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Fig. 2 Pourbaix diagram for
trans
-(bpy)
2
Ru(OH
2
)
2
2+
showing pKas (
vertical lines
)
and oxidation potentials (
bold
lines
) determined by cyclic
voltammetry [
33
] and our
calculated pKas and oxidation
potentials using DFT(MO6)
and Poisson-Boltzmann
continuum solvation (
red
).
Ru
III
/(OH)
2
denotes, for
example, the region of
stability of
trans
-
(bpy)
2
Ru
III
(OH)
2
1+
Ru
VI
1.0
(O)
2
0.8
Ru
IV
Ru
V
0.6
0.4
Ru
III
0.2
(OH
2
)
2
(OH)
2
E
1/2
0.0
-0.2
-0.4
-0.6
Ru
II
-0.8
(OH)
(OH
2
)
0
2
4
6
8
10
12
pH
of free energy. The changes in free energy associated with redox processes deter-
mine the driving force behind many catalytic cycles. Coupled with the energies of
transition states between intermediates, these tools allow
predictive
work in appli-
cations of homogeneous catalysis to problems in synthetic and energy-related
reactions. Given that spin-orbit coupling corrections are important for open-shell
wavefunctions of heavy elements and have been computed to useful accuracy [
37
],
such corrections may be incorporated into (5).
Having described a hybrid approach that integrates a first-level QM-DFT
approximation with a continuum-level implicit APBS solvation model, as a multi-
paradigm stratagem to study the effects of solvation on reactivity, we now return to
describing further approximations to (1).
2.2.2 Treat the Nuclei as Classical Particles Moving on a PES
The PES found via the adiabatic approximation described in the previous section
portrays the hyper landscape over which a nucleus moves, in the classical sense,
while under the influence of other nuclei of a particular system. This is useful for
describing vibrations or reactions. Electronic contributions have been averaged
into each point on the PES, and their effect considered for that particular nuclear
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