Chemistry Reference
In-Depth Information
Fig. 9.1 Grotthuss mechanism. ''Structural diffusion'' of an excess proton through the H-bond
network of water molecules. The process includes the sequential cleavage and formation of
covalent bond
and the strength can be classified by d
O-O
. For normal H bond, the d
O-O
is *2.8 Å
and the double-well potential with a relatively high barrier is expected, where the
H atom is covalently bonded to one of the O atoms (Fig.
9.3
a). The ground state of
the shared H is much below than the barrier and the wave packet is localized in one
well. In this case H transfer takes place via the over-barrier or tunneling process.
On the other hand, when the d
O-O
becomes *2.5 Å, the H transfer barrier is
significantly reduced and the zero-point nuclear motion plays a decisive role
(Fig.
9.3
b). In this situation the zero-point energy (ZPE) overcomes the reduced
barrier and the probability amplitude of the shared H/proton is localized around the
center of two O atoms. This type of H bond is called ''a low barrier
H bond'' or ''a symmetric H bond'', where the H transfer via tunneling is
negligible and the simple transition-state theory no longer works. The smaller
d
O-O
, less than 2.5 Å, results in a single-well potential and a very strong H bond.
The strength of H bonds is characterized by a significant red-shift of m(OH).
H-bonded complexes H
5
O
2
+
and H
3
O
2
-
are considered as a prototype to
examine such a strong H bonding. Tuckerman et al. highlighted the impact of
quantum nature of the shared proton in H
5
O
2
+
and H
3
O
2
-
[
3
]. They investigated
the relative influence of thermal and quantum fluctuations on the proton transfer
with ab initio path-integral molecular dynamics (PIMD). In PIMD, both the
electrons and nuclei are treated as quantum particles in contrast to traditional
molecular dynamics in which the nuclei are treated as classical point-like particles
(only electrons are treated as quantum particles). The PIMD calculations predicted
that no barrier exists for the shared proton in H
5
O
2
+
and results in a strong H bond,
while H
3
O
2
-
forms ''a low-barrier H bond'' and the ZPE plays a crucial role. Such
a symmetric H bond is actually observed in the x-ray diffraction of a compressed
ice, wherein the d
O-O
reached 2.4 Å under * 60 GPa [
9
]. Additionally, isotope
substitution of the shared H into deuterium has a significant impact on the strength
of H-bond because of the influence of the mass on tunneling rates, the ZPE, and
the motional properties. Indeed, many isotope effects are found in kinetics and
even for geometrical parameters of H-bonded systems; the latter is known as the
Ubbelohde effect [
10
]. Although this kind of structural isotope effect virtually
