Molecular mechanics for multiple spin states of transition metal complexes

Abstract

Empirical Ligand Field Molecular Mechanics (LFMM) parameters for CoIII–F and CoIII–CN bonds are developed from Density Functional Theory (DFT) calculations on octahedral [CoF6]3− and [Co(CN)6]3−. In addition to the 5T2g and 1A1g 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 t2g3.6eg2.4 configuration in which the ligand field stabilisation energy is formally zero. DFT orbital energies are used to estimate the dependence of Δoct on the Co–L distance which, when used in conjunction with the relation that the DFT spin state energy difference ΔEspin(5T2g–1A1g) = 2Δoct − (5B + 8C), provides a measure of the interelectron repulsion energy. Finally, the ratio of eσ to eπ 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 b1g1.2b2g1.2a1g1.2eg2.4 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 A, 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) 1A1g is relatively more stable than 5T2g 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.