Molecular mechanics for multiple spin states of transition metal complexes

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 (right triangle)oct on the Co-L distance which, when used in conjunction with the relation that the DFT spin state energy difference (delta)Espin(5T2g-1A1g)= 2(right triangle)oct-(5B+ 8C), provides a measure of the interelectron repulsion energy. Finally, the ratio of e(sigma) to e(pi) 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 (angstrom), 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.