Density Functional Theory Calculations Support the Additive Nature of Ligand Contributions to the pKa of Iron Hydride Phosphine Carbonyl Complexes.

The acid dissociation constant Ka of a transition-metal hydride complex is a key thermodynamic quantity for evaluating reactivity and stability of the complexes and their conjugate bases in stoichiometric and catalytic reactions. It can be estimated using a simple ligand acidity constant (LAC) empirical equation for a wide range of complexes. Here, we provide the first density functional theory (DFT) study that supports the additive nature of ligand contributions to the pKa of metal hydride complexes. Specifically, the pKa values of iron hydride complexes [FeH(CO)x(PR3)(5-x)]+ in either tetrahydrofuran or dichloromethane solutions are estimated using the LAC method and DFT calculations. There is a linear correlation between these two methods, and both predict a surprisingly linear increase in pKa over a wide range from approximately -15 for x = 5 to approximately 40 for x = 0. The LAC equation predicts that pKaTHF or pKaDCM increases by 9 units with the replacement of each CO ligand with a trialkylphosphine ligand in a stepwise fashion, whereas the DFT calculations predict the step size will be approximately 11. The two methods agree with pKDCM data available for x = 3 and qualitative data for x = 1 and 0, but further quantitative measurements over a wider range are needed to firmly establish the trend. The free energy of protonation and the energy of the highest occupied molecular orbital of Fe(CO)x(PR3)(5-x) (mainly nonbonding d electrons) increase linearly with phosphine substitution, and this increases the pKa value as observed.