Introduction:
MXenes are a family of two-dimensional inorganic nanomaterials composed of transition-metal carbides and nitrides, well known for their high electrical conductivity, hydrophilic surfaces, and tunable surface chemistry, which make them promising candidates for advanced energy materials. These properties make them attractive in the next generation of energy storage and conversion equipment, including batteries and supercapacitors.

Methods:
In this study, density functional theory calculations are performed on finite cluster models of Ti₂C and Ti₂N MXenes to investigate their local electronic structure, bonding, and relative stability. The analysis is based on important electronic descriptors, namely total electronic energies, HOMO–LUMO gaps, charge distributions, dipole moments, symmetry properties, and differences in Ti–C and Ti–N bonding interactions.

Results:
The calculated results show clear contrasts between carbide and nitride MXenes. Ti₂C exhibits a total electronic energy of −47256.9008 eV with a HOMO–LUMO gap of 1.39 eV, indicating narrow-gap electronic behavior and favorable local electronic characteristics. In contrast, Ti₂N shows a lower total electronic energy of −47713.4497 eV, reflecting higher relative stability, along with spin-dependent HOMO–LUMO gaps of about 1.50 eV (α spin) and 1.72 eV (β spin). The Ti₂N cluster also has a finite dipole moment of 1.0858 Debye, fits within the CS point-group symmetry, and has a doublet spin state characteristic, indicating stronger polarization effects and stronger Ti–N bonding as compared to Ti–C. The systematically weakened HOMO–LUMO gaps and stronger interactions between the metals and nitrogen in the nitride MXenes indicate favorable electronic characteristics for energy applications and stronger bonding when compared to their carbide counterparts, which is also adjusted to parameters of thickness and composition.

Conclusions:
These findings show how first-principles electronic structure calculations can directly link atomic-scale bonding and electronic behavior to energy-relevant properties in MXenes. The results support the rational design of titanium carbide and nitride MXenes as advanced energy materials and underline the suitability of density functional theory-based electronic structure analysis for understanding and optimizing next-generation two-dimensional energy materials.