Reaction of aluminum clusters with water.

Abstract

The atomistic mechanism of rapid hydrogen production from water by an aluminum cluster is investigated by ab initio molecular dynamics simulations on a parallel computer. A low activation-barrier mechanism of hydrogen production is found, in which a pair of Lewis acid and base sites on the cluster surface plays a crucial role. Hydrogen production is assisted by rapid proton transport in water via a chain of hydrogen-bond switching events similar to the Grotthuss mechanism, where hydroxide ions are converted to water molecules at the Lewis-acid sites and hydrogen atoms are supplied at the Lewis-base sites. The activation free energy is estimated along various reaction paths associated with hydrogen production, and the corresponding reaction rates are discussed based on the transition state theory.

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THE JOURNAL OF CHEMICAL PHYSICS 134, 244702 (2011)
Reaction of aluminum clusters with water
Satoshi Ohmura,1,2Fuyuki Shimojo,1,2,a)Rajiv K. Kalia,1Manaschai Kunaseth,1
Aiichiro Nakano,1,b)and Priya Vashishta1
1Collaboratory for Advanced Computing and Simulations, Department of Physics & Astronomy,
Department of Chemical Engineering & Materials Science, and Department of Computer Science,
University of Southern California, Los Angeles, California 90089-0242, USA
2Department of Physics, Kumamoto University, Kumamoto 860-8555, Japan
(Received 16 February 2011; accepted 2 June 2011; published online 22 June 2011)
The atomistic mechanism of rapid hydrogen production from water by an aluminum cluster is inves-
tigated by ab initio molecular dynamics simulations on a parallel computer. A low activation-barrier
mechanism of hydrogen production is found, in which a pair of Lewis acid and base sites on the clus-
ter surface plays a crucial role. Hydrogen production is assisted by rapid proton transport in water
via a chain of hydrogen-bond switching events similar to the Grotthuss mechanism, where hydroxide
ions are converted to water molecules at the Lewis-acid sites and hydrogen atoms are supplied at the
Lewis-base sites. The activation free energy is estimated along various reaction paths associated with
hydrogen production, and the corresponding reaction rates are discussed based on the transition state
theory. © 2011 American Institute of Physics. [doi:10.1063/1.3602326]
I. INTRODUCTION
Exothermic reaction of metal particles with water pro-
duces hydrogen,1–5and the understanding of its atomistic
mechanism has gained importance in the context of renew-
able energy.6,7Meanwhile, it has been realized that the chem-
ical reactivity at the nanoscale differs drastically from its
macroscopic counterpart.8–10For example, flame propaga-
tion speeds for metallic nanoparticles embedded in oxidiz-
ers are accelerated to km/s, compared with cm/s in the case
of micron-size particles.11Such rapid nano-reaction cannot
be explained by conventional mechanisms based on mass
diffusion of reactants, and thus various mechanisms for en-
hanced nano-energetic reactions have been proposed.11–13For
the case of aluminum (Al) clusters in oxidizers, these nano-
reaction mechanisms include accelerated mass transport due
to large residual stresses.11–13Furthermore, metal nanoclus-
ters possess catalytic behaviors that are distinct from larger
particles.14–16A remarkable example is size-selective reac-
tivity of Al clusters with water,17,18where an anion of the
Al cluster, Al−
with water molecules in gas phase. The enhanced reactiv-
ity has been attributed to the dissociative chemisorption of
water at two specific surface sites that, respectively, act as
a Lewis acid and a Lewis base where OH and H preferen-
tially bind.17,18In the proposed gas-phase reaction mecha-
nism with the adsorption of multiple water molecules onto
an Al17cluster, the energy barrier of the production of H2
from two H atoms generated on the cluster surface has been
estimated to be about 1 eV.17How the reactivity of these Al
“superatoms”17,19changes in bulk water is of great interest
both scientifically and technologically.
Here, we perform ab initio molecular dynamics simu-
lations on a parallel computer to study the reaction of an
n(for instance, n = 12 or 17), reacts strongly
a)Electronic mail: shimojo@kumamoto-u.ac.jp.
b)Electronic mail: anakano@usc.edu.
