| FUNCTIONAL NANOMATERIALS |
| Computational Energy Research at CFN
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There are several efforts under way at the Center for Functional Nanomaterials (CFN) to extend computations to the nanoscale, including hydrogen storage in aluminum compounds doped with titanium, new gold-containing catalysts for removing carbon monoxide impurities from hydrogen gas, water splitting on gallium nitride films, and the geometrical structure of small gold particles.
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Nanoparticle properties are different, in some cases dramatically so, from those of small molecules or bulk crystalline materials. These properties represent the opportunity of nanoscience: a whole new world of material and chemical properties waits to be discovered. The challenge is that traditional theoretical approaches often fail. For example, quantum chemistry has difficulty reaching thousands of atoms, while the developed physics of bulk solids is not designed to account for quantum size effects, surfaces, and local chemical bonding. Nanoparticles are often too small for experimental X-ray and neutron diffraction techniques to be useful.
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Quantum Calculations
The atomic scale structure of matter is described by quantum mechanics. Without quantum effects, it is impossible to calculate molecular sizes, chemical bonding, or optical absorption. In fact, it is possible to prove, as Freeman Dyson did many years ago, that matter treated classically (without quantum effects) is unstable—it would spontaneously break apart into individual atoms. |
| Quantum effects are described by the Schrödinger equation, a partial differential equation (PDE) that yields the wave function, the absolute square of which is the (electronic) charge density. Despite its importance, only a few exact solutions of the Schrödinger equation are known. One example is the hydrogen atom, where the Coulomb interaction between the positively charged nucleus and the negatively charged electron is spherically symmetric, and the single electron has no other electrons with which to interact. |
Nanoparticle properties represent the opportunity of nanoscience: a whole new world of material and chemical properties waits to be discovered. |
| A standard approach is to expand the wave function in a basis set, which converts the PDE into a matrix diagonalization problem. Most chemistry codes use Gaussian functions centered on atomic sites, and most condensed matter physics codes use plane waves, or combinations of plane waves and localized functions. The energy of a molecule or cluster is given by the eigenvalues of the Hamiltonian (or energy) matrix, while the wave function itself is given by the eigenfunctions. |
| The advantage of Gaussians is that the integrals representing the individual matrix elements can all be evaluated analytically. The disadvantage is that a relatively large number of Gaussians is required to accurately represent the wave functions. It is not unusual to have 50 Gaussians per atom, so that a 1,000-atom calculation would require repeated diagonalization of a 50,000 x 50,000 matrix. Also, matrix diagonalization scales as N3 (50,0003 in this case), clearly a difficulty for nanoscale systems. Another disadvantage is that it can be difficult to find an accurate basis—and it is difficult to systematically improve it for greater accuracy should that be required. |
| Plane wave methods have an important advantage: a systematic improvement in the basis is possible simply by raising the maximum kinetic energy of the plane waves (corresponding to the minimum wavelength in a Fourier expansion). They also benefit from extensive use of fast Fourier transforms, routines that are normally optimized for new computer architectures as soon as they are available. Finally, the codes themselves are relatively simple, which enables rapid changes for new physical properties and a rapid learning curve for students and other new users. |
| There are disadvantages in using the plane wave method. For instance, these codes assume crystalline periodicity. Finite clusters need to be studied in supercells, such as periodic arrays of clusters with large enough gaps between adjacent clusters. On the other hand, many important nanoscale systems, such as catalysts, involve clusters on the surface of a support—a problem for which periodicity is relevant. A second disadvantage is that because of communication requirements among processors in massively parallel machines, fast Fourier transforms do not scale well beyond thousands of processors, which is a potential problem on machines of the future where tens of thousands of processors or more will be common. |
Without quantum effects, it is impossible to calculate molecular sizes, chemical bonding, or optical absorption. |
| The Schrödinger equation for one electron is a PDE in three spatial variables. For N electrons, it is a PDE in 3N variables. This multi-electron wave function can be represented as a product of single-particle wave functions. Because of the Pauli exclusion principle, the products must be antisymmetric (change sign) under interchange of any two electron coordinates. These are conventionally written as Slater determinants that automatically change sign under interchange of rows. Each determinant is called a configuration. The full solution is a superposition of many configurations, and the number of possible configurations grows exponentially with N. |
| The Hartee-Fock method, which uses the optimal (in a variational sense) single determinant wave function, is equivalent to solving a single electron problem and therefore reverts to N3 scaling. However, Hartee-Fock is known to produce poor results for chemical bond energies as well as for crystals. |
| Many modern electronic structure calculations rely on density functional theory (DFT) for which Walter Kohn shared the Nobel prize in chemistry in 1998 (John Pople was the other recipient for his leadership in the development of Gaussian-based methods). In DFT, the many-electron problem for the total energy and charge density is reduced to an effective single-electron Schrödinger equation, and thus the scaling returns to N3. "Effective" means that the Coulomb interaction in the Schrödinger equation is replaced by an effective interaction that depends on the charge density. The problem is that the precise form of the effective interaction is not known, although a number of excellent approximations are available. Still, there are a number of known deficiencies in DFT, and more complete methods are sometimes needed for which scaling is usually much worse than N3. |
In cases where DFT is successful, there are efforts under way to obtain linear scaling. Because the energy of a large system (where surface effects can be neglected) scales linearly with the system size, it should be possible to calculate it in the same linear way.
