Molecular mechanics for multiple spin states of transition metal complexes

Abstract

Empirical Ligand Field Molecular Mechanics (LFMM) parameters for Co^III–F and Co^III–CN bonds are developed from Density Functional Theory (DFT) calculations on octahedral [CoF₆]³⁻ and [Co(CN)₆]³⁻. In addition to the ⁵T_2g and ¹A_1g ground states of [CoF₆]³⁻ and [Co(CN)₆]³⁻ respectively, DFT can also access the low-spin form of [CoF₆]³⁻ and the high-spin form of [Co(CN)₆]³⁻ as well as the averaged d configuration (ADC) state corresponding to a t_2g^3.6e_g^2.4 configuration in which the ligand field stabilisation energy is formally zero. DFT orbital energies are used to estimate the dependence of Δ_oct on the Co–L distance which, when used in conjunction with the relation that the DFT spin state energy difference ΔE_spin(⁵T_2g–¹A_1g) = 2Δ_oct − (5B + 8C), provides a measure of the interelectron repulsion energy. Finally, the ratio of e_σ to e_π ligand field parameters is obtained via fitting the DFT orbital energies of hypothetical square planar [CoF₄]⁻ and [Co(CN)₄]⁻ complexes using an ADC corresponding to a b_1g^1.2b_2g^1.2a_1g^1.2e_g^2.4 configuration. The LFMM parameters are derived solely from the homoleptic systems but are nevertheless able to reproduce the structures and spin-state energies of the eight mixed-ligand systems in between. The latter are estimated theoretically since no experimental data exist. The high-spin and low-spin structures have Co–L rms errors of 0.06 and 0.03 Å, respectively. Explicit recognition of d–d interelectron repulsion energies provides a common reference for both spin states which facilitates a direct LFMM calculation of the spin-state energy difference. Both LFMM and DFT predict: (i) a change from high to low spin after replacement of a single fluoride ligand; (ii) the difference increases with each subsequent replacement and (iii) ¹A_1g is relatively more stable than ⁵T_2g for cis and mer compared to trans and fac, respectively. The spin-state energy difference rms error is ∼7 kcal mol⁻¹ but there is a systematic overestimation for the mixed-ligand systems since the LFMM does not fully capture the cis and trans influences.