Supplementary Information for Hydrogen Production from Water Using Aluminum-Cluster Catalysts

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1 Supplementary Information for Hydrogen Production from Water Using Aluminum-Cluster Catalysts Fuyuki Shimojo, a,b Satoshi Ohmura, a,b Rajiv K. Kalia, a Aiichiro Nakano, a and Priya Vashishta a a Collaboratory for Advanced Computing and Simulations, Department of Computer Science, Department of Physics & Astronomy, Department of Chemical Engineering & Materials Science, University of Southern California, Los Angeles, CA b Department of Physics, Kumamoto University, Kumamoto , Japan Ab initio molecular dynamics The electronic states are calculated using the projector-augmented-wave (PAW) method [1, 2], which is an all-electron electronic-structure-calculation method within the frozen-core approximation in the framework of density functional theory (DFT). The generalized gradient approximation (GGA) [3] is used for the exchange-correlation energy with non-linear core corrections [4]. The momentum-space formalism is utilized [5], 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 minimized iteratively using a preconditioned conjugate-gradient method [6, 7]. The Γ 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 implemented on parallel computers [7] by a hybrid approach combining spatial decomposition (i.e., distributing real-space or reciprocalspace 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 (MPI) library for interprocessor communications. The 6 ps simulations reported here took 400 hours on 64 AMD Opteron (2.33 GHz) processors. Molecular dynamics (MD) simulations are carried out at temperatures of 300, 500 and 1000 K in the canonical ensemble using the Nosè-Hoover thermostat technique [8, 9]. The equations 1

2 of motion are integrated numerically using an explicit reversible integrator [10] with a time step of 11 a.u. (~ fs). Two systems are studied in our MD simulations: (1) an Al 17 cluster + 84 H 2 O molecules (in total of 269 atoms) in a box of dimensions Å 3 ; and (2) an Al 12 cluster + 56 H 2 O molecules (180 atoms) with dimensions Å 3. The system sizes are determined from the density of water in ambient conditions, and periodic boundary conditions are imposed. Bond overlap population analysis To quantify the change in the bonding properties of atoms associated with the hydrogenproduction reaction, we use a bond-overlap population analysis [11, 12] by expanding the electronic wave functions in an atomic-orbital basis set [13, 14]. Based on the formulation generalized to the PAW method [15], we obtain the gross population Z i (t) for the i th atom and the bond-overlap population O ij (t) for a pair of i th and j th atoms as a function of time t. From Z i (t), we estimate the charge of atoms, and O ij (t) gives a semi-quantitative estimate of the strength of covalent bonding between atoms. As the atomic-basis orbitals, we use numerical eigenfunctions of atoms, which are obtained for a chosen atomic energy so that the first node occurs at the desired cutoff radius [16]. To increase the efficiency of the expansion, the numerical basis orbitals are augmented with the split-valence method [17]. The resulting charge spillage, which estimates the error in the expansion, is only 0.3 %, indicating the high quality of the basis orbitals. Nudged elastic band calculation of activation energy To find minimum energy paths of chemical reactions, we adopt the nudged elastic band (NEB) method [18, 19]. As a discrete representation of a path from the reactant configuration R 0 to the product configuration R M, M 1 replicas of the system are created and connected together with springs. The images are then relaxed towards the minimum energy path. In this paper, we use M = 15. Activation free energy calculation The NEB method explained above gives energy profiles at zero temperature. We also study the effect of finite temperatures on chemical reactions by calculating free energies. We carry out 2

3 additional ab initio MD simulation at temperature T = 300 K by imposing geometrical constraints to obtain the free energy profile [20] along the reaction path of the H 2 production reaction, Al-OH 2 + Al-H Al-OH + Al + H 2, which has been found in our ab initio MD simulation. For this purpose, a system consisting of an isolated Al cluster, one H 2 O molecule, and one extra H atom is used. The Lagrange multiplier λ(r) is introduced to constrain the distance r between one of the H atoms in the H 2 O molecule and the extra H atom during simulations (Fig. S1(a)). By taking time average, we obtain the average Lagrange multiplier. The canonical-ensemble simulation at the room temperature is carried out for 1 ps at each distance r. In the initial configuration, an H 2 O molecule is placed on the Lewis acid site on the Al cluster [21], and the extra H atom is introduced on one of the Lewis base sites. The average Lagrange multiplier becomes nearly zero at r 0 = 1.4 Å. The value of r is decreased from this distance, and we observe that the H atoms are dissociated from both the H 2 O molecule and the Al cluster at r d = 1.0 Å. The relative free energies are obtained for by the following integral [22]:. The calculated free energy barrier for the reaction path, Al-OH 2 + Al-H Al-OH + Al + H 2, is only 0.08 ev (Fig. S1(a)). We have also examined several other reactions of the Al cluster with water to see whether they are competitive with the mechanism presented above. One possible product of Al-water reaction is Al-O, the production rate k 3 of which may be estimated as follows. To oxidize an Al cluster, the hydroxide ions on the Al cluster must dissociate as, e.g., Al-OH + Al-H Al-O + Al + H 2. It is found that the energy barrier for this reaction is about 1.6 ev (Fig. S1(b)), which is twenty times larger than that for the Al-OH formation [23]. Another possible reaction is the formation of a hydrogen molecule from two hydrogen atoms on an Al cluster, Al-H + Al-H Al + Al + H 2, which has an activation free energy of 0.9 ev (Fig. S1(b)), which is an order-ofmagnitude higher than that for Al-OH 2 + Al-H Al-OH + Al + H 2. 3

