Is copper(I) hard or soft? A density functional study of mixed ligand complexes

Fully optimized structures of three- and four-coordinated Ni (0), Cu(I) and Zn(II) complexes with varied combination of hard $(H_2O \hspace{2mm} or H_3N)$ and soft $(H_2S, H_3P)$ ligands were computed using density functional theory (DFT). Frequency calculations were carried out to ascertain that the structures were true minima. In the case of Cu(I) and Zn(II), the heat of formation (HOF) values are smaller with larger number of soft ligands. The increase in the HOF on replacing a soft ligand with a hard ligand is less for Cu(I) than for Zn(II). The corresponding HOF is negative for Ni(0) which is not stable with a complement of four hard ligands. The calculated chemical hardness parameters based on vertical ionization potentials clearly indicate the preference of four hard ligands for Zn(II) and four soft ligands for Ni(0). Significantly, the maximum chemical hardness was computed for Cu(I) complex $[Cu(PH_3)_3(NH_3)]^+$, a combination of three soft and one hard ligand. The conclusions derived from absolute hardness data computed for the complexes closely parallel the experimentally observed stability of Cu(I) with an optimum number of hard and soft ligands in its coordination sphere in solution