14
K. P. Kepp
to the SCO thermodynamics. This question can be directly addressed by dispersioncorrected DFT [91], because the dispersion energy correction is calculated explicitly
and is separated from the remaining electronic energy of the system [54].
Strained five-coordinate iron(III)porphyrins with variable substituted axial ligands have been studied with and without dispersion forces included [54]. It was
found that dispersion forces contribute already for the single molecule by affecting
the free energy gap of (2) by often 10 kJ/mol or more. Considering that the total
H SCO is in the order of 5–20 kJ/mol, this makes account of the dispersion forces
critical. Four of the porphines had axial phenyl ligands attached directly by Fe–C
bonds with 3–5 fluorides as phenyl substituents. This produces unusual short-range
interactions and clashes between the fluorine and hydrogen atoms and the porphyrin
ring in these particular systems.
However, with the advent of computational dispersion corrections to DFT, it was
discovered that also in most other, unstrained single molecules, intramolecular dispersion tends to favor LS due to the stronger electronic stabilization of the more
compact LS state [52]. This suggests that there is a generic, intrinsic contribution of
dispersion interactions to the SCO tendency arising for the first coordination sphere
of any complex of typically 5–15 kJ/mol which contributes to the real, observed T ½
[36, 52]. This contribution may then be compensated or increased by other ligand–ligand interactions. In bulky systems with ligand–ligand strain from close contacts,
which tend to expand the first coordination sphere and favor HS, dispersion will
further remedy some of the strain and reduce the expansion, and thus by itself favor
LS.
This discovery of a generic first coordination sphere dispersion contribution to
SCO arises because the attractive close-range dispersion energy favors the more
compact LS state more than the HS state. As an example of consequence, if dispersion
is included in B3LYP (as in B3LYP-D3), the SCO prediction becomes better because
the intrinsic first coordination sphere contribution to SCO is included and counteracts
the HS bias, and thus B3LYP-D3 is generally more accurate than B3LYP [36, 94].
It has now been found repeatedly that the dispersion forces of the SCO process
work to favor the LS state of the single-molecule first coordination sphere [36, 95, 96].
The effect can easily reach 15–20 kJ/mol and averages 10 kJ/mol for the 30SCOFE
database [36]. Thus, in order to model and predict the relative thermodynamics, SCO
tendency, and T ½ of a series of compounds, dispersion forces need to be explicitly
included.
3.3 Relativistic Stabilization of LS
Most studies of first-row transition metal systems do not include relativistic contributions to the energy. This is probably because relativistic effects are relatively
less important for Sc–Zn, and partly because relativistic computations can be very
demanding in terms of computational resources. However, relativistic effects can
be substantial already for the first row of the d-transition series [97], and, e.g., for
K. P. Kepp
to the SCO thermodynamics. This question can be directly addressed by dispersioncorrected DFT [91], because the dispersion energy correction is calculated explicitly
and is separated from the remaining electronic energy of the system [54].
Strained five-coordinate iron(III)porphyrins with variable substituted axial ligands have been studied with and without dispersion forces included [54]. It was
found that dispersion forces contribute already for the single molecule by affecting
the free energy gap of (2) by often 10 kJ/mol or more. Considering that the total
H SCO is in the order of 5–20 kJ/mol, this makes account of the dispersion forces
critical. Four of the porphines had axial phenyl ligands attached directly by Fe–C
bonds with 3–5 fluorides as phenyl substituents. This produces unusual short-range
interactions and clashes between the fluorine and hydrogen atoms and the porphyrin
ring in these particular systems.
However, with the advent of computational dispersion corrections to DFT, it was
discovered that also in most other, unstrained single molecules, intramolecular dispersion tends to favor LS due to the stronger electronic stabilization of the more
compact LS state [52]. This suggests that there is a generic, intrinsic contribution of
dispersion interactions to the SCO tendency arising for the first coordination sphere
of any complex of typically 5–15 kJ/mol which contributes to the real, observed T ½
[36, 52]. This contribution may then be compensated or increased by other ligand–ligand interactions. In bulky systems with ligand–ligand strain from close contacts,
which tend to expand the first coordination sphere and favor HS, dispersion will
further remedy some of the strain and reduce the expansion, and thus by itself favor
LS.
This discovery of a generic first coordination sphere dispersion contribution to
SCO arises because the attractive close-range dispersion energy favors the more
compact LS state more than the HS state. As an example of consequence, if dispersion
is included in B3LYP (as in B3LYP-D3), the SCO prediction becomes better because
the intrinsic first coordination sphere contribution to SCO is included and counteracts
the HS bias, and thus B3LYP-D3 is generally more accurate than B3LYP [36, 94].
It has now been found repeatedly that the dispersion forces of the SCO process
work to favor the LS state of the single-molecule first coordination sphere [36, 95, 96].
The effect can easily reach 15–20 kJ/mol and averages 10 kJ/mol for the 30SCOFE
database [36]. Thus, in order to model and predict the relative thermodynamics, SCO
tendency, and T ½ of a series of compounds, dispersion forces need to be explicitly
included.
3.3 Relativistic Stabilization of LS
Most studies of first-row transition metal systems do not include relativistic contributions to the energy. This is probably because relativistic effects are relatively
less important for Sc–Zn, and partly because relativistic computations can be very
demanding in terms of computational resources. However, relativistic effects can
be substantial already for the first row of the d-transition series [97], and, e.g., for