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

Abstract

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.

Low-temperature lifetimes of metastable high-spin states in spin-crossover and in low-spin iron(II) compounds: The rule and exceptions to the rule

“…In fact, all the different functionals give very similar results provided basis sets of high quality are used (see Ref. [26] for computational details). Table 1 gives average values as determined from the results obtained using the different functionals with basis sets of valence triple-ζ polarised quality, and Fig.…”

“…This gives an experimental estimate of E el HL of 3500-6000 cm −1 . Table 2 gives the electronic energy difference between the highspin and the low-spin state, E el HL = E el HS − E el LS , calculated for a number of different functionals using basis sets of valence triple-ζ polarised quality [26]. The calculated values depend very much on the functional used.…”

“…In fact, most functionals fail to approach the experimental estimate. The large spread in calculated values of E el HL was ascribed to the inability of the exchange part of the correlation-exchange functionals to properly account for the variation of exchange when the spin polarisation and the metal-ligand bond length significantly vary [26]. Thus, with the PBE, BP86, PW91 functionals which Table 1. are generalised gradient approximations (GGAs), the exchange is underestimated which translates into the overestimation of E el HL .…”

“…The more recent RPBE GGA corrects for the underestimation of exchange, and gives the best results, along with the B3LYP * hybrid functional which conversely corrects for the overestimate of exchange of the other hybrids B3LYP and PBE0. Relative spin-state energetics thus provide a stringent criterion for assessing the performance of exchangecorrelation functionals [26,28]. The results obtained for the spin-state energetics of [Fe(bpy) 3 ] 2+ are discussed in more detail in Ref.…”

“…The results obtained for the spin-state energetics of [Fe(bpy) 3 ] 2+ are discussed in more detail in Ref. [26]. For our purpose, it suffices to retain that GGA and hybrid functionals give as expected an accurate and consistent description of both the low-spin and high-spin geometries of [Fe(bpy) 3 ] 2+ , and that reliable results for the high-spin/low-spin energetics were obtained only with the RPBE and B3LYP * functionals, which give values for E el HL of ∼6800 and ∼3400 cm −1 , respectively.…”