Chemistry Reference
In-Depth Information
Fig. 10.10
Calculated vibrational mode for an H
2
O-(OH)
2
and D
2
O-(OH)
2
on a Cu(110) surface
!
ð
10
:
9
Þ
ðj
eV
j
X
Þ
2
2r
ph
1
r
ph
q
ph
ð
X
;
r
ph
; x
Þ¼
p
exp
2p
The motivatiobn for a Gaussian distribution is to take into account all broad-
ening effects in a single parameter q
ph
, in particular the nature of the broad
spectrum of the OH (OD) stretch mode in a single hydrogen bond, but also other
effects such as temperature, intrinsic life-time broadening, and instrumental ones
[
10
]. Finally, when several, distinct vibration modes are involved in the process,
the total reaction yield should be expressed as the sum over the accepting modes
contributions:
Z
j
eV
j
X
Y
ð
V
Þ¼
1
V
K
eff
q
i
ph
ð
X
i
;
r
i
ph
; x
Þðj
eV
j
hx
Þ
ð
10
:
10
Þ
0
i
Here the index i represents the specific vibration mode. Figure
10.9
is sche-
matic expression of Eq.
10.10
. We can find a broad (narrow) distribution of the
vibrational density of state (DOS) results in a moderate (rapid) increase in the
reaction yield.
10.2.6 The Mechanism of Hydrogen-Atom Relay Reactions
As shown by the solid curves in Fig.
10.8
a, Eq.
10.10
reproduces the experimental
data using the parameters given in the Table
10.1
. These parameters suggest that
three characteristic vibrational modes (free OH/OD stretch, OH*/OD* stretch, and
H
2
O scissors, where H*/D* denotes the shared H/D atom in the H bond) are
involved in the relay reaction in the range of voltages where the transfer yield
could be observed. The observed onset around 430 [320] mV for an H
2
O-(OH)
2
[D
2
O-(OD)
2
] can be associated with the free OH [OD] stretch mode. At lower
voltages we assign modes centered at 310 and 262 meV for H
2
O-(OH)
2
and D
2
O-
(OD)
2
to the shared OH*/OD* stretch modes. In the case of H
2
O-(OH)
2
a third
mode around 213 meV is taken into account and associated with the H
2
O scissors
mode. On the other hand, for D
2
O-(OD)
2
the scissors mode is well below the
voltage range where the yield is observable. It is noted that the OH*/OD* stretch
modes
are
significantly
red-shifted
from
the
free
OH/OD
stretch
and
also
