Figure 5. (a) Average desorption energy
(<Ed>) calculated with/without
ZPE as a function of cluster size, (b) Stepwise desorption energy
(ΔEd) and (c) activation barrier (Eb)
for MgmH2m (m = 3-6) clusters, (d)
Relation between stepwise desorption energy and activation barrier of
MgmH2m (m = 3-6) clusters.
To understand the kinetic properties of desorption reaction, we
calculate the barrier height (Eb) for each step of
desorption reaction of MgmH2m (m = 3-6)
clusters and the reaction profiles are shown in Figure. S1 (Supporting
information). Figure 5c shows the activation barrier as a function of
number of hydrogen atoms in the clusters. For
Mg6Hn, the activation barrier first
rises from 1.88 eV to 2.06 eV, and then decrease dramatically for
n<8. For Mg5Hn (n=8-4),
Mg4Hn and
Mg3Hn, the dissociation barrier tends to
be lower as the number of the adsorbed hydrogen atoms decreases, which
indicates that the hydrogen desorption reaction become more favorable.
This trend is similar to the change of the stepwise desorption energy
with the lower hydrogen content in the clusters. Figure 5d shows the
relation between the stepwise desorption energy and the dissociation
barrier. The scatter points are fitted with a linear function with the
slope of 1.459, intercept of -0.409 eV and mean absolute error (MAE) of
0.20 eV. The linear energy relation is so-called
Brønsted–Evans–Polanyi (BEP) relation, which describes the linear
correlations between transition states and reactions energies.