basis set incompleteness (F12) the experimental value of +3.8 kcal mol
À1 was
confirmed. One should therefore be careful when using DMC data for spin states
as reference data, since they may have an intrinsic bias toward high-spin states; it
would be interesting to see the effect of the choice of orbitals (Kohn-Shamvs. Hartree-Fock) in DMC calculations. The failure of DMC was corroborated in a
recent study with the DLPNO and canonical variants of CCSD(T) by Neese and
co-workers [139] that confirmed the much smaller ΔE HL value for [Fe
II (NCH) 6 ]
2+ .
Early 2019, a second benchmark study was published [166], now focusing
mainly (but not exclusively) on coupled cluster (CC) approaches. This largely
confirmed what Mikael Johansson had reported at WATOC2017 when he discussed
results for the DLPNO variant of CC for a simple Fe(II) complex with bipyridine
ligands and argued for using SSB-D [73] as the reference because it gave automatically (and fast) the correct answer. Feldt and Harvey made a systematic study of the
effect of all kinds of choices to be made when dealing with spin states and coupled
cluster: (1) which orbitals to use, HF or Kohn-Sham; (2) restricted or unrestricted
orbitals to be used; (3) solving CC equations in restricted or unrestricted fashion;
(4) which level of CC is needed (CCSD, CCSD(T), CCSDT, CCSDT(Q)); and
(5) how good are approximated CC such as local CC or DLPNO CC for spin states.
They focused on model systems for high-valent metal-oxo species, [Fe
IV (O)
(NH 3 ) 5 ]
2+ and [Fe
IV (O)(He) 5 ]
2+ with methane as substrate, to study the oxidation
reaction energy profile; they used the helium “ligand” (with shortened Fe-He
distance to make sure the spin density remains similar to that observed with the
ammonia ligands) for enabling the CCSDT and CCSDT(Q) calculations. From all
the different flavors of CC, the UKS-UCCSD(T) was found to perform best when
comparing with the CCSDT/CCSDT(Q) data for the helium systems and with
DMRG/CASPT2 for the ammonia systems. Not surprisingly, using restricted
open-shell Kohn-Sham orbitals and solving the CC equations in spin-restricted
fashion (ROKS-RCCSD(T)) was the worst of the four options. Both the local CC
and DLPNO-CCSD(T) approaches, although promising new approaches, are not yet
robust enough to serve as benchmark references [166].
The barriers for the oxidation reaction in either the triplet state (24.6 kcal mol
À1 )
or the quintet state (13.7 kcal mol
À1
) confirm the previous study by Shaik and
co-workers [167] that showed the smaller barrier when following the quintet state,
but also that a spin-switch must be made when starting from the complex in the
triplet ground state. Note that Feldt, Harvey, and co-workers argued [166] that the
barrier for the
3 TS was slightly too low. Interestingly, this slight upshift brings it very
close to the barriers as predicted by OPBE (already the best performing DFA in the
Shaik study [167]), which showed values [166] of 27.3 and 12.9 kcal mol
À1 (arguably, both within 1 kcal mol
À1 from the most accurate CC results, and hence a
confirmation of its excellent behavior for first-row transition metals). In a follow-up
study [168], Feldt and co-workers showed that the local CC and DLPNO-CCSD(T)
methods seemed to have systematic biases, DLPNO overstabilizing high-spin states
and local CC overestimating triplet states.
In a series of papers, Cao and Ryde focused on the mechanism of nitrogenase,
carrying out systematic approaches with, e.g., a large number of broken-symmetry
Dealing with Spin States in Computational Organometallic Catalysis
205
À1 was
confirmed. One should therefore be careful when using DMC data for spin states
as reference data, since they may have an intrinsic bias toward high-spin states; it
would be interesting to see the effect of the choice of orbitals (Kohn-Shamvs. Hartree-Fock) in DMC calculations. The failure of DMC was corroborated in a
recent study with the DLPNO and canonical variants of CCSD(T) by Neese and
co-workers [139] that confirmed the much smaller ΔE HL value for [Fe
II (NCH) 6 ]
2+ .
Early 2019, a second benchmark study was published [166], now focusing
mainly (but not exclusively) on coupled cluster (CC) approaches. This largely
confirmed what Mikael Johansson had reported at WATOC2017 when he discussed
results for the DLPNO variant of CC for a simple Fe(II) complex with bipyridine
ligands and argued for using SSB-D [73] as the reference because it gave automatically (and fast) the correct answer. Feldt and Harvey made a systematic study of the
effect of all kinds of choices to be made when dealing with spin states and coupled
cluster: (1) which orbitals to use, HF or Kohn-Sham; (2) restricted or unrestricted
orbitals to be used; (3) solving CC equations in restricted or unrestricted fashion;
(4) which level of CC is needed (CCSD, CCSD(T), CCSDT, CCSDT(Q)); and
(5) how good are approximated CC such as local CC or DLPNO CC for spin states.
They focused on model systems for high-valent metal-oxo species, [Fe
IV (O)
(NH 3 ) 5 ]
2+ and [Fe
IV (O)(He) 5 ]
2+ with methane as substrate, to study the oxidation
reaction energy profile; they used the helium “ligand” (with shortened Fe-He
distance to make sure the spin density remains similar to that observed with the
ammonia ligands) for enabling the CCSDT and CCSDT(Q) calculations. From all
the different flavors of CC, the UKS-UCCSD(T) was found to perform best when
comparing with the CCSDT/CCSDT(Q) data for the helium systems and with
DMRG/CASPT2 for the ammonia systems. Not surprisingly, using restricted
open-shell Kohn-Sham orbitals and solving the CC equations in spin-restricted
fashion (ROKS-RCCSD(T)) was the worst of the four options. Both the local CC
and DLPNO-CCSD(T) approaches, although promising new approaches, are not yet
robust enough to serve as benchmark references [166].
The barriers for the oxidation reaction in either the triplet state (24.6 kcal mol
À1 )
or the quintet state (13.7 kcal mol
À1
) confirm the previous study by Shaik and
co-workers [167] that showed the smaller barrier when following the quintet state,
but also that a spin-switch must be made when starting from the complex in the
triplet ground state. Note that Feldt, Harvey, and co-workers argued [166] that the
barrier for the
3 TS was slightly too low. Interestingly, this slight upshift brings it very
close to the barriers as predicted by OPBE (already the best performing DFA in the
Shaik study [167]), which showed values [166] of 27.3 and 12.9 kcal mol
À1 (arguably, both within 1 kcal mol
À1 from the most accurate CC results, and hence a
confirmation of its excellent behavior for first-row transition metals). In a follow-up
study [168], Feldt and co-workers showed that the local CC and DLPNO-CCSD(T)
methods seemed to have systematic biases, DLPNO overstabilizing high-spin states
and local CC overestimating triplet states.
In a series of papers, Cao and Ryde focused on the mechanism of nitrogenase,
carrying out systematic approaches with, e.g., a large number of broken-symmetry
Dealing with Spin States in Computational Organometallic Catalysis
205