The Electronic Determinants of Spin Crossover Described …
23
of HS; this has been shown in multiple studies [52, 143, 153]. From Swart’s study,
OPBE gives ~80 kJ/mol in favor of HS [143]. Notably, OPBE is known to do well for
SCO systems also from the same study [143], and confirmed by us [94]. Thus, one
cannot expect the 80 kJ/mol estimate for the relaxed H SCO to be in much error, even
when correcting for the systematic dispersion, relativistic, and ZPE effects described
above. This value of ~80 kJ/mol is quite similar to the CASPT2 value obtained by
Pierloot and Vancoille [152]. From all of these studies, it thus emerges that B3LYP
at 60 kJ/mol has an error probably not larger than ~20 kJ/mol for [Fe(NH 3 ) 6 ]
2+ .
In stark contrast to these findings is a new benchmark using diffusion Monte Carlo
(DMC) based on HF nodal surfaces, which suggests that B3LYP favors LS too much
by more than 60 kJ/mol for [Fe(NH 3 ) 6 ]
2+ , and TPPSh by almost 100 kJ/mol [153].
DMC in that study suggests that HS is 120 kJ/mol below LS, which seems too much
and is 40 kJ/mol more in favor of HS than CASPT2. Similar surprising results with
DMC can also be deduced by comparison of Fe(NCH) 6 ]
2+ of the new study [153] to
the study by Lawson Daku et al. [154] and Kepenekian et al. [155].
One explanation could be that DMC applied to spin-state energetics is very sensitive to the use of the HF nodes for the highly spin-polarized HS state, but this remains
to be further investigated. If true, it again illustrates a post-HF bias but this time via
the applied fixed node used in DMC. This suspicion is enhanced by a study [156] that
investigated the use of different orbitals for the Slater−Jastrow trial wave function
with DMC: CASSCF and HF orbitals give similar results and much higher absolute
energies by 0.01 a.u. for the HS state and 0.03 a.u. for the LS state than the DFT
Kohn–Sham orbitals, showing that the latter orbitals become better correlated during
the full computation, as expected from the considerations above (i.e., the removal of
the initial HF bias is very difficult). Confirming the suspicion further, the difference
amounts to 0.02 a.u. in the computed HS–LS gap, or ~50 kJ/mol, very similar to the
hypothesized error in DMC(HF) that can be deduced from the work discussed above
[153].
This discussion illustrates (1) the effect of correlation on DMC using DFT rather
than HF orbitals for the fixed node approximation, (2) that any quantum-mechanical
method that starts from the HF picture will keep some bias toward this state unless
fully correlated, which is in practice very hard; and (3) that extreme care should
be applied when using supposedly high-level quantum-chemical methods as direct
benchmark, rather than experimental data. CASPT2, rather than CCSD(T) which
cannot describe non-dynamic correlation as well, is arguably the current “golden
standard” of computational spin crossover and may stay so as the use of larger more
appropriate active spaces and basis sets become computationally tractable.
4.4 Toward Spin-State-Balanced Density Functionals
The goal of current efforts in theoretical chemistry is to achieve a state where theory
becomes truly predictive and thus, accurate enough to explain and design new systems
of interest. For DFT, this would mean that a functional can be applied to chemistry
23
of HS; this has been shown in multiple studies [52, 143, 153]. From Swart’s study,
OPBE gives ~80 kJ/mol in favor of HS [143]. Notably, OPBE is known to do well for
SCO systems also from the same study [143], and confirmed by us [94]. Thus, one
cannot expect the 80 kJ/mol estimate for the relaxed H SCO to be in much error, even
when correcting for the systematic dispersion, relativistic, and ZPE effects described
above. This value of ~80 kJ/mol is quite similar to the CASPT2 value obtained by
Pierloot and Vancoille [152]. From all of these studies, it thus emerges that B3LYP
at 60 kJ/mol has an error probably not larger than ~20 kJ/mol for [Fe(NH 3 ) 6 ]
2+ .
In stark contrast to these findings is a new benchmark using diffusion Monte Carlo
(DMC) based on HF nodal surfaces, which suggests that B3LYP favors LS too much
by more than 60 kJ/mol for [Fe(NH 3 ) 6 ]
2+ , and TPPSh by almost 100 kJ/mol [153].
DMC in that study suggests that HS is 120 kJ/mol below LS, which seems too much
and is 40 kJ/mol more in favor of HS than CASPT2. Similar surprising results with
DMC can also be deduced by comparison of Fe(NCH) 6 ]
2+ of the new study [153] to
the study by Lawson Daku et al. [154] and Kepenekian et al. [155].
One explanation could be that DMC applied to spin-state energetics is very sensitive to the use of the HF nodes for the highly spin-polarized HS state, but this remains
to be further investigated. If true, it again illustrates a post-HF bias but this time via
the applied fixed node used in DMC. This suspicion is enhanced by a study [156] that
investigated the use of different orbitals for the Slater−Jastrow trial wave function
with DMC: CASSCF and HF orbitals give similar results and much higher absolute
energies by 0.01 a.u. for the HS state and 0.03 a.u. for the LS state than the DFT
Kohn–Sham orbitals, showing that the latter orbitals become better correlated during
the full computation, as expected from the considerations above (i.e., the removal of
the initial HF bias is very difficult). Confirming the suspicion further, the difference
amounts to 0.02 a.u. in the computed HS–LS gap, or ~50 kJ/mol, very similar to the
hypothesized error in DMC(HF) that can be deduced from the work discussed above
[153].
This discussion illustrates (1) the effect of correlation on DMC using DFT rather
than HF orbitals for the fixed node approximation, (2) that any quantum-mechanical
method that starts from the HF picture will keep some bias toward this state unless
fully correlated, which is in practice very hard; and (3) that extreme care should
be applied when using supposedly high-level quantum-chemical methods as direct
benchmark, rather than experimental data. CASPT2, rather than CCSD(T) which
cannot describe non-dynamic correlation as well, is arguably the current “golden
standard” of computational spin crossover and may stay so as the use of larger more
appropriate active spaces and basis sets become computationally tractable.
4.4 Toward Spin-State-Balanced Density Functionals
The goal of current efforts in theoretical chemistry is to achieve a state where theory
becomes truly predictive and thus, accurate enough to explain and design new systems
of interest. For DFT, this would mean that a functional can be applied to chemistry