Computational studies have played a pivotal role in advancing the understanding of graphitic carbon nitride (g-C₃N₄) nanomaterials, particularly in elucidating their electronic structure, catalytic behavior, and mechanical properties. Density functional theory (DFT) simulations have been instrumental in predicting key characteristics that guide experimental synthesis and application. These theoretical insights have often been validated by subsequent experimental work, reinforcing the reliability of computational approaches in nanomaterial design.

The electronic structure of g-C₃N₄ has been extensively investigated using DFT. Simulations reveal that the bandgap of pristine g-C₃N₄ typically ranges between 2.6 to 2.8 eV, depending on the level of theory and functional used. This semiconducting property makes it suitable for photocatalytic applications. DFT calculations further show that the valence band maximum is dominated by nitrogen 2p orbitals, while the conduction band minimum consists of carbon 2p orbitals. This charge separation facilitates electron-hole pair generation under visible light irradiation. Modifications such as doping or defect engineering have been computationally screened to optimize band alignment. For instance, phosphorus doping was predicted to narrow the bandgap by introducing mid-gap states, a result later confirmed experimentally through UV-Vis spectroscopy.

Catalytic active sites in g-C₃N₄ have been systematically explored using DFT. The nitrogen-rich framework provides multiple potential sites for catalytic reactions, particularly the triazine or heptazine units. Simulations of hydrogen evolution reaction (HER) mechanisms indicate that the carbon atoms adjacent to nitrogen vacancies serve as the most active sites, with computed Gibbs free energies close to the ideal value of zero. Proton adsorption and reduction pathways have been mapped, showing that the nitrogen lone pairs facilitate proton transfer. CO₂ reduction simulations predict that the edge-terminated nitrogen sites preferentially stabilize key intermediates like *COOH, aligning with experimental observations of enhanced CO₂ conversion rates on defect-engineered samples. Oxygen reduction reaction (ORR) studies suggest a preferential 4-electron pathway on metal-doped g-C₃N₄, later verified by rotating disk electrode measurements.

Mechanical properties of g-C₃N₄ have been assessed through DFT-based stress-strain calculations. The in-plane Young’s modulus is estimated around 210 GPa, indicating moderate stiffness comparable to graphene oxide but lower than pristine graphene. Shear deformation simulations reveal anisotropic behavior, with higher resistance to strain along the heptazine ring plane. Stacking interactions between layers exhibit a binding energy of approximately 20 meV/atom, explaining the ease of exfoliation into few-layer structures. These predictions correlate well with nanoindentation and AFM-based mechanical testing data.

Charge carrier dynamics in g-C₃N₄ have been modeled using time-dependent DFT and non-adiabatic molecular dynamics. The simulations predict electron-hole recombination lifetimes on the order of nanoseconds, with exciton binding energies around 0.5 eV. Doping with sulfur or boron was calculated to prolong carrier lifetimes by introducing shallow trapping states, a finding later supported by transient absorption spectroscopy. The spatial localization of photoexcited carriers at nitrogen vacancy sites was also predicted before being observed via ultrafast microscopy.

Thermal conductivity has been investigated using molecular dynamics simulations with reactive force fields. The calculated in-plane thermal conductivity ranges from 1.5 to 3.0 W/mK at room temperature, significantly lower than graphene due to phonon scattering at the porous structure. Cross-plane conductivity is even lower (0.5 W/mK), confirming the anisotropic thermal transport observed in experimental measurements.

DFT studies have also guided the design of g-C₃N₄-based heterostructures. Simulations of interface formation with graphene indicate charge transfer from graphene to g-C₃N₄, creating a built-in electric field that enhances photocatalytic activity. Similar calculations for MoS₂/g-C₃N₄ composites predict type-II band alignment facilitating charge separation, later demonstrated in photoelectrochemical experiments.

Defect engineering strategies have been computationally optimized before experimental implementation. Nitrogen vacancies were shown to lower the formation energy of key reaction intermediates in CO₂ reduction by 0.3-0.5 eV compared to pristine surfaces. Carbon vacancies, while less favorable thermodynamically, were predicted to create more dramatic changes in electronic structure, including localized states near the Fermi level.

Machine learning approaches have recently augmented traditional DFT studies by enabling high-throughput screening of g-C₃N₄ modifications. Neural network potentials trained on DFT data have been used to predict the stability of thousands of potential doped structures, identifying promising candidates for specific applications. These methods have successfully predicted several stable doped configurations later synthesized and characterized.

The accuracy of computational predictions has been demonstrated through multiple experimental validations. Calculated bandgaps typically deviate less than 0.2 eV from optical measurements. Predicted catalytic activities show linear correlations with experimental turnover frequencies (R² > 0.85) across multiple reaction systems. Mechanical property predictions fall within 15% of nanoindentation measurements.

Multiscale modeling approaches combining DFT with continuum methods have provided insights into macroscopic behavior. Finite element analysis based on DFT-derived parameters accurately reproduces the stress distribution in g-C₃N₄-polymer composites under load. Similar approaches have successfully predicted the thermal expansion behavior observed in temperature-dependent XRD studies.

Recent advances in computational methods continue to refine the understanding of this material. Many-body perturbation theory (GW approximation) has provided more accurate quasiparticle band structures, while real-time TDDFT offers improved descriptions of excited state dynamics. These developments further bridge the gap between theoretical predictions and experimental observations, solidifying the role of computational studies in the rational design of graphitic carbon nitride nanomaterials.