DFT methods applied to answer the question: how accurate is the ligand acidity constant method for estimating the pK a of transition metal hydride complexes MHXL 4 when X is varied?

Density functional theory (DFT) is used to calculate the relative free energies of deprotonation of the isomers of iron-group hydride complexes MHXL ₄ where M = Fe, Ru, Os, L ₄ = (CO) ₄ or (PMe ₂ CH ₂ CH ₂ PMe ₂ ) ₂ for a wide range of anionic ligands X. The free energies of the most stable isomers are used to calculate relative pK _a values where K _a refers to the acid dissociation constant for the equilibrium MHXL ₄ → [MXL ₄ ] ^- + H ⁺ . These are used to test the proposal that the pK _a for a given metal complex in THF can be simply calculated by adding the contributions to the total pK _a value from each ligand L; these are called ligand acidity constants (LAC) A _L used in the LAC equation [R. H. Morris, J. Am. Chem. Soc., 2014, 136, 1948-1959]. The A _L are calculated using A _L = 0.2 as a reference for the hydride ligand. The A _L of certain less polarizable X ligands are found to be fairly constant (±1 to ±2 units) and consistent with the proposed LAC method for a range of the complexes considered: 2 for Me ^- , 1 for OH ^- , 1 for NH ₂ ^- , 0 for B(OCH ₂ CH ₂ O ^- ) ^- , -1 for OMe ^- , -2 for SH ^- and -2 for SMe ^- . Other ligands have more variable A _L values (±3 to ±5 units) because of high polarizability or other reasons: 1 for OtBu ^- , -1 for F ^- , -2 for BMe ₂ ^- , -2 for NMe ₂ ^- , -3 for Cl ^- , -3 for PMe ₂ ^- , -3 for Br ^- , -5 for I ^- , -6 for CN ^- and -12 for SiCl ₃ ^- . Iodide stabilizes the anion [MIL ₄ ] ^- more than does fluoride in [MFL ₄ ] ^- making iodide the more acidifying ligand despite its lower electronegativity. DFT is also used to validate the charge correction in the LAC equation.