Published: November 22, 2011 r2011 American Chemical Society 152 dx.doi.org/10.1021/ct200681k | J. Chem. Theory Comput. 2012, 8, 152–161 ARTICLE pubs.acs.org/JCTC Alternative Mechanisms in Hydrogen Production by Aluminum Anion Clusters Paul N. Day,* ,†,‡ Kiet A. Nguyen, †,§ and Ruth Pachter* ,† † Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright Patterson Air Force Base, Ohio 45433, United States ‡ General Dynamics Information Technology, Inc., Dayton, Ohio 45431, United States § UES, Inc., Dayton, Ohio 45432, United States b S Supporting Information ABSTRACT: Possible mechanisms for the reaction of aluminum anion clusters with water have been studied theoretically using density functional theory for four different size clusters. Our results confirm the previously found (Reber et al. J. Phys. Chem. A 2010, 114, 6071) importance of Lewis-acid and Lewis-base sites on the cluster in the size specificity of the reactivity. However, alternative viable mechanisms have been found using both LangmuirÀHinshelwood and EleyÀRideal kinetics. Grotthuss-like mechanisms appear to be the most energetically favorable. We show that while the superatom theory successfully predicts reactivity of smaller clusters, it is less useful for the larger clusters. I. INTRODUCTION The reaction of aluminum with water to produce hydrogen gas is of interest as an alternative energy source. While aluminum in bulk reacts too slowly for practical applications, evidence sug- gests much faster rates for micro- or nano-sized aluminum particles. 1,2 As with other metal nanoparticles, structure and properties vary by cluster size, and these variations may be at least partially explained or predicted through the use of “super-atom” theory and “magic numbers”, which are related to the spherical jellium model. 3À8 In the superatom theory, the valence electrons in a cluster of metal atoms are sufficiently delocalized such that the wave function solution, in analogy with atomic wave func- tions, fills “super-atom” electronic shells designated as 1S, 1P, 1D, 2S, 1F, 2P, 1G, 2D, 3S, ..., thus generating the following series of magic numbers: 2, 8, 18, 20, 34, 40, 58, 68, 70, ... A cluster with a magic number of valence electrons should be particularly stable, in analogy with an inert gas. The aluminum atom has three valence electrons, and the superatom theory correctly predicts the inertness of Al 13 À1 , with 40 valence electrons, as well as of Al 11 À1 , with 34 valence electrons. The high reactivity of Al 12 À1 , with 37 valence electrons, and of Al 17 À1 , with 52 valence electrons, is also consistent with the theory. The production of hydrogen gas from the reaction of alumi- num nanoclusters with water was observed in a fast-flow reactor. 9,10 Reber et al. 10 investigated possible correlations between the reactivity with water and various calculated properties of the clusters, including dipole moment, binding energy, transition state energy, product energy, and orbital energies. The Al 12 À1 cluster has a relatively large dipole moment and reacts rapidly with water (although apparently does not produce H 2 ), but the symmetric Al 17 À1 has a zero dipole moment and also reacts rapidly with water, including the release of H 2 . The Al 12 À1 cluster also has a large binding energy with water and a low barrier for the OH bond-breaking, but these properties alone are not sufficient to predict the reactivity for each cluster size. The energy and structure of the KohnÀSham molecular orbitals were found to be important, particularly that of the highest occupied molecular orbital (HOMO) and lowest un- occupied molecular orbital (LUMO). In systems with an odd number of electrons (Al 12 À1 and Al 20 À1 ), the singularly occupied molecular orbital will be labeled SOMO, the lowest completely unoccupied orbital LUMO, and the highest doubly occupied orbital SOMOÀ1. Positions on the cluster where the LUMO protrudes out in space are Lewis-acid sites, which tend to attract the lone-pair of electrons of the oxygen atom in the water molecule. A water molecule will bind at these sites with a typical stabilization energy of 0.3À0.6 eV. If an adjacent aluminum atom has a strong contribution from the HOMO (the SOMO for odd-electron species), it can act as a Lewis-base, and one of the hydrogen atoms from the water molecule can bind to it, breaking its bond to the oxygen atom, resulting in the H and the OH being bound on adjacent aluminum atoms. For some clusters, the barrier for this reaction is less than the stabilization energy of the initial water binding, and this step is exothermic by over 1.0 eV, making the reaction thermally favorable. Other water molecules can react with other Lewis-acidÀLewis-base pairs on the alumi- num cluster. Because of the exothermicity of this reaction, the system may have enough energy for two hydrogen atoms on adjacent aluminum atoms to form a bond and be released as H 2 . This is the LangmuirÀHinshelwood (LH) mechanism described by Reber et al. 10 Alternative mechanisms that they describe include the EleyÀRideal (ER) type, where the second water molecule does not undergo bond-breaking on the surface but instead transfers a hydrogen atom directly to the bound hydro- gen to form H 2 , and a “direct” mechanism, where neither water molecule undergoes surface bond-breaking but instead each directly contributes a hydrogen atom to form H 2 . In studies utilizing molecular dynamics (MD), 11,12 a lower barrier for the first step of the reaction was found through a Grotthuss-like Received: September 27, 2011