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Storing Hydrogen in Lightweight Containers
Hydrogen storage is a bottleneck in the development of hydrogen-fueled vehicles. The conventional storage method, compressed H2 gas, requires a large tank volume, and the possibility of a tank rupture poses a significant safety risk. Other methods involve condensing and cooling the H2 gas to 20 K (-252.8°C; -423.0°F), where it forms liquid H2. |
| Alane clusters (aluminum-hydrogen, AlxHy) are believed to be carriers of hydrogen (for mass transport), which serve as an intermediate species in the production of a variety of materials such as alanates like LiAlH4 and NaAlH4. Among these alane species, AlH3 is currently the best candidate for hydrogen storage. It can store up to 10% hydrogen (by weight) and can be made reversible under ambient conditions for automobile applications. Different theoretical and computational techniques can be used to understand the atomistic mechanisms behind the formation of simple AlxHy clusters on Al(111) surfaces and their further evolution leading towards the formation of larger alane species. The mobility of hydrogen and different AlxHy clusters plays a key role in alane formation. |
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| Illustration: A. Tovey; Source: Theory and Computation Group, CFN, BNL |
| Figure 1. Titanium-doped aluminum(111) surface with steps, kinks, terraces, isolated adatoms, and adatom islands. The terraces of Al(111) surface are shown in different colors for clarity. |
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| Another key factor in alane formation is the adsorption and dissociation of H2 at ambient temperatures on aluminum surfaces. The following questions arise: what is the effect of a titanium dopant on hydrogen adsorption and its diffusion on aluminum surfaces? How does the presence of titanium change the kinetics of formation and the diffusivities of AlxHy species? |
| CFN's recently developed modeling framework (DFT-based kinetic Monte Carlo) enables the study of the steady-state conditions of dissociative adsorption of hydrogen, its diffusion, and its reaction with aluminum adatoms leading to the formation of alane species on titanium-doped aluminum surfaces. In other words, to bridge the gap between theoretical and experimental time/length scales, a computational paradigm was adopted in which information from the atomic and microscopic level can be used to determine the behavior of the system at much larger (namely, experimental) length and time scales. Such phenomena include, but are not limited to, the formation and temporal evolution of alane on aluminum surfaces. |
| The model system consists of an Al(111) surface with terraces, kinked steps, aluminum adatom islands, and isolated adatoms, as shown in figure 1 (p39). In this model, atomistic processes, such as the dissociative adsorption of H2, reaction of hydrogen with aluminum adatoms and AlxHy, and diffusion of all the AlxHy species, are considered. |
| Theoretical studies show that an embedded titanium atom creates a well in the potential energy surface of Al(111) as probed by a hydrogen atom. This well reduces the diffusivity of hydrogen adatoms. The potential energy surface was scanned by placing a hydrogen adatom at different places on an Al(111) surface. These calculations were carried out using DFT (VASP code) in a pseudopotential plane-wave method applying the generalized gradient approximation. The model system for these calculations consists of four layers of a 4 x 4 Al(111) surface with one titanium atom replacing the aluminum atom in the middle of the top layer. |