4 FIG. S1. (a) Free-energy profile (solid curve) at a temperature of 300 K along the reaction path of molecular hydrogen production, Al-OH 2 + Al-H Al-OH + Al + H 2, as a function of the distance between the two hydrogen atoms that form a hydrogen molecule. The dashed curve is the energy profile obtained by nudged-elastic-band calculation. (b) Free-energy profiles along the reaction paths of molecular hydrogen production, Al-OH + Al-H Al-O + Al + H 2 (black curve) and Al-H + Al-H Al + Al + H 2 (red curve), as a function of the distance between the two hydrogen atoms that form a hydrogen molecule. We have considered another mechanism of initial Al oxidation, i.e., the formation of a bridging O atom before the dissociation of the hydroxide ion. The energy barrier for this mechanism is estimated to be 0.5 ev (Fig. S2), and the associated reaction rate, k 3 = 10 5 s 1 is 4

5 much smaller than and. Therefore, the dominant hydrogen-production mechanism at room temperature (which is also the one observed in our MD simulation) is the production of a hydroxide group on the surface of the Al n cluster as one hydrogen molecule is produced. FIG S2. Free-energy profile at a temperature of 300 K along the reaction path for a hydroxide ion to move to a site bridging two Al atoms. Energy profiles for the production of H atom on Al clusters We have calculated the energy profile along the reaction path for the production of a hydroxide ion and a hydrogen atom on the Al cluster, Al-OH 2 + mh 2 O + Al Al-OH + mh 2 O + Al -H, by the NEB method for different numbers, m, of water molecules (see Fig. S3). The energy barrier has the highest value, 0.42 ev, when only single H 2 O molecule (m = 0) is involved (open circles). This energy barrier is lowered when extra bulk H 2 O molecules are incorporated, i.e. m 1. The lowest energy barrier is 0.20 ev for the case of m = 1 (solid circles). The energy barriers for m = 2 and 3 are 0.25 and 0.30 ev, respectively. Note that the energy barrier increases at a rate of about 0.05 ev/molecule for m 1. From these values, the energy barrier for Al-OH 2 + mh 2 O + Al Al-OH + mh 2 O + Al -H is estimated to be m ev for m 1, which indicates that the energy to split H 2 O into H + and OH is 0.15eV and the energy to form one hydronium ion (H 3 O + ) is 0.05 ev in the reaction with extra bulk H 2 O as well as one H 2 O bonded to the Al cluster. 5

6 FIG. S3. Energy profiles along the reaction paths for the production of a hydroxide ion and a hydrogen atom on an Al 12 cluster through the Grotthuss mechanism, Al-OH 2 + mh 2 O + Al Al-OH + mh 2 O + Al -H with m = 0 (open circles), m = 1 (solid circles), m = 2 (open squares), and m = 3 (solid triangle), obtained by nudged elastic band calculations. r OH is the average length of OH bonds that are broken in the reaction. References for Supplementary Information [1] P. E. Blöchl, Phys. Rev. B 50, (1994). [2] G. Kresse, and D. Joubert, Phys. Rev. B 59, 1758 (1999). [3] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). [4] S. G. Louie, S. Froyen, and M. L. Cohen, Phys. Rev. B 26, 1738 (1982). [5] J. Ihm, A. Zunger, and M. L. Cohen, J. Phys. C 12, 4409 (1979). [6] G. Kresse, and J. Hafner, Phys. Rev. B 49, (1994). [7] F. Shimojo et al., Comp. Phys. Commun. 140, 303 (2001). [8] S. Nosè, Mol. Phys. 52, 255 (1984). 6

7 [9] W. G. Hoover, Phys. Rev. A 31, 1695 (1985). [10] M. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys. 97, 1990 (1992). [11] R. S. Mulliken, J. Chem. Phys. 23, 1833 (1955). [12] R. S. Mulliken, J. Chem. Phys. 23, 1841 (1955). [13] D. Sánchez-Portal, E. Artacho, and J. M. Soler, J. Phys.: Condens. Matter 8, 3859 (1996). [14] M. D. Segall et al., Phys. Rev. B 54, (1996). [15] F. Shimojo et al., Phys. Rev. E 77, (2008). [16] O. F. Sankey, and D. J. Niklewski, Phys. Rev. B 40, 3979 (1989). [17] J. M. Soler et al., J. Phys.: Condens. Matter 14, 2745 (2002). [18] H. Jonsson, G. Mills, and K. Jacobsen, in Classical and Quantum Mechanics in Condensed Phase Simulations (World Scientific, Singapore, 1998). [19] G. Henkelman, and H. Jonsson, J. Chem. Phys. 113, 9978 (2000). [20] K. C. Hass et al., Science 282, 265 (1998). [21] P. J. Roach et al., Science 323, 492 (2009). [22] A. Curioni et al., J. Am. Chem. Soc. 119, 7218 (1997). [23] We have not observed any dissociation of the hydroxide ions (Al-OH) in our MD simulation, which is consistent with its estimated high activation barrier. 7