Assertion and validation of the performance of the B3LYP⋆ functional for the first transition metal row and the G2 test set

Salomon, Oliver; Reiher, Markus; Heß, Bernd A.

doi:10.1063/1.1493179

Cited by 552 publications

(593 citation statements)

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“…HL of the [Fe(bpy) 3 ] 2 + complex points to the inherent difficulty of XC functionals to predict the relative energies of states of different spin multiplicities correctly, particularly for spin-crossover systems [27,49,[60][61][62] but also for spin-forbidden chemical reactions. [88] This is emphasised by the fact that for the TZP basis set the 5 E and the 5 A 1 components of the quintet state are consistently predicted to be nearly degenerate, that is within the chemical accuracy of 350 cm À1 , by functionals which behave quite differently when it comes to evaluating the HS--LS energy gap.…”

Section: The Hs-ls Energy Gapmentioning

confidence: 99%

“…HL values for a 0 values of between 0.10 and 0.15, the value a 0 = 0.15 being actually used in the B3LYP* functional by Reiher et al [60,61] For an exact-exchange contribution smaller than 10 %, the HS--LS energy gap is overestimated as a consequence of the underestimation of the exchange energy. This is best illustrated by considering the a 0 = 0 limit.…”

Section: The Hs-ls Energy Gapmentioning

confidence: 99%

“…They recommended a reduced a 0 value of 0.15 for which the resulting B3LYP* functional correctly predicts the ground state of a number of iron(II) complexes. [60,61] Nevertheless, in the particular case of the spin-crossover Fe(1,10-phenantroline) 2 (NCS) 2 complex, even the B3LYP* functional incorrectly gives the HS state as the ground state. [62] As pointed out by Reiher, this suggests that the amount of exact exchange may be further reduced in the case of this complex.…”

Section: Dft Characterisation Of Ls and Hs States Of Iron(ii) Complexesmentioning

confidence: 99%

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

et al. 2005

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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.

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Section: The Hs-ls Energy Gapmentioning

confidence: 99%

Section: The Hs-ls Energy Gapmentioning

confidence: 99%

Section: Dft Characterisation Of Ls and Hs States Of Iron(ii) Complexesmentioning

confidence: 99%

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

et al. 2005

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“…However, the strong chemistry-dependence of HF exchange effects on spin-state ordering 18,[21][22]28 has motivated diverging proposals of either low 22,[29][30][31] or high 21, 32-33 HF exchange fractions in order to accurately predict transition metal complex properties. Explicit incorporation of exact exchange also remains computationally expensive in the context of periodic, plane-wave DFT.…”

Section: Introductionmentioning

confidence: 99%

Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering

2017

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Prediction of spin-state ordering in transition metal complexes is essential for understanding catalytic activity and designing functional materials. Semi-local approximations in density functional theory, such as the generalized-gradient approximation (GGA), suffer from several errors notably including delocalization error that give rise to systematic bias for more covalently bound low-spin electronic states. Incorporation of exact exchange is known to counteract this bias, instead favoring high-spin states, in a manner that has recently been identified to be ligand-field dependent. In this work, we introduce a tuning strategy to identify the effect of incorporating the Laplacian of the density (i.e., a meta-GGA) in exchange on spinstate ordering. We employ a diverse test set of M(II) and M(III) first-row transition metal ions from Ti to Cu as well as octahedral complexes of these ions with ligands of increasing field strength (i.e., H 2 O, NH 3 , and CO). We show that the sensitivity of spin-state ordering to meta-GGA exchange is highly ligand-field dependent, stabilizing high-spin states in strong-field (i.e., CO) cases and stabilizing low-spin states in weak-field (i.e., H 2 O, NH 3 , and isolated ions) cases. This diverging behavior leads to generally improved treatment of isolated ions and strong field complexes over a standard GGA but worsened treatment for the hexa-aqua or hexa-ammine complexes. These observations highlight the sensitivity of functional performance to subtle changes in chemical bonding.2

