Evaluation of CO₂ Adsorption and Activation in Cu_xSc_y Nanoclusters by Analyzing DFT and PDOS/TDOS Signatures

The adsorption and activation of CO₂ on Cu_xSc_y nanoclusters with x + y equal to 4 were analyzed using DFT and PDOS and TDOS signatures. The geometries of Cu₃Sc, Cu₂Sc₂, and CuSc₃ were optimized in the gas phase, and the minima were verified by frequencies in ORCA using M06-2X/def2-TZVP. Multiplicities 1, 3, and 5, temperatures between 298 and 400 K, and four CO₂ coordination modes R1 to R4 were evaluated. Naked and complex cluster comparison panels were constructed, and two energy windows, −18 to −10 eV and −8 to 6 eV around the Fermi level, were analyzed, complemented by frontier orbitals and charge maps. Thermodynamics indicated that mode and multiplicity control the adsorption energy, with ANOVA p-values of 0.002 and 0.008, while temperature was not significant (p = 0.682). In Cu₃Sc–C₂v(1), the R1 singlet at 298 K showed E_ads −33.43 kcal·mol⁻¹ with spin contamination, while alternative modes in the singlet were unfavorable. In PDOS and TDOS, the bare cluster exhibits a Cu d band at −11 to −10 eV and a valley around −5 eV. The exergonic complexes show CO₂ signals near the Fermi level, superimposed on Cu and Sc states, with state filling and broadening. Transferable indicators based on CO₂ intensity in the −8 to 6 eV range and metal–adsorbate overlap are proposed as predictors of exergonic adsorption.