Theoretical Study of Spin Crossover in 30 Iron Complexes.

Iron complexes are important spin crossover (SCO) systems with vital roles in oxidative metabolism and promising technological potential. The SCO tendency depends on the free energy balance of high- and low-spin states, which again depends on physical effects such as dispersion, relativistic effects, and vibrational entropy. This work studied 30 different iron SCO systems with experimentally known thermochemical data, using 12 different density functionals. Remarkably general entropy-enthalpy compensation across SCO systems was identified (R = 0.82, p = 0.002) that should be considered in rational SCO design. Iron(II) complexes displayed higher ΔH and ΔS values than iron(III) complexes and also less steep compensation effects. First-coordination sphere ΔS values computed from numerical frequencies reproduce most of the experimental entropy and should thus be included when modeling spin-state changes in inorganic chemistry (R = 0.52, p = 3.4 × 10(-3); standard error in TΔS ≈ 4.4 kJ/mol at 298 K vs 16 kJ/mol of total TΔS on average). Zero-point energies favored high-spin states by 9 kJ/mol on average. Interestingly, dispersion effects are surprisingly large for the SCO process (average: 9 kJ/mol, but up to 33 kJ/mol) and favor the more compact low-spin state. Relativistic effects favor low-spin by ∼9 kJ/mol on average, but up to 24 kJ/mol. B3LYP*, TPSSh, B2PLYP, and PW6B95 performed best for the typical calculation scheme that includes ZPE. However, if relativistic and dispersion effects are included, only B3LYP* remained accurate. On average, high-spin was favored by LYP by 11-15 kJ/mol relative to other correlation functionals, and by 4.2 kJ/mol per 1% HF exchange in hybrids. 13% HF exchange was optimal without dispersion, and 15% was optimal with all effects included for these systems.