Theoretical study of the bonding of ammonia, carbon monoxide, and ethylene, to copper atom, dimer, and trimer

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Abstract
Kohn–Sham density functional theory (KS‐DFT) calculations were performed for the association complexes Cu n –L, with n=1, 2, 3 and L=NH3, CO, and C2H4. Two geometries for Cu2–L are considered; with the ligand bonded to a single copper atom (‘‘atop,’’ or A), and with the ligand bonded to both atoms (‘‘bridge,’’ or B). In addition to A and B, a third geometry was considered for Cu3–L, with the ligand bonded to all three copper atoms; in each case, no minimum was found for that third geometry. I report fully optimized equilibrium geometries and harmonic frequencies calculated within the local spin density (LSD) approximation for all the bound complexes and estimates of their binding energies obtained with a gradient‐corrected exchange‐correlation functional. Structure A is the most stable in all cases but, for Cu3CO and Cu3C2H4, structure B is only a few kcal/mol higher in energy. The energetic contribution from the geometrical relaxation of Cu3 ranges from essentially zero (Cu3NH3 B) to 3.4 kcal/mol (Cu3CO B). In agreement with previous calculations on Cu n –C2H2 and with experiments, the calculated Cu n –L binding energy is found to increase with n for all ligands. Although the bonding mechanism differs among the three ligands, repulsion of a filled ligand orbital with the half‐filled 4s orbital of copper (or 4s‐derived molecular orbitals of Cu2 and Cu3) always plays an important role and is responsible for the smaller binding energies in the CuL complexes. This repulsion decreases from Cu to Cu2 because of charge accumulation in Cu–Cu midbond region and of the greater polarizability of Cu2. The Cu3L binding energies are larger than those of Cu2L mostly because of the greater involvement of copper 4p orbitals in bonding to the ligand. The ligand vibrational frequency shifts relative to the free molecules are compared to experiment and discussed in relation to the nature of the metal–ligand interaction. In particular, an interesting correlation, between the frequency of the NH3 umbrella mode and the metal–NH3 binding energy, is likely due to the electrostatic nature of the bond.