Chemistry Reference
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interchange events. The distribution of the time intervals between the events was
obtained at several different tunneling currents (gap resistance), and three of them
are shown in Fig.
5.8
b. Fitting the distribution to an exponential decay function
provides the interchange rate. Here the slope represents the rate because the
vertical axis in Fig.
5.8
b is logarithmic scale. The slopes in Fig.
5.8
b are almost
independent on the three tunneling currents, indicating the tip effect to the inter-
change is negligible under the tunneling conditions employed. The interchange
rate is determined to be (6.0 ± 0.6) 9 10 s
-1
for an (H
2
O)
2
, while it is 1.0 ±
0.6 s
-1
for a (D
2
O)
2
. Thus the isotope ratio of the interchange rate is *60. Such a
large isotope ratio indicates the process involves quantum tunneling.
It is assumed that the donor-acceptor interchange proceeds in a double-well
potential as schematically shown in Fig.
5.8
f. The DFT calculations predict the
transition state of C
2v
symmetry, and the barrier is calculated to be 23 kJ/mol on a
Cu(110) surface while it is 21 kJ/mol on Pd(111). These barriers cannot be
overcome via mere thermal process at experimental temperature, 6 K, being
consistent with the interpretation that the interchange includes quantum tunneling.
In the meantime, the interchange rate of a gas-phase (H
2
O)
2
estimated from the
tunneling splitting in vibration-rotation-tunneling spectra is 10
9
s
-1
. The reduction
of the rate by seven orders of magnitude partly results from the increase in the
barrier height from 2.48 kJ/mol (gas-phase value) to 23 kJ/mol. In contrast to free
dimers, the interchange requires substantial displacement of oxygen atoms for
dimers adsorbed on surfaces. For a water dimer on Pd(111), the interchange
process was divided into two, which were treated separately with classical and
quantum models [
12
]. This hypothesis succeeded in rationalizing an anomalously
higher mobility of water dimer than the monomer on Pd(111) at 40 K. For the
dimer on Cu(110), however, the displacement of the acceptor molecule may be
restricted due to relatively high barrier of 8 kJ/mol. Additionally, the azimuthal
rotation of the acceptor around the donor, as observed on Pd(111), is inhibited on
Cu(110) due to the anisotropic structure. I propose that tunneling proceeds along
the optimal directions on the multidimensional potential energy surface with
motions not only of hydrogen but also of oxygen atoms [
15
]. The multidimen-
sional treatment of the tunneling process is essential for the quantitative descrip-
tion of the interchange motion.
I now turn to the voltage dependence of the interchange rate. Figure
5.8
c shows
the rate as a function of applied bias voltage. The rate shows no dependence and
increase below and above 40 mV, respectively. The threshold voltage of the
increase is determined to be 45 ± 1 (41 ± 1) mV for an H
2
O(D
2
O) dimer. The
current dependence of the rate at V
s
= 54 mV is also investigated (Fig.
5.8
d). The
rate is plotted as a function of tunneling current, where the intrinsic contribution
(60 s
-1
) is subtracted from the rate to evaluate the interchange induced by
tunneling electron. The interchange rate shows a linear dependence onto tunneling
current, indicating that the interchange is induced via a single-electron process.
For comparison, the rate at V
s
= 24 mV is also shown in Fig.
5.8
d, which shows
no dependence on tunneling current. The same dependence is observed at the
negative
bias
region.
The
above
results
indicate
the
enhancement
of
the