Al17cluster in bulk water, with the goal of exploring differ-
ent mechanisms with more enhanced reactivity than the gas-
phase mechanism mentioned above. We find rapid hydrogen-
production processes, which are assisted by rapid proton
transport20,21via a chain of hydrogen-bond switching events
similar to the Grotthuss mechanism.22–24Although one of the
hydrogen-production reactions observed in our molecular dy-
namics (MD) simulations has been reported earlier,25this pa-
per is the first to provide a full description of all the reaction
processes.
II. METHOD OF CALCULATION
The electronic states are calculated using the projector-
augmented-wave (PAW) method,26,27which is an all-electron
electronic-structure-calculation method within the frozen-
core approximation. In the framework of density functional
theory, the generalized gradient approximation28is used
for the exchange-correlation energy with non-linear core
corrections.29The momentum-space formalism is utilized,30
where the plane-wave cutoff energies are 30 and 250 Ry
for the electronic pseudo-wave functions and the pseudo-
charge density, respectively. The energy functional is mini-
mized iteratively using a preconditioned conjugate-gradient
method.31,32The ? point is used for Brillouin zone sampling.
Projector functions are generated for the 3s, 3p, and 3d states
of Al, the 2s and 2p states of O, and the 1s state of H.
The electronic-structure-calculation code has been im-
plemented on parallel computers32by a hybrid approach
combining spatial decomposition (i.e., distributing real-space
or reciprocal-space grid points among processors) and band
decomposition (i.e., assigning the calculations of different
Kohn-Sham orbitals to different processors). The program has
been implemented using the message passing interface library
for interprocessor communications. The 6 ps simulations
0021-9606/2011/134(24)/244702/8/$30.00© 2011 American Institute of Physics
134, 244702-1
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244702-2Ohmura et al.J. Chem. Phys. 134, 244702 (2011)
FIG. 1. Snapshot of the Al17+ water system, where green, red, and white
spheres represent aluminum, oxygen, and hydrogen atoms, respectively.
reported here took 400 h on 64 AMD Opteron (2.33 GHz)
processors.
MD simulations are carried out at temperatures of
300, 500, and 1000 K in the canonical ensemble using
the Nosè-Hoover thermostat technique.33,34The equations
of motion are integrated numerically using an explicit re-
versible integrator35with a time step of 11 a.u. (∼0.264 fs).
The system studied in our MD simulations consists of
an Al17 cluster and 84 H2O molecules (in total of
269 atoms) in a box of dimensions 12.58 ×12.58 × 18.87 Å3
(see Fig. 1). The system size is determined from the density
of water in the ambient condition, and periodic boundary con-
ditions are imposed.
To quantify the change in the bonding properties of
atoms associated with the hydrogen-production reaction, we
use a bond-overlap population analysis36,37by expanding the
electronic wave functions in an atomic-orbital basis set.38,39
Based on the formulation generalized to the PAW method,40
we obtain the gross population Zi(t) for the ith atom and
the bond-overlap population Oij(t) for a pair of ith and jth
atoms as a function of time t. From Zi(t), we estimate the
charge of atoms, and Oij(t) gives a semi-quantitative estimate
of the strength of covalent bonding between atoms. As the
atomic-basis orbitals, we use numerical pseudo-atomic or-
bitals, which are obtained for a chosen atomic energy so that
the first node occurs at the desired cutoff radius.41To increase
FIG. 2. Time evolution of the number of chemical bonds NbH–H(t) for H–H.
Two atoms are considered bonded when their distance is less than a cutoff
distance Rc= 1.0 Å during a prescribed bond lifetime of 24 fs. (See Ref. 20.)
the efficiency of the expansion, the numerical basis orbitals
are augmented with the split-valence method.42The resulting
charge spillage, which estimates the error in the expansion, is
only 0.3%, indicating the high quality of the basis orbitals.
III. RESULTS AND DISCUSSION
A. Hydrogen-production processes
In our simulation at room temperature (300 K), six wa-
ter molecules bond to the Al cluster. Formation of these
Al–O bonds enhances the Lewis-base character of Al atoms
that are not connected to the water molecules, thereby pre-
venting further bonding of water molecules to the Al clus-
ters. Dissociation of water molecules is not observed within
the limited simulation time (several ps) at this temperature.