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“…9 The focus has frequently been on the comparison of DFT calculations with experimental results for medium-and large-sized compounds. So far, our own contribution to this area has been a detailed comparison of DFT calculations with ligand field and ab initio results for the relatively small ''textbook example'' of ͓Fe(H 2 O) 6 ͔ 2ϩ ͑Ref. 8͒.…”

mentioning

confidence: 99%

Comparison of density functionals for energy and structural differences between the high- [5T2g:(t2g)4(eg)2] and low- [1A1g:(t2g)6(eg)] spin states of iron(II) coordination compounds. II. More functionals and the hexaminoferrous cation, [Fe(NH3)6]2+

Fouqueau

Casida

Daku

et al. 2005

The Journal of Chemical Physics

166

164

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Comparison of density functionals for energy and structural differences between the high- † 5 T 2g :"t 2g … The ability of different density functionals to describe the structural and energy differences between the high-͓ 5 T 2g :(t 2g ) 4 (e g ) 2 ͔ and low-͓ 1 A 1g :(t 2g ) 6 (e g ) 0 ͔ spin states of small octahedral ferrous compounds is studied. This work is an extension of our previous study of the hexaquoferrous cation, ͓Fe(H 2 O) 6 ͔ 2ϩ , ͓J. Chem. Phys. 120, 9473 ͑2004͔͒ to include a second compound-namely, the hexaminoferrous cation, ͓Fe(NH 3 ) 6 ͔ 2ϩ -and several additional functionals. In particular, the present study includes the highly parametrized generalized gradient approximations ͑GGAs͒ known as HCTH and the meta-GGA VSXC ͓which together we refer to as highly parametrized density functionals ͑HPDFs͔͒, now readily available in the GAUSSIAN03 program, as well as the hybrid functional PBE0. Since there are very few experimental results for these molecules with which to compare, comparison is made with best estimates obtained from second-order perturbation theory-corrected complete active space self-consistent field ͑CASPT2͒ calculations, with spectroscopy oriented configuration interaction ͑SORCI͒ calculations, and with ligand field theory ͑LFT͒ estimations. While CASPT2 and SORCI are among the most reliable ab initio methods available for this type of problem, LFT embodies many decades of empirical experience. These three methods are found to give coherent results and provide best estimates of the adiabatic low-spin-high-spin energy difference, ⌬E LH adia , of 12 000-13 000 cm Ϫ1 for ͓Fe(H 2 O) 6 ͔ 2ϩ and 9 000-11 000 cm Ϫ1 for ͓Fe(NH 3 ) 6 ͔ 2ϩ . All functionals beyond the purely local approximation produce reasonably good geometries, so long as adequate basis sets are used. In contrast, the energy splitting, ⌬E LH adia , is much more sensitive to the choice of functional. The local density approximation severely over stabilizes the low-spin state with respect to the high-spin state. This ''density functional theory ͑DFT͒ spin pairing-energy problem'' persists, but is reduced, for traditional GGAs. In contrast the hybrid functional B3LYP underestimates ⌬E LH adia by a few thousands of wave numbers. The RPBE GGA of Hammer, Hansen, and Nørskov gives good results for ⌬E LH adia as do the HPDFs, especially the VSXC functional. Surprisingly the HCTH functionals actually over correct the DFT spin pairing-energy problem, destabilizing the low-spin state relative to the high-spin state. Best agreement is found for the hybrid functional PBE0. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1839854͔ I. INTRODUCTIONThe identification of the spin symmetry of the ground and low-lying excited states is important for the comprehension of chemical reactivity. However, many interesting cases occur, especially among transition metal coordination compounds, where the competition between the splitting of nearly degenerate orbitals with the electron pairing energy makes the prediction of relative spin-s...

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Assertion and validation of the performance of the B3LYP⋆ functional for the first transition metal row and the G2 test set

Cited by 552 publications

References 25 publications

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

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

Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering

Comparison of density functionals for energy and structural differences between the high- [5T2g:(t2g)4(eg)2] and low- [1A1g:(t2g)6(eg)] spin states of iron(II) coordination compounds. II. More functionals and the hexaminoferrous cation, [Fe(NH3)6]2+

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