12
K. P. Kepp
by Sorai [24]. The intrinsic hysteresis probably reflects the simple volume reordering
effects of the first coordination sphere, which is approximately similar for all SCO
systems (although the expansion depends on ligand and metal type as discussed
above). Additional contributions to T ½ can arise from larger reorganizations due
to bulky groups or intermolecular interactions beyond the local volume changes of the
first coordination sphere that is generic to all SCO systems; this distinction between
two parts of the hysteresis (which is, as a disclaimer, only the author’s view) probably
warrants further exploration.
As shown in Fig. 3b, Fe(II) systems exhibit some of the largest geometric changes
upon SCO among d
4 –d
7 systems [52]. Consistent with the volume-friction interpretation discussed above, this probably explains why Fe(II) more commonly displays
hysteresis in comparison with other SCO systems [2]. This observation seems to confirm that hysteresis at least partly arises from the geometric friction of the heating
and cooling processes caused by the different free energy minima at different molar
volumes for HS and LS. The intermolecular interactions that define the transition
are diverse and harder to systematize than the electronic structure of the molecule
itself, but the intrinsic contribution from the first coordination sphere, as discussed
above, seems to be predictable by DFT, which computes geometric changes with
good accuracy.
3 Important Contributions to Single-Molecule SCO
3.1 Zero-Point Vibrational Energy
The vibrational zero-point energy (ZPE) is one of the electronic effects that always
contribute to the SCO tendency regardless of the environment. It has been known
for a long time, and was described clearly in the pioneering DFT work on SCO by
Paulsen et al. [34], that the differential ZPE of the HS and LS states is an important
contribution to the SCO process. This paper also reported the strong bias toward
LS of the non-hybrid GGA functionals and the preference for HS for the hybrid
B3LYP functional, an important observation that, for example, motivated the later
development of the B3LYP* functional by Reiher et al. with a smaller 15% HF
exchange [60].
The importance of ZPE lies both in the fact that its magnitude is of the order
of 10 kJ/mol [34, 64], similar to the typical values of the full H SCO [36], and it
is systematic, as it almost exclusively favors the HS state. This favoring follows
directly from the longer and weaker M–L bonds of the HS state, which accordingly
have smaller ZPEs than the LS states. Not only the SCO process but also a general
chemical process involving multiple spin states will experience this effect. On an
energy profile of competing spin states, neglect of ZPE will tend to provide an
artificial bias in favor of the LS states in the reaction coordinate diagram.
K. P. Kepp
by Sorai [24]. The intrinsic hysteresis probably reflects the simple volume reordering
effects of the first coordination sphere, which is approximately similar for all SCO
systems (although the expansion depends on ligand and metal type as discussed
above). Additional contributions to T ½ can arise from larger reorganizations due
to bulky groups or intermolecular interactions beyond the local volume changes of the
first coordination sphere that is generic to all SCO systems; this distinction between
two parts of the hysteresis (which is, as a disclaimer, only the author’s view) probably
warrants further exploration.
As shown in Fig. 3b, Fe(II) systems exhibit some of the largest geometric changes
upon SCO among d
4 –d
7 systems [52]. Consistent with the volume-friction interpretation discussed above, this probably explains why Fe(II) more commonly displays
hysteresis in comparison with other SCO systems [2]. This observation seems to confirm that hysteresis at least partly arises from the geometric friction of the heating
and cooling processes caused by the different free energy minima at different molar
volumes for HS and LS. The intermolecular interactions that define the transition
are diverse and harder to systematize than the electronic structure of the molecule
itself, but the intrinsic contribution from the first coordination sphere, as discussed
above, seems to be predictable by DFT, which computes geometric changes with
good accuracy.
3 Important Contributions to Single-Molecule SCO
3.1 Zero-Point Vibrational Energy
The vibrational zero-point energy (ZPE) is one of the electronic effects that always
contribute to the SCO tendency regardless of the environment. It has been known
for a long time, and was described clearly in the pioneering DFT work on SCO by
Paulsen et al. [34], that the differential ZPE of the HS and LS states is an important
contribution to the SCO process. This paper also reported the strong bias toward
LS of the non-hybrid GGA functionals and the preference for HS for the hybrid
B3LYP functional, an important observation that, for example, motivated the later
development of the B3LYP* functional by Reiher et al. with a smaller 15% HF
exchange [60].
The importance of ZPE lies both in the fact that its magnitude is of the order
of 10 kJ/mol [34, 64], similar to the typical values of the full H SCO [36], and it
is systematic, as it almost exclusively favors the HS state. This favoring follows
directly from the longer and weaker M–L bonds of the HS state, which accordingly
have smaller ZPEs than the LS states. Not only the SCO process but also a general
chemical process involving multiple spin states will experience this effect. On an
energy profile of competing spin states, neglect of ZPE will tend to provide an
artificial bias in favor of the LS states in the reaction coordinate diagram.