Theoretical Investigation of the Electronic Structure of Fe(II) Complexes at Spin-State Transitions

The electronic structure relevant to low spin (LS)↔high spin (HS) transitions in Fe(II) coordination compounds with a FeN₆ core are studied. The selected [Fe(tz)₆]²⁺ (1) (tz = 1H-tetrazole), [Fe(bipy)₃]²⁺ (2) (bipy = 2,2'-bipyridine), and [Fe(terpy)₂]²⁺ (3) (terpy = 2,2':6',2″-terpyridine) complexes have been actively studied experimentally, and with their respective mono-, bi-, and tridentate ligands, they constitute a comprehensive set for theoretical case studies. The methods in this work include density functional theory (DFT), time-dependent DFT (TD-DFT), and multiconfigurational second order perturbation theory (CASPT2). We determine the structural parameters as well as the energy splitting of the LS-HS states (ΔE_HL) applying the above methods and comparing their performance. We also determine the potential energy curves representing the ground and low-energy excited singlet, triplet, and quintet d⁶ states along the mode(s) that connect the LS and HS states. The results indicate that while DFT is well suited for the prediction of structural parameters, an accurate multiconfigurational approach is essential for the quantitative determination of ΔE_HL. In addition, a good qualitative agreement is found between the TD-DFT and CASPT2 potential energy curves. Although the TD-DFT results might differ in some respect (in our case, we found a discrepancy at the triplet states), our results suggest that this approach, with due care, is very promising as an alternative for the very expensive CASPT2 method. Finally, the two-dimensional (2D) potential energy surfaces above the plane spanned by the two relevant configuration coordinates in [Fe(terpy)₂]²⁺ were computed at both the DFT and CASPT2 levels. These 2D surfaces indicate that the singlet-triplet and triplet-quintet states are separated along different coordinates, i.e., different vibration modes. Our results confirm that in contrast to the case of complexes with mono- and bidentate ligands, the singlet-quintet transitions in [Fe(terpy)₂]²⁺ cannot be described using a single configuration coordinate.