Spin Propensities of Octahedral Complexes From Density Functional Theory

The fundamental balance between high- and low-spin states of transition metal systems depends on both the metal ion and the ligands surrounding it, as often visualized by the spectrochemical series. Most density functionals do not reproduce this balance, and real spin state propensities depend on orbital pairing and vibrational entropies absent in the spectrochemical series. Thus, we systematically computed the tendency toward high or low spin of "text-book" octahedral metal complexes versus ligand and metal type, using eight density functionals. Dispersion effects were generally <5 kJ/mol, favoring low-spin states. Zero-point energies favored high-spin states up to 33 kJ/mol for strong ligands, but down to a few kilojoules per mole for weak ligands. Vibrational entropy also favored high-spin states up to 40 kJ/mol, most for strong ligands. Jahn−Teller distortion in Co(II) low-spin states, particularly stable d⁶ low-spin states, and entropy corrections were consistent with experiment. Entropy and zero-point energy corrections were markedly lower for Co(II) and Mn(III), viz., the differential ligand field stabilization energy, and can only be ignored for weak ligands. The data enable simple assessment of spin state propensities versus ligand and metal type and reveal, e.g., that CN^- is consistently weaker than CO for M(II) but stronger than CO for M(III) and SCN^- and NCS^- change order in M(II) versus M(III) complexes. Contrary to expectation based on the spectrochemical series, Cl^- and Br^- are very close in spin state propensity because the pairing penalty for low spin is smaller in Br^-. Thus, for the M(II) complexes, we find a consensus order of Br^- ∼ Cl^- <H2O <SCN^- <NCS^- ∼ NH3 <CN^- <CO, whereas for the M(III) complexes, an approximate order is Br^- ∼ Cl^- <H2O ∼ NCS^- ∼ SCN^-<NH3 <CO <CN^-.