smaller model systems to include (a portion of) electron correlation (by definition,
the correlation energy obtained with a certain basis set is the full-CI energy minus the
HF energy). This all changed with the rise of reasonable density functional approximations (DFAs) in the 1990s (e.g., BP86 [59, 60], B3LYP [61, 62], or PBE [63]),
with many new DFAs having been proposed ever since. Because of the large amount
of possible DFAs to choose from, each with their pros and cons, in 2010 we started
an annual popularity poll [64], in order to probe the preference of the computational
chemistry community and provide feedback for researchers that are starting to
use DFAs.
3.1 Density Functional Theory
The first systematic study on how the choice of DFA affects the description of spin
states in transition-metal complexes was performed by Trautwein and co-workers in
2001 [65]. They investigated Fe(II) spin-crossover compounds, which at low temperatures are observed in a (S ¼ 0) low-spin state and at a certain (transition)
temperature suddenly switch to a high-spin (S ¼ 2) state. As mentioned above,
this sudden switch is a cooperative effect of an ensemble of these compounds, but to
a reasonable extent, the temperature can be estimated by taking into account the
enthalpy and entropy [66]. Most importantly, the DFAs available at that time were
unable to correctly describe these SCO compounds: LDA and early GGAs predicted
a low-spin state with the high-spin at such elevated energy that a transition temperature of thousands of K would be needed to reach it; hybrid functionals like B3LYP
on the other hand often already predicted a high-spin state at 0 K. Hence, no DFA
was able to correctly characterize these compounds as being SCO. Shortly after, and
independently, Reiher and co-workers reported [67] on a set of SCO compounds and
showed how the spin-state preferences depended linearly on the amount of HF
exchange (A HF ) used within the hybrid DFAs and proposed to lower it to 15%
(B3LYP*) instead of the usual 20% (B3LYP). This led Reiher [68] to divide
transition-metal compounds into three classes:
1. Standard: spin-state splitting is hardly affected by A HF .
2. Critical: splitting is dependent on A HF , but spin state does not change in range
(0, 0.25), although the reaction energetics can be affected significantly.
3. Complicated: splitting is dependent on A HF , and a change in spin state is
observed, together with changes in reaction energetics.
Since then, many validation studies have been performed, arguing for the use of
OPBE [63, 69–71], revPBE [72], SSB-D [73], S12g [74], TPSSh [75], B2PLYP
[76], optimally tuned range-separated functional [77], etc. [78–81].
198
M. Swart
the correlation energy obtained with a certain basis set is the full-CI energy minus the
HF energy). This all changed with the rise of reasonable density functional approximations (DFAs) in the 1990s (e.g., BP86 [59, 60], B3LYP [61, 62], or PBE [63]),
with many new DFAs having been proposed ever since. Because of the large amount
of possible DFAs to choose from, each with their pros and cons, in 2010 we started
an annual popularity poll [64], in order to probe the preference of the computational
chemistry community and provide feedback for researchers that are starting to
use DFAs.
3.1 Density Functional Theory
The first systematic study on how the choice of DFA affects the description of spin
states in transition-metal complexes was performed by Trautwein and co-workers in
2001 [65]. They investigated Fe(II) spin-crossover compounds, which at low temperatures are observed in a (S ¼ 0) low-spin state and at a certain (transition)
temperature suddenly switch to a high-spin (S ¼ 2) state. As mentioned above,
this sudden switch is a cooperative effect of an ensemble of these compounds, but to
a reasonable extent, the temperature can be estimated by taking into account the
enthalpy and entropy [66]. Most importantly, the DFAs available at that time were
unable to correctly describe these SCO compounds: LDA and early GGAs predicted
a low-spin state with the high-spin at such elevated energy that a transition temperature of thousands of K would be needed to reach it; hybrid functionals like B3LYP
on the other hand often already predicted a high-spin state at 0 K. Hence, no DFA
was able to correctly characterize these compounds as being SCO. Shortly after, and
independently, Reiher and co-workers reported [67] on a set of SCO compounds and
showed how the spin-state preferences depended linearly on the amount of HF
exchange (A HF ) used within the hybrid DFAs and proposed to lower it to 15%
(B3LYP*) instead of the usual 20% (B3LYP). This led Reiher [68] to divide
transition-metal compounds into three classes:
1. Standard: spin-state splitting is hardly affected by A HF .
2. Critical: splitting is dependent on A HF , but spin state does not change in range
(0, 0.25), although the reaction energetics can be affected significantly.
3. Complicated: splitting is dependent on A HF , and a change in spin state is
observed, together with changes in reaction energetics.
Since then, many validation studies have been performed, arguing for the use of
OPBE [63, 69–71], revPBE [72], SSB-D [73], S12g [74], TPSSh [75], B2PLYP
[76], optimally tuned range-separated functional [77], etc. [78–81].
198
M. Swart