24
K. P. Kepp
broadly, and to SCO specifically, with predictive accuracy, making the functional
“universal” [157–159]. The discussion above suggests that we must continue to
improve the quality of density functionals, which will ultimately be used for predicting SCO behavior in larger systems and in batches of many systems, where other
quantum-mechanical methods are too computationally slow. However, we should
also carefully understand the biases in the quantum-mechanical benchmark methods
themselves. Finally, in order to ensure that this process works, we should use the
experimental data available for smaller systems where several quantum-chemical
methods can be applied.
As has been widely discussed in the literature, different density functionals produce very different HS–LS gaps [28, 30, 36, 49, 52, 61, 64, 89, 118, 129, 132,
143, 160–163]. From these many studies, some consensus is, however, starting to
emerge. In this author’s humble view, functionals emerging as accurate for SCO
include B3LYP* [61] (B3LYP [127, 128, 142] with 15% HF exchange), TPSSh [62,
164] (a meta hybrid with 10% HF exchange), and the double-hybrid B2PLYP [91].
Among GGA functionals, OLYP and OPBE are promising [94, 143]; it uses Handy
and Cohen’s optimized exchange [139, 141] which favors HS more than other nonhybrid GGA exchange functionals. If combined with LYP [142, 165] it gives even
more HS stabilization because LYP is a HS-favoring correlation functional compared
to, e.g., PBE, PW91, and P86 [36]. Particularly, encouraging is also the SSB functional which switches between PBE and OPBE [144], utilizing the high accuracy of
the O exchange functional for spin-state energetics.
Even within iron SCO, which would supposedly be considered one type of systems
for one type of purpose, there are system dependencies in method performance
relating to oxidation state, i.e., even for the subset of iron SCO, there is no “universal”
functional. It turns out that typical density functionals produce different errors in the
spin-state balance for Fe(III) and Fe(II) SCO systems. Thus, for example, B3LYP*
is not equally accurate for Fe(III) and Fe(II) systems, and in fact tends to produce too
much high spin in Fe(II) systems and too much LS in Fe(III) systems [36]. Hybrid
functionals tend to not only favor HS as explained above but also favor HS too much
in Fe(II) compared to Fe(III), which has been called the “Fe(II)–Fe(III) bias” of DFT
and which readily grows to 20 kJ/mol [94].
One of the more promising, recent avenues is the use of range-separated hybrids
to study SCO processes, because these functionals can have several other advantages
such as a small self-interaction error and more accurate transition-state energetics. One example of such a range-separated hybrid functional for use in SCO is
CAMB3LYP [166]. This functional works surprisingly well by itself, but the 2018customized versions with slightly less HF exchange (15–17%) are even more accurate [94]. Another example, also from 2018, is the optimally tuned range-separated
hybrid (OT-RSH) studied by Prokopiou and Kronik [167], who also found that the
short-range HF percentage is the most important parameter for achieving spin-state
balance. Thus, for the broader study of transition metal catalysis where transition
states are involved of variable spin states, the CAMB3LYP functional is probably
among the best currently available, although this remains to be tested by additional
benchmark studies.
K. P. Kepp
broadly, and to SCO specifically, with predictive accuracy, making the functional
“universal” [157–159]. The discussion above suggests that we must continue to
improve the quality of density functionals, which will ultimately be used for predicting SCO behavior in larger systems and in batches of many systems, where other
quantum-mechanical methods are too computationally slow. However, we should
also carefully understand the biases in the quantum-mechanical benchmark methods
themselves. Finally, in order to ensure that this process works, we should use the
experimental data available for smaller systems where several quantum-chemical
methods can be applied.
As has been widely discussed in the literature, different density functionals produce very different HS–LS gaps [28, 30, 36, 49, 52, 61, 64, 89, 118, 129, 132,
143, 160–163]. From these many studies, some consensus is, however, starting to
emerge. In this author’s humble view, functionals emerging as accurate for SCO
include B3LYP* [61] (B3LYP [127, 128, 142] with 15% HF exchange), TPSSh [62,
164] (a meta hybrid with 10% HF exchange), and the double-hybrid B2PLYP [91].
Among GGA functionals, OLYP and OPBE are promising [94, 143]; it uses Handy
and Cohen’s optimized exchange [139, 141] which favors HS more than other nonhybrid GGA exchange functionals. If combined with LYP [142, 165] it gives even
more HS stabilization because LYP is a HS-favoring correlation functional compared
to, e.g., PBE, PW91, and P86 [36]. Particularly, encouraging is also the SSB functional which switches between PBE and OPBE [144], utilizing the high accuracy of
the O exchange functional for spin-state energetics.
Even within iron SCO, which would supposedly be considered one type of systems
for one type of purpose, there are system dependencies in method performance
relating to oxidation state, i.e., even for the subset of iron SCO, there is no “universal”
functional. It turns out that typical density functionals produce different errors in the
spin-state balance for Fe(III) and Fe(II) SCO systems. Thus, for example, B3LYP*
is not equally accurate for Fe(III) and Fe(II) systems, and in fact tends to produce too
much high spin in Fe(II) systems and too much LS in Fe(III) systems [36]. Hybrid
functionals tend to not only favor HS as explained above but also favor HS too much
in Fe(II) compared to Fe(III), which has been called the “Fe(II)–Fe(III) bias” of DFT
and which readily grows to 20 kJ/mol [94].
One of the more promising, recent avenues is the use of range-separated hybrids
to study SCO processes, because these functionals can have several other advantages
such as a small self-interaction error and more accurate transition-state energetics. One example of such a range-separated hybrid functional for use in SCO is
CAMB3LYP [166]. This functional works surprisingly well by itself, but the 2018customized versions with slightly less HF exchange (15–17%) are even more accurate [94]. Another example, also from 2018, is the optimally tuned range-separated
hybrid (OT-RSH) studied by Prokopiou and Kronik [167], who also found that the
short-range HF percentage is the most important parameter for achieving spin-state
balance. Thus, for the broader study of transition metal catalysis where transition
states are involved of variable spin states, the CAMB3LYP functional is probably
among the best currently available, although this remains to be tested by additional
benchmark studies.