Even when the temperature is raised to 500 K, still no water
molecule dissociates. The atomistic process of hydrogen pro-
duction is successfully observed in MD simulation at 1000 K.
Figure 2 shows the time evolution of the number of chem-
ical bonds between two H atoms. In total, three hydrogen
molecules are produced at 1.54, 3.45, and 3.51 ps, within the
simulation time of 6 ps. As a reference, we have simulated
water without an Al cluster at the same temperature. This
simulation did not produce any hydrogen molecule, and it is
therefore concluded that the Al cluster is necessary for the
hydrogen production even at such a high temperature. Below,
we describe the reaction processes observed in the MD sim-
ulation at 1000 K in detail in order to discuss reaction paths
for hydrogen production. Here, we use the high-temperature
simulation as a way to find transition paths in a very complex
system within the timescale accessible to MD simulation. We
will then discuss the kinetics of the reactions related to hy-
drogen production at room temperature based on the energy
barriers along the found reaction paths, as will be discussed
in Sec. III B.
To find the production mechanism of the three hydrogen
molecules, we investigate the time evolution of atomic config-
uration along with bond-overlap populations Oij(t). Figure 3
shows the production process of the first hydrogen molecule
observed at 1.54 ps. In the snapshot at 1.48 ps (Fig. 4), one
H atom labeled “H1” bonds to an Al atom labeled “Al1,” and
one water molecule consisting of H2, H3, and O1 bonds to
another Al atom labeled "Al3." In Fig. 3, Oij(t) for H1–Al1
and O1–Al3, as well as those for O1–H2 and O1–H3
within the water molecule, take finite values for t < 1.5 ps,
signifying chemical bonds between these atoms. At about
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244702-3 Reaction of aluminum clusters with waterJ. Chem. Phys. 134, 244702 (2011)
FIG. 3. Production process of the first hydrogen molecule on the Al clus-
ter observed in MD simulation. Time evolution of bond-overlap populations
Oij(t) associated with atoms labeled in the snapshots of atomic configurations
in Fig. 4.
1.5 ps, OH1–H2(t) and OH1–Al2(t) begin to increase (Al2 is an
Al atom adjacent to Al3), and at the same time OH1–Al1(t)
decreases rapidly. In the snapshot at 1.52 ps in Fig. 4, H1
atom bonds partially to those three (H2, Al1, and Al2) atoms.
While OH1–Al2(t) decreases after 1.52 ps, OH1–H2(t) contin-
ues to increase and maintains a quite large value ∼0.8 after
1.54 ps, i.e., a hydrogen molecule (H1–H2) is formed as
shown in the snapshots at 1.54 and 1.6 ps in Fig. 4. The chem-
ical bond between O1 and Al3 strengthens as OO1–Al3(t) ex-
ceeds 0.8, which is accompanied by the breakage of one of the
O–H bonds (O1–H2) in the water molecule, leaving a hydrox-
ide ion (O1–H3) at 1.54 ps. Subsequently, the OH group turns
into a H2O molecule by the Grotthuss mechanism22–24with
another hydrogen atom (H4) supplied by surrounding water
molecules (see the snapshot at 1.6 ps in Fig. 4). OO1–H4(t)
increases gradually after 1.55 ps, and simultaneously
OO1–Al3(t) decreases. This hydrogen-production reaction is
summarized as
Al−OH2+ Al−H → Al−OH + Al + H2.
As mentioned above, it is notable that the Al–OH prod-
uct of this reaction thermally fluctuates back to Al–OH2, the
mechanism of which will be elucidated below.
