A DFT analysis of the effect of chelate ring size on metal ion selectivity in complexes of polyamine ligands

Abstract DFT calculations were carried out using the dmol 3 program to investigate the thermodynamics of complex formation of polyamine complexes of M(II) ions (M = metal) in the gas-phase, and in aqueous solution, where the cosmo module of dmol 3 models aqueous solution as a structureless dielectric medium with a dielectric constant appropriate for water. The calculations that included relativistic effects employed the all electron scalar relativity option available in dmol 3. The values of ΔH(aq)(DFT) and ΔG(aq)(DFT) for reactions such as [M(H2O)6]2+ + en = [M(H2O)4en]2+ + 2H2O (en = ethylenediamine) in aqueous solution for M = Ca, Cr, Mn, Fe, Co, Ni, Cu, Zn, and Cd were found to correlate well with the corresponding values in aqueous solution. Values of ΔH(g)(DFT) for reactions such as [M(H2O)4en]2+ + tn = [M(H2O)4tn]2+ + en (tn = 1,3-diaminopropane) calculated in the gas-phase for M = Ca, Cr, … Cu showed the effect of changing chelate ring size from 5-membered for en to 6-membered for tn in that complexes of smaller metal ions such as Cu(II) were less destabilized by the increase in chelate ring size than larger metal ions such as Ca(II). This supports the chelate ring-size rule (R.D. Hancock, A.E. Martell, Chem. Rev. 89 (1989) 1875) that states that increase of chelate ring size stabilizes the complexes of smaller metal ions relative to those of larger metal ions. Use of cosmo to simulate the change from the en to the tn complexes in aqueous solution showed only a small response to change in metal ion size, as is found to be the case experimentally. An important aspect here is that the change in log K1 on changing chelate ring size in passing en to tn complexes is of the same order of magnitude as the probable uncertainty in the energies obtained from the DFT calculations. The DFT calculations show how aqueous solution dampens out chelate effects for small ligands such as en and tn, and also removes the effects of polarizability seen in the gas-phase. The chelate ring size rule is supported by calculations on Ni(II) complexes of pairs of polyamine ligands such as dien (diethylenetriamine) and dptn (1,5,9-triazanonane), or trien (triethylenetetramine) and 2,3,2-tet (1,4,8,11-tetraazaundecane), where the first member of the pair of ligands forms only 5-membered chelate rings, while the second member forms at least one 6-membered chelate ring in place of a 5-membered chelate ring formed by the first member. The DFT calculations show that increase of chelate ring size usually leads to a decrease in stability of the Ni(II) complex, but correctly predict that the 2,3,2-tet complex will be more stable than the trien complex, which is an unusual example where replacing a 5-membered chelate ring with a 6-membered chelate ring leads to higher complex stability. The role of polarizability effects in the thermodynamics of complex-formation is discussed. Polarizability effects stabilize complexes of larger ligands such as dptn relative to those of smaller analogs such as dien in the gas-phase by more effectively dispersing the cationic charge over the complex. Also discussed is the possible role of specific solvation by water molecules in the thermodynamics of complex-formation in aqueous solution, which effect is not taken into account by the cosmo module used in this paper.