| Diffusion barriers for the hydrogen adatom and other AlxHy in different regions of the Al(111) surface are obtained from the potential energy surface scan. The diffusion barrier for the hydrogen atom moving around the embedded titanium atom is lower than that for the hydrogen atom moving away from the embedded titanium atom. The diffusion barrier for a hydrogen atom on Al(111) far from the embedded titanium atom is significantly lower than the depth of the potential well created by the titanium atom. This arrangement suggests a high mobility of hydrogen adatoms on the Al(111) surface away from the doped titanium atoms and significantly low mobility in the neighboring regions of the doped titanium atoms. On the other hand, doped titanium atoms do not much affect the diffusivities of aluminum adatoms and AlH. A diffusing aluminum adatom or AlH species does not feel the presence of the well in the potential energy surface around doped titanium atoms. Therefore, the diffusivities of aluminum adatoms and AlH are significantly greater than the diffusivity of the adsorbed hydrogen atoms. |
Because of emerging applications for onboard purification and production of hydrogen for fuel cell vehicles, there is an increased interest in the water-gas-shift reaction. |
| Moreover, the role of titanium in hydrogen dissociation on aluminum surfaces is generally acknowledged if not well understood. Catalytically active titanium sites act as sources of isolated hydrogen adatoms available to aluminum adatoms for reaction. Dissociation barriers were obtained at different active sites in the vicinity of the doped-titanium atom using the above-mentioned DFT method regarding the adsorption and dissociation of H2. CFN has compiled a database of these and many other aluminum adatom and AlxHy diffusion processes (for example, detachment of aluminum from step edges and etching triggered by aluminum vacancy formation) with the associated energy barriers. |
| CFN scientists used this database of diffusion barriers and H2 dissociation barriers at different active sites in the kinetic Monte Carlo code to obtain results of diffusivity as a function of titanium-dopant concentration at a temperature of 300 K. The diffusion trajectory of a hydrogen adatom in the presence of several dopant titanium atoms typically shows that a diffusing hydrogen adatom in proximity to a titanium atom on the Al(111) surface falls into the associated potential energy well and gets trapped in neighboring low energy regions. |
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| Illustration: A. Tovey; Source: Theory and Computation Group, CFN, BNL |
| Figure 2. Trajectory of the diffusing hydrogen adatom (red) on Al(111) (blue spheres) in the presence of titanium atoms (yellow). |
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| By analyzing diffusion trajectories of hydrogen adatoms, as shown in figure 2 (p40), diffusivity was calculated as a function of the titanium atom concentration and found to decrease exponentially with increasing concentration of titanium dopant atoms. At the same time, the surface coverage of hydrogen adatoms increases almost linearly with titanium concentration. These results are consistent with CFN experimental observations. Furthermore, reaction barriers (reaction of aluminum adatoms and AlxHy with adsorbed hydrogen leading to alane species) were added in the database, which helped to study and model the kinetics of alane formation under various temperature and pressure conditions. |
The results indicate that diffusing aluminum adatoms on Al(111) are made available by such atomistic mechanisms as vacancy formation, surface etching, and step edge detachment. Doped titanium creates a well in the potential energy surface for adsorbed hydrogen on Al(111) that reduces the diffusivity of hydrogen atoms on the surface. This, in turn, leads to a decrease in the production rate of surface alane species. Because of the low diffusivity of hydrogen, most of the adsorbed hydrogen adatoms stay in the vicinity of the doped titanium atoms. Adsorbed hydrogen gets "harvested" by diffusing aluminum and AlH on the Al(111) surface. This process cleans the area around the titanium atoms and makes room for further adsorption and dissociation of additional H2 molecules. Doped titanium promotes hydrogen dissociation on Al(111) surfaces but also slows down the kinetics of alane formation. Consistent with experimental findings, there is an optimum titanium concentration for alane production at which H2 dissociation is matched to alane formation.
