Chemistry Reference
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Fig. 9.13 Adiabatic potential energy for the [110]-complex along the minimum-energy path of
proton transfer between O atoms. The curve was obtained by a cubic spline fit to the calculated
data. As the proton transfers, the binding site of the original OH group changes gradually from the
bridge site to the top site, and that of the water molecule in the opposite way. The transition state
lies in the off-centered position along the path, resulting in the potential curvature of asymmetric
shape
energies (Fig.
9.12
). Since H atom is expected to move much faster than heavy
O and Cu atoms, the ZPE associated with the H atom transfer coordinate can be
calculated by determining the static PES, where the degrees of freedom except for
the shared H atom are frozen and the one-dimensional Schrödinger equations is
solved. The calculated ZPEs are 107 and 76 meV for the asymmetric and
symmetric configurations, respectively. The symmetric state has lower kinetic
energy by *30 meV and thus is stabilized in total energies (dashed lines). This
suggests barrier less motion of the shared proton and thus formation of a
symmetric H bond. The zero-point motion of the other degrees of freedom should
be taken into account, but we assume the effect of their classical treatment is minor
and negligible. I note that a D
2
O-OD complex appeared almost similar to an
H
2
O-OH in the STM image, suggesting that it is still in the symmetric configu-
ration, although the preference in the kinetic energy is reduced due to the doubled
mass. As mentioned in introduction, the most suitable method is path integral
ab initio calculation which can exactly take into account the ZPE of the system.
However, it requires the massive platform for the calculation. Therefore we
thought of ZPE in more feasible way.
For comparison, the adiabatic potential of a [110]-complex was also calculated
(Fig.
9.13
). The transfer of the shared H requires the change in the adsorption site
from the bridge (top) to top (bridge) for the original OH group (water molecule).
Therefore, the potential barrier is relatively high (0.2 eV), suggesting that the side-
on complex retains an asymmetric H bond (normal H bond). The present result has
an implication to the water-hydroxyl complexes formed at elevated temperatures
