Assessment of Density Functionals for the High-Spin/Low-Spin Energy Difference in the Low-Spin Iron(II) Tris(2,2′-bipyridine) Complex

• Published in: Chemphyschem 2005-07, Vol.6 (7), p.1393-1410
• Main Authors: Lawson Daku, Latévi Max, Vargas, Alfredo, Hauser, Andreas, Fouqueau, Antony, Casida, Mark Earl
• Format: Article
• Language: English
• Subjects: Atomic and molecular physics; Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations); density functional calculations; Density-functional theory; Electronic structure of atoms, molecules and their ions: theory; Exact sciences and technology; Ferrous Compounds - chemistry; high-spin-low-spin relaxation; iron(II) complexes; Models, Chemical; Physics; Pyridines - chemistry; Quantum Theory; spin crossover; time-resolved spectroscopy
• ISSN: 1439-4235; 1439-7641
• DOI: 10.1002/cphc.200400584

In the iron(II) low‐spin complex [Fe(bpy)3]2+, the zero‐point energy difference between the 5T2g(t${{{4\hfill \atop 2g\hfill}}}$${e{{2\hfill \atop g\hfill}}}$) high‐spin and the 1A1g(t${{{6\hfill \atop 2g\hfill}}}$) low‐spin states, ΔE${{{0\hfill \atop HL\hfill}}}$, is estimated to lie in the range of 2500–5000 cm−1. This estimate is based on the low‐temperature dynamics of the high‐spin→low‐spin relaxation following the light‐induced population of the high‐spin state and on the assumption that the bond‐length difference between the two states ΔrHL is equal to the average value of ≈0.2 Å, as found experimentally for the spin‐crossover system. Calculations based on density functional theory (DFT) validate the structural assumption insofar as the low‐spin‐state optimised geometries are found to be in very good agreement with the experimental X‐ray structure of the complex and the predicted high‐spin geometries are all very close to one another for a whole series of common GGA (PB86, PW91, PBE, RPBE) and hybrid (B3LYP, B3LYP*, PBE1PBE) functionals. This confirmation of the structural assumption underlying the estimation of ΔE${{{0\hfill \atop HL\hfill}}}$ from experimental relaxation rate constants permits us to use this value to assess the ability of the density functionals for the calculation of the energy difference between the HS and LS states. Since the different functionals give values from −1000 to 12000 cm−1, the comparison of the calculated values with the experimental estimate thus provides a stringent criterion for the performance of a given functional. Based on this comparison the RPBE and B3LYP* functionals give the best agreement with experiment. The high‐spin/low‐spin energy difference (Δ${{{\rm E}{{{\rm {\rm el}}.\hfill \atop {\rm {\rm HL}}\hfill}}}$) in the low‐spin iron(II) tris(2,2′‐bipyridine) complex was deduced from the low‐temperature dynamics of the high‐spin→low‐spin relaxation, assuming that the FeN bond‐length difference (ΔrHL) between the two spin states is ≈0.2 Å, as found experimentally for spin‐crossover systems. The density functional characterisation of the complex in the two spin states allowed the validation of this structural assumption (see picture).