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Cleaning Up Hydrogen—New Catalysts from Gold
Because of emerging applications for onboard purification and production of H2 for fuel cell vehicles, there is an increased interest in the water-gas-shift (WGS) reaction, whereby carbon monoxide and water are converted into carbon dioxide and hydrogen. |
| For example, in some industrial operations, copper-based catalysts are used for a WGS reaction at relatively low temperature (470-520 K). However, for automotive applications, problems such as condensation of water and subsequent deactivation of the catalysts persist. The design and optimization of WGS catalysts are hindered by controversy about basic questions regarding the nature of the active sites and the reaction mechanism. A central challenge is the difficulty of characterizing the active state of the catalyst and the reaction mechanism. |
| Gold-ceria (Au/CeO2) and gold-titania (Au/TiO2) nanomaterials have recently been reported to be very efficient WGS catalysts. These findings are remarkable because bulk gold, ceria, and titania are not known as WGS catalysts. The nature of the active phase(s) in these metal/oxide nanocatalysts is unclear. Is it the AuOx, metallic gold, or oxide nanoparticle? A coordinated theoretical and experimental study has been initiated by CFN to understand WGS active sites and reaction mechanisms on promising gold/oxide catalysts. Because it is extremely difficult to identify experimentally the exact active sites in metal/oxide catalysts, theory plays an essential role. |
| Coupled with extensive experimental efforts, DFT calculations were used to investigate the WGS reaction on an Au29 cluster (1.2 nm in diameter) seen on CeO2(111) with the scanning tunneling microscope. Figure 3 (p41) shows the calculated energy profile of the WGS reaction on Au29. Compared to Au(100), water and CO bind to Au29 more strongly by occupying the corner sites, which are generally considered more active than the terrace sites due to their low coordination. The water dissociation on the top of the cluster is also found to be more facile. The rate-limiting step for both Au29 and Au(100) is the same: water dissociation. Within a micro-kinetic model based on the DFT calculations, WGS activity was estimated, which decreases in a sequence: Au29 > Au(100). |
In the pursuit of hydrogen, a portable and clean form of energy, one technique under investigation is using sunlight to split water into hydrogen and oxygen. |
| The calculations agree well with the experiments (Au/CeO2 >> Cu(100) > Au/ZnO(000ι) > Au(111)), where ZnO was found to act only as a support for the nanoparticles and did not participate directly in the reaction. That is, compared to the bulk, the gold nanoparticle is a better catalyst in the WGS reaction by lowering the activation barrier for water dissociation. However, the improvement is not enough. On a gold nanoparticle alone, the WGS reaction cannot proceed as well as on copper. In contrast, the WGS activity of the gold nanoparticle appears to be significantly improved when supported on TiO2 or CeO2. Therefore, an oxide can have the essential role for the activity of supported gold nanocatalysts. The importance of cooperative effects cannot be overstressed. |
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| Illustration: A. Tovey; Source: Theory and Computation Group, CFN, BNL |
| Figure 3. Upper panel: calculated reaction profile for the WGS reaction on Au(100), a Au29 nanoparticle, Au10/TiO2(110), and TiO2/Au(100) model catalysts. Transition states are denoted as TS1, TS2, and TS3. Lower panel: optimized structures of some of the important intermediates involved in the WGS reaction on different systems. Big yellow: Au; big light gray: Ti; small red: O; small dark gray: C; small light gray: H. |
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| To further address the roles of the metal and oxide, the WGS reaction was investigated on the Au10/TiO2(110) and the inverse TiO2/Au(111) model catalysts (figure 3). The inverse catalyst is an excellent system for examining the role of the oxide support in the WGS reaction. For the real WGS catalysts, for instance, the gold nanoparticle is dispersed on a nanotitania support, and the oxide support may not be a simple spectator in the system. In addition, experimental results showed that Au(111) covered by 20% to 30% of CeO2 or TiO2 nanoparticles display activities comparable to good WGS catalysts (for example, Cu(100), Cu(111)). |
| As shown in figure 3, the model of Au10/TiO2(110) has been indicated to be a reasonable conformation to describe the CO oxidation on Au/TiO2. The model of TiO2/Au(111) contains chains of a TiO2 over Au(111) in a 3 x 1 array. This model catalyst exposes not fully coordinated titanium centers, as expected for TiO2 nanoparticles, and allows the study of the Au-TiO2 interface. Calculations showed the bottleneck of the WGS reaction on gold surface and nanoparticle (water dissociation) is overcome by combining gold with TiO2. As shown in figure 3, water can be easily dissociated at the Au10-TiO2 interface and the TiO2 cluster supported on Au(111). The remaining reactions are able to proceed at a reasonable speed on both systems. The rate-limiting step for the WGS reaction on Au10/TiO2(110) and TiO2/Au(111) is the formation of carboxyl (HOCO*). However, in both cases, the corresponding barriers for the rate limiting step are lower than those for water dissociation on Au29 and gold bulk, and therefore a better WGS activity is expected. The calculations agree well with the experiments. |
The DFT calculations allow an understanding of the experimental observations for the WGS reaction on metal/oxide. Researchers gain insight into the reaction mechanism and active sites. The model Au10/TiO2(110) and TiO2/Au(111) catalysts combine the advantages of both TiO2 and gold, and readily perform the WGS process. TiO2 helps the adsorption and dissociation of water, while CO adsorbs on sites of the gold substrate located nearby (bