Spin propensities of octahedral complexes from density functional theory

Area of Science:

• Computational Chemistry
• Inorganic Chemistry
• Quantum Mechanics

Background:

• The spin state of transition metal complexes is crucial for their properties but is not accurately predicted by the spectrochemical series alone.
• Density functional theory (DFT) calculations often fail to capture the subtle balance between high- and low-spin states, which is influenced by factors like orbital pairing and vibrational effects.

Purpose of the Study:

• To systematically compute the spin state propensities (high-spin vs. low-spin) of common octahedral metal complexes.
• To evaluate the performance of eight different density functionals in predicting these spin states.
• To elucidate the contributions of ligand type, metal ion, dispersion effects, zero-point energies, and vibrational entropies to the spin state balance.

Main Methods:

• Systematic computation of spin state tendencies using eight density functionals for various "text-book" octahedral metal complexes.
• Inclusion of dispersion effects, zero-point energies, and vibrational entropy corrections in the calculations.
• Comparison of computational results with experimental data, particularly for Jahn-Teller distortions and entropy effects.

Main Results:

• Dispersion effects generally favor low-spin states (<5 kJ/mol).
• Zero-point energies and vibrational entropy significantly favor high-spin states (up to 33 kJ/mol and 40 kJ/mol, respectively), especially for strong ligands.
• Established new consensus orders for ligand strength concerning spin state propensity for M(II) and M(III) complexes, refining the spectrochemical series.
• Identified that Cl(-) and Br(-) have very similar spin state propensities, contrary to traditional expectations.

Conclusions:

• Spin state determination in transition metal complexes requires considering orbital pairing, zero-point energies, and vibrational entropies, not just the spectrochemical series.
• The findings provide a framework for assessing spin state propensities based on metal and ligand identity.
• The study highlights discrepancies with the spectrochemical series and offers refined ligand ordering for M(II) and M(III) systems.