Nature of the metal–ligand bond in some [(CO)4M ← BIIM(R)] {M = Cr, Mo, W; R = H, F, Cl, Br} complexes: A theoretical study

Quantitative and Chemically Intuitive Evaluation of the Nature of M-L Bonds in Paramagnetic Compounds: Application of EDA-NOCV Theory to Spin Crossover Complexes

To improve understanding of M-L bonds in 3d transition metal complexes, analysis by energy decomposition analysis and natural orbital for chemical valence model (EDA-NOCV) is desirable as it provides a full, quantitative and chemically intuitive ab initio description of the M-L interactions. In this study, a generally applicable fragmentation and computational protocol was established and validated by using octahedral spin crossover (SCO) complexes, as the transition temperature (T1/2 ) is sensitive to subtle changes in M-L bonding. Specifically, EDA-NOCV analysis of Fe-N bonds in five [FeII (Lazine )2 (NCBH3 )2 ], in both low-spin (LS) and paramagnetic high-spin (HS) states led to: 1) development of a general, widely applicable, corrected M+L6 fragmentation, tested against a family of five LS [FeII (Lazine )3 ](BF4 )2 complexes; this confirmed that three Lazine are stronger ligands (ΔEorb,σ+π =-370 kcal mol-1 ) than 2 Lazine +2 NCBH3 (=-335 kcal mol-1 ), as observed. 2) Analysis of Fe-L bonding on LS→HS, reveals more ionic (ΔEelstat ) and less covalent (ΔEorb ) character (ΔEelstat :ΔEorb 55:45 LS→64:36 HS), mostly due to a big drop in σ (ΔEorb,σ ↓50 %; -310→-145 kcal mol-1 ), and a drop in π contributions (ΔEorb,π ↓90 %; -30→-3 kcal mol-1 ). 3) Strong correlation of observed T1/2 and ΔEorb,σ+π , for both LS and HS families (R2 =0.99 LS, R2 =0.95 HS), but no correlation of T1/2 and ΔΔEorb,σ+π (LS-HS) (R2 =0.11). Overall, this study has established and validated an EDA-NOCV protocol for M-L bonding analysis of any diamagnetic or paramagnetic, homoleptic or heteroleptic, octahedral transition metal complex. This new and widely applicable EDA-NOCV protocol holds great promise as a predictive tool.

Kinetic and Potential Energy Contributions to a Chemical Bond from the Charge and Energy Decomposition Scheme of Extended Transition State Natural Orbitals for Chemical Valence

This work provides novel physical insight into the nature of a chemical bond by exploring qualitative and quantitative relations between the natural orbitals for chemical valence (NOCV)-based deformation density bonding channels Δρ _i ( i = σ, π, δ, etc.) and the corresponding kinetic Δ T_i and potential energy Δ V_i contributions within the charge and energy decomposition scheme ETS-NOCV implemented in the Kohn-Sham-based Amsterdam Density Functional (ADF) package. It is determined that interfragment dative and covalent-type electron charge reorganizations upon formation of a series of strong and weak bonds employing main-group elements are due to lowering of the negative kinetic energy contributions, as opposed to the intrafragment polarizations (e.g., hyperconjugations in ethane), which are, in contrary, driven by the potential energy (electrostatic) component. Complementary, formation of π-contributions in N₂ is accompanied by lowering of both kinetic and potential energy constituents. Remarkably, well-known globally stabilizing back-donation (M → ligand, where M is a transition metal) and donation (ligand → M) processes, ubiquitous in organometallic species, have been discovered for the first time to be driven by the opposite Δ T_i/Δ V_i mechanisms, namely, the former contribution is associated with the negative kinetic term (which outweighs the positive potential energy), whereas the latter charge delocalization into electrophilic transition metals leads to an attractive electrostatic stabilization (and positive kinetic energy).