The Electronic Determinants of Spin Crossover Described …
13
More systematic studies of the ZPE contribution indicate that the differential ZPE
is very dependent on the type ligand and to a lesser extent the type of metal ion [52]:
Typical differential ZPEs in favor of HS range from 5 to 25 kJ/mol and grow more
or less monotonically with the ligand field strength. Accordingly, for weak ligands
such as halides, the differential ZPE can be almost neglected, whereas for strong-field
π-acceptor ligands such as CN
− and CO, the ZPE dramatically favors HS by more
than 20 kJ/mol. Thus, the importance of remembering the ZPE correction depends
very much on the system of interest. This follows trivially from the fact that the
ZPE scales monotonically with the overall strength of the M–L bond, which again
scales with the ligand field strength. In the middle range, typical ligands relevant to
SCO systems have differential ZPEs of 10–15 kJ/mol [52]. The ZPE can also vary
by >10 kJ/mol due to metal ion and d
q configuration. This also affects the bond
strengths of the M–L bonds in the two spin states, but since these d
q configurations
vary substantially in terms of electronic structure and some, such as HS Mn(III) and
LS Co(II) induce strong Jahn–Teller distortions, this metal effect is not trivial to
interpret.
3.2 Dispersion Contributions to the Spin Crossover
Equilibrium
Dispersion effects are the second-order interaction of instantaneously induced dipole
moments of electron densities that affect bonding in all systems. Dispersion is not
intrinsically included in most modern density functionals, and the most popular
way to do so is by using an empirically parameterized correction to the electronic
energies computed by the functional, such as the popular D3 correction by Grimme
and coworkers [91]. Within the last decade, dispersion corrections have become
increasingly mandatory in DFT calculations of chemical structure and reactivity.
Since the dispersion forces contribute substantially to the intermolecular interactions, their inclusion is important if one wants to understand the transition behavior
[92, 93]. Dispersion interactions also affect T ½ itself, by favoring either HS or LS.
Depending on the nature of the ligands and their packing, dispersion forces will
either compress or expand the first coordination sphere, shifting the potential energy
surface either toward longer M–L bonds to favor HS or to shorter M–L bonds favoring LS. The favoring of HS or LS may be very dependent on the intermolecular
ligand–ligand interactions.
A priori, dispersion effects might not be expected to contribute to the SCO tendency of single molecules in solution with simple monodentate ligands having no
systematic steric strain. Dispersion would be expected to mainly affect closely interacting parts of different molecules, or bulky parts of the same molecule. With the
advent of empirical dispersion corrections of DFT, one could explore whether dispersion forces also contribute to this important process even at the single-molecule
level, i.e., if there is a generic first coordination sphere contribution from dispersion
13
More systematic studies of the ZPE contribution indicate that the differential ZPE
is very dependent on the type ligand and to a lesser extent the type of metal ion [52]:
Typical differential ZPEs in favor of HS range from 5 to 25 kJ/mol and grow more
or less monotonically with the ligand field strength. Accordingly, for weak ligands
such as halides, the differential ZPE can be almost neglected, whereas for strong-field
π-acceptor ligands such as CN
− and CO, the ZPE dramatically favors HS by more
than 20 kJ/mol. Thus, the importance of remembering the ZPE correction depends
very much on the system of interest. This follows trivially from the fact that the
ZPE scales monotonically with the overall strength of the M–L bond, which again
scales with the ligand field strength. In the middle range, typical ligands relevant to
SCO systems have differential ZPEs of 10–15 kJ/mol [52]. The ZPE can also vary
by >10 kJ/mol due to metal ion and d
q configuration. This also affects the bond
strengths of the M–L bonds in the two spin states, but since these d
q configurations
vary substantially in terms of electronic structure and some, such as HS Mn(III) and
LS Co(II) induce strong Jahn–Teller distortions, this metal effect is not trivial to
interpret.
3.2 Dispersion Contributions to the Spin Crossover
Equilibrium
Dispersion effects are the second-order interaction of instantaneously induced dipole
moments of electron densities that affect bonding in all systems. Dispersion is not
intrinsically included in most modern density functionals, and the most popular
way to do so is by using an empirically parameterized correction to the electronic
energies computed by the functional, such as the popular D3 correction by Grimme
and coworkers [91]. Within the last decade, dispersion corrections have become
increasingly mandatory in DFT calculations of chemical structure and reactivity.
Since the dispersion forces contribute substantially to the intermolecular interactions, their inclusion is important if one wants to understand the transition behavior
[92, 93]. Dispersion interactions also affect T ½ itself, by favoring either HS or LS.
Depending on the nature of the ligands and their packing, dispersion forces will
either compress or expand the first coordination sphere, shifting the potential energy
surface either toward longer M–L bonds to favor HS or to shorter M–L bonds favoring LS. The favoring of HS or LS may be very dependent on the intermolecular
ligand–ligand interactions.
A priori, dispersion effects might not be expected to contribute to the SCO tendency of single molecules in solution with simple monodentate ligands having no
systematic steric strain. Dispersion would be expected to mainly affect closely interacting parts of different molecules, or bulky parts of the same molecule. With the
advent of empirical dispersion corrections of DFT, one could explore whether dispersion forces also contribute to this important process even at the single-molecule
level, i.e., if there is a generic first coordination sphere contribution from dispersion