states [169], the resting state and adding 1–4 electrons (E 0 -E 4 ) with at least 50 possible positions for the proton for each case [170], and a combination of molecular
dynamics, quantum mechanical (QM) cluster, combined QM and molecular
mechanics (QM/MM), QM/MM with Poisson-Boltzmann and surface area solvation, QM/MM thermodynamic cycle perturbations, and quantum refinement
methods to settle the most probable protonation state of the homocitrate ligand in
nitrogenase [171]. They needed this diversified approach because the DFAs used
typically in the study on nitrogenase show no consensus on where the protons should
go in the E 0 –E 4 states; the primary reason for this is that the DFAs give relative
energies that differ by close to 140 kcal mol
À1 (!!) [172], which is 4–30 times larger
than what is observed for other systems. It is caused mainly because the hydrogens
can bind as protons to carbides or sulfides or as hydrides to metals. The preference
for one or the other seemed to correlate with the amount of HF exchange present in
the DFA, but without a clear conclusion which DFA gives the best results for
nitrogenase. Some gave better results for the structures, while others gave better
results for the H 2 dissociation energies. Most importantly, no DFA was able to
predict the stability of an E 4 structure with two bridging hydride ions as lowest in
energy, as spectroscopic experiments indicated [172].
4 Multi-state Reactivity
Most reactions in chemistry follow a single potential energy surface, because in
general these spin-allowed reactions are much faster than spin-forbidden alternatives
[173]. However, sometimes the spin-forbidden reactions are favored with spinswitching accelerating the reactions or allowing them thermodynamically; this is
in particular true when the reactions are carried out in the gas phase or when
(transition) metals are involved. For instance, for the energy profiles shown in
Fig. 6, the favored spin state of the reactant shows a larger barrier for the reaction
than the other spin state. Therefore, during the reaction, it may be favorable to switch
spin states through, e.g., a MECP or spin-orbit coupling (see Sects. 2.1.1 and 2.1.2),
which has a much smaller energetic cost than the reaction barrier; after the barrier has
been passed, the reaction can proceed following the same spin state, or with a second
spin-state switching, the original spin state can be retrieved. Much depends on the
kinetic energy with which the complex goes down after the barrier, the exothermicity
of the reaction on both spin states, and the temperature at which the reaction takes
place. The reactions of, e.g., MH
+ with methane (M ¼ Fe, Co, Ni) in the gas phase
are good examples [173, 174] of these spin-forbidden reactions; with FeH
+ and
CoH
+
, the barrier of the starting spin state (Fig. 6, in red, quintet for FeH
+
, quartet for
CoH
+
) shows a large barrier, where in the gas phase there is not enough energy
available to surmount it. Switching spin state also does not help because also the
lower-spin state (Fig. 6, in blue, triplet for FeH
+
, doublet for CoH
+
) still has to cross
a barrier that is higher in energy than is available (Fig. 6, left). For NiH
+ on the other
hand, the spin-state switching from the triplet (red) to singlet (blue) state leads to a
206
M. Swart
dynamics, quantum mechanical (QM) cluster, combined QM and molecular
mechanics (QM/MM), QM/MM with Poisson-Boltzmann and surface area solvation, QM/MM thermodynamic cycle perturbations, and quantum refinement
methods to settle the most probable protonation state of the homocitrate ligand in
nitrogenase [171]. They needed this diversified approach because the DFAs used
typically in the study on nitrogenase show no consensus on where the protons should
go in the E 0 –E 4 states; the primary reason for this is that the DFAs give relative
energies that differ by close to 140 kcal mol
À1 (!!) [172], which is 4–30 times larger
than what is observed for other systems. It is caused mainly because the hydrogens
can bind as protons to carbides or sulfides or as hydrides to metals. The preference
for one or the other seemed to correlate with the amount of HF exchange present in
the DFA, but without a clear conclusion which DFA gives the best results for
nitrogenase. Some gave better results for the structures, while others gave better
results for the H 2 dissociation energies. Most importantly, no DFA was able to
predict the stability of an E 4 structure with two bridging hydride ions as lowest in
energy, as spectroscopic experiments indicated [172].
4 Multi-state Reactivity
Most reactions in chemistry follow a single potential energy surface, because in
general these spin-allowed reactions are much faster than spin-forbidden alternatives
[173]. However, sometimes the spin-forbidden reactions are favored with spinswitching accelerating the reactions or allowing them thermodynamically; this is
in particular true when the reactions are carried out in the gas phase or when
(transition) metals are involved. For instance, for the energy profiles shown in
Fig. 6, the favored spin state of the reactant shows a larger barrier for the reaction
than the other spin state. Therefore, during the reaction, it may be favorable to switch
spin states through, e.g., a MECP or spin-orbit coupling (see Sects. 2.1.1 and 2.1.2),
which has a much smaller energetic cost than the reaction barrier; after the barrier has
been passed, the reaction can proceed following the same spin state, or with a second
spin-state switching, the original spin state can be retrieved. Much depends on the
kinetic energy with which the complex goes down after the barrier, the exothermicity
of the reaction on both spin states, and the temperature at which the reaction takes
place. The reactions of, e.g., MH
+ with methane (M ¼ Fe, Co, Ni) in the gas phase
are good examples [173, 174] of these spin-forbidden reactions; with FeH
+ and
CoH
+
, the barrier of the starting spin state (Fig. 6, in red, quintet for FeH
+
, quartet for
CoH
+
) shows a large barrier, where in the gas phase there is not enough energy
available to surmount it. Switching spin state also does not help because also the
lower-spin state (Fig. 6, in blue, triplet for FeH
+
, doublet for CoH
+
) still has to cross
a barrier that is higher in energy than is available (Fig. 6, left). For NiH
+ on the other
hand, the spin-state switching from the triplet (red) to singlet (blue) state leads to a
206
M. Swart