The production mechanism of the second hydrogen
molecule observed at 3.45 ps is almost the same as that of
the first molecule. Figures 5 and 6 respectively, show the time
evolution of Oij(t) and the atomic configuration in the produc-
tion process of the second molecule. In the atomic configu-
ration at 3.40 ps (Fig. 6), a H atom H5 is attached to an Al
atom Al4, and a water molecule, consisting of O2, H6, and
H7, is attached to another Al atom Al5. The chemical bonds
for H5–Al4 and O2–Al5, as well as those for O2–H6 and
O2–H7 within the water molecule, are reflected in the fi-
nite values of Oij(t) between these atoms for t < 3.43 ps,
as shown in Fig. 5. At about 3.43 ps, OH5–H6(t) starts to in-
crease and maintains a fairly large value ∼0.8 after 3.48 ps,
i.e., the second hydrogen molecule (H5–H6) is formed as
shown in the snapshots at 3.45 and 3.51 ps. Accompany-
ing the formation of chemical bonds for H5–H6, those for
H5–Al4 and O2–H6 are broken, as OH5–Al4(t) and OO2–H6(t)
(1)
FIG. 4. Production process of the first hydrogen molecule on the Al clus-
ter observed in MD simulation. Atomic configurations are shown at time t
= 1.48, 1.52, 1.54, and 1.60 ps, where white, red, and green spheres repre-
sent H, O, and Al atoms, respectively.
decreases to almost zero. A hydroxide ion (O2–H7), attached
to Al5, is left, and this hydrogen-production reaction is again
summarized as Eq. (1). Unlike the previous process, how-
ever, a third Al atom, such as Al2 in Figs. 3 and 4, is
not involved in the process shown in Figs. 5 and 6, indi-
cating that such Al atom is not necessary for the hydrogen
production.
The third hydrogen molecule is produced at 3.51 ps in a
different way from the former two cases (see Fig. 7). First,
H atoms associated with four water molecules move by the
Grotthuss mechanism as indicated by the yellow arrows in
the snapshot at 3.5 ps. After the formation and breakage of
some chemical bonds, the third hydrogen molecule, as well
as a H3O2product and two water molecules, are formed as
displayed in the snapshot at 3.51 ps. After some OH-bond
exchanges following the magenta arrows, the H3O2 prod-
uct is dissolved into water molecules, leaving a hydroxide
ion on the surface of the Al cluster (see the snapshot at
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244702-4Ohmura et al.J. Chem. Phys. 134, 244702 (2011)
FIG. 5. Production process of the second hydrogen molecule on the Al clus-
ter observed in MD simulation. Time evolution of bond-overlap populations
Oij(t) associated with atoms labeled in the snapshots of atomic configurations
in Fig. 6.
FIG. 6. Production process of the second hydrogen molecule on the Al clus-
ter observed in MD simulation. Atomic configurations are shown at time
t = 3.40, 3.43, 3.45, and 3.51 ps, where white, red, and green spheres repre-
sent H, O, and Al atoms, respectively.
FIG. 7. Production process of the third hydrogen molecule on the Al cluster
observed in MD simulation. Atomic configurations at time t = 3.50, 3.51, and
3.52 ps, where white, red, and green spheres represent H, O, and Al atoms,
respectively. Yellow and magenta arrows represent the motion of H atoms.
3.52 ps). We should note that this process is influenced by
the periodic boundary condition (see the periodic image of
the Al cluster at the right edge of each snapshot in Fig. 7).
Nevertheless, a similar reaction is expected to occur, if two
Al clusters approach to each other in water. Even with one
Al cluster, the Grotthuss mechanism still allows such a re-
action to occur between Lewis-base and Lewis-acid sites,
which are relatively far apart from each other on the cluster
surface.
In all processes shown in Figs. 3–7, a hydrogen atom is
generated before the formation of the H2molecule. Figure 8
shows atomic configurations for the adsorption of a hydro-
gen atom on the Al cluster during the MD simulation, which
shows how the Grotthuss mechanism assists the production
of hydrogen molecules. Two of the total of three hydrogen
atoms on the surface of the Al cluster in Figs. 4 and 7 are gen-
erated in this way. The reaction begins with the dissociation
of a H2O molecule bonding to an Al atom (the magenta circle
in Fig. 8), as one of its hydrogen atoms moves toward a neigh-
boring H2O molecule to form a hydronium ion (H3O+). This
is followed by a chain of hydrogen bond switching events (de-
noted by the yellow arrows in Fig. 8) that involves in total of
four H2O molecules, and finally a hydrogen atom bonds to an
Al atom after 190 fs (the cyan circle in Fig. 8). This process
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244702-5Reaction of aluminum clusters with water J. Chem. Phys. 134, 244702 (2011)
FIG. 8. Adsorption of a hydrogen atom on the Al cluster through the
Grotthuss mechanism observed in MD simulation.
is summarized as
Al−OH2+ 3H2O + Al?→ Al−OH + 3H2O + Al?−H,
(2)
where Al and Al?, respectively, denote the aluminum atoms
with Lewis acid and base characters involved in the reac-
tion. This proton transfer is induced by the Lewis acid-base
characters of the participating Al atoms.17(Similar phenom-
ena were observed in water with hydrogen-bonded acid-base
complexes43or charged solutes.44)
Another process of hydrogen-atom adsorption on the Al
cluster observed in MD simulation is shown in Fig. 9. As dis-
played in the snapshot at 1.97 ps (Fig. 9(b)), a water molecule,
consisting of O3, H5, and H8, approaches to an Al atom la-
beled Al6. The chemical bond is formed between O3 and Al6,
as Oij(t) for these atoms begins to increase around 1.97 ps
(Fig. 9(a)). One of the OH bonds within the water molecule
is broken, and hydrogen atom H5 is attached to the Al cluster
as seen in the atomic configuration at 2.02 ps. OO3–H5(t) de-
creases abruptly to zero at about 2 ps, while OO3–H8(t) main-
tains finite values. This reaction is summarized as
Al−OH2+Al?→ Al−OH + Al?−H.
Note that this process is influenced by an extra water
molecule. Since OO3–H9(t) has small but finite values during
the reaction, a weak covalentlike interaction exists between
O3 and H9, which assists H5 in breaking the O3–H5 bond.
(3)
B. Activation energy
To find the minimum energy paths of chemical reactions,
we adopt the nudged elastic band (NEB) method.45,46As a
discrete representation of a path from the reactant configura-
tion R0to the product configuration RM, M−1 replicas of the
system are created and connected together with springs. The
images are then relaxed toward the minimum energy path. In
this paper, we use M = 15–28.
The NEB method gives energy profiles at zero tem-
perature. We also study the effect of finite temperatures on
chemical reactions by calculating free energies. For this pur-
pose, additional ab initio MD simulations are carried out at
temperature T = 300 K by imposing geometrical constraints
to obtain the free energy profile47along the reaction path. The
Lagrange multiplier λ(r) is introduced to constrain the dis-
tance r between atoms to be reacted. By taking time average,
FIG. 9. Adsorption of a hydrogen atom on the Al cluster observed in MD
simulation. (a) Time evolution of bond-overlap populations Oij(t) associated
with atoms labeled in the snapshots of atomic configurations. (b) Atomic
configurations at time t = 1.97 and 2.02 ps, where white, red, and green
spheres represent H, O, and Al atoms, respectively.
we obtain the average Lagrange multiplier ?λ(r)?. The
canonical-ensemble simulation at the room temperature is
carried out for 1 ps at each distance r. The average Lagrange
multiplier ?λ(r)? becomes zero at an equilibrium distance r0.
The value of r is decreased (or increased depending on the
reaction path) from this distance, and again ?λ(r)? becomes
zero at a critical distance rdof the energy barrier. The relative
free energies are obtained for r0≥ r ≥ rdby the following
integral:48
?r
?F(r) =
r0
?λ(r?)?dr?.
(4)
In order to estimate the rate of the hydrogen-production
reaction, Eq. (1), we calculate the energy profile along the
corresponding reaction path, using a system consisting of an
isolated Al cluster, one H2O molecule, and one extra H atom.
In the initial configuration, a H2O molecule is placed on the
Lewis acid site on the Al cluster,17and the extra H atom is
introduced on one of the Lewis base sites. From the result
shown by the dashed line in Fig. 10, the activation energy is
estimated by the NEB method to be ? = 0.1 eV. The finite-
temperature effect by calculating the activation free energy
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