DFT-based study of the Al₁₂N₁₂ nanocage for sensing and capturing perfluorinated greenhouse gases

Density functional theory (DFT) was used to study the adsorption of environmentally harmful perfluorocarbon greenhouse gases (PFCs) CF₄, C₂F₆ and C₃F₈ on clean and Mn-doped Al₁₂N₁₂ nanocages. All energetics reported here were obtained with the dispersion-corrected B3LYP-D3(BJ) functional and the triple-zeta 6-311++G(d,p) basis set. On the pristine cage, all three gases adsorb with favourable electronic and enthalpic energies (ΔE_ads = -5.65 to -7.65 kcal mol^-1; ΔH_ads = -4.05 to -6.04 kcal mol^-1), although the corresponding Gibbs free energies are positive at 298 K, showing that capture is enthalpically driven but entropically opposed under standard conditions. Doping one surface aluminium atom with manganese collapses the HOMO-LUMO gap of the bare cage from 3.88 to 2.89 eV, and this reduced gap is only weakly perturbed by subsequent gas adsorption (2.76-2.91 eV for the three loaded complexes), showing that it is the act of doping, not the act of capture, that switches on the electronic response needed for sensing. Doping does not uniformly strengthen binding: C₂F₆ and C₃F₈ remain bound with electronic energies comparable to, or slightly weaker than, those on the pristine cage, while the CF₄ complex located on the Mn-doped surface is not a genuine minimum at this level of theory (two small imaginary frequencies; ΔE_ads = +4.88 kcal mol^-1) and is reported with that caveat. Frontier molecular orbital (FMO), density of states (DOS), electron density difference (EDD), non-covalent interaction (NCI)/QTAIM and natural bond orbital (NBO) analyses are used to characterise the adsorption mechanism and electronic response; the NBO analysis gives a charge-transfer magnitude of 0.12-0.22e across the six complexes, largest for C₃F₈@Mn-Al₁₁N₁₂ (0.216e) and smallest for C₂F₆@Mn-Al₁₁N₁₂ (0.12e). Taken together, the results identify Mn-doped Al₁₂N₁₂ primarily as an electronically responsive sensing platform for CF₄, C₂F₆ and C₃F₈, whose principal value lies in the doping-induced narrowing of the frontier gap rather than in a uniform enhancement of capture strength.