carbon framework, the impact of electrocatalytic enhancements for the ORR will be retained for a long time. On the other hand, DFT can provide useful information about the ORR mechanisms, and how chemical doping impacts the electronic structure of the electrocatalyst [40]. Although two heteroatoms with the same amount of valence electrons can have distinct effects on the electrocatalytic performance of the substrate, an atom's large atomic radius and strong electron donating capacity make it an excellent candidate for doping carbon materials. In general, previous studies have revealed that heteroatom chemical doping, such as P atoms or other atoms on carbon, plays a key role in ORR catalysts [52,53]. Due to the electron-withdrawing role of oxygen atoms in these systems, the doped heteroatom on the substrate works as a link between oxygen and carbon atoms [54]. Previously, researchers have shown that doping phosphorus atoms in graphene sheets causes major structural changes, which has a beneficial ORR activity [40].

In this study, DFT calculations are employed to analyze the probable mechanisms of ORR on a P-doped C2N (P@C2N) substrate. The major reasons for using P as a doping agent on C2N are its low cost, ease of availability, and stability during the reaction. To better comprehend the ORR process, the geometry and electronic structure of the proposed electrocatalyst are thoroughly explored. The adsorption of all species participated in the ORR over P@C2N is also examined. The most favorable pathways for the oxygen reduction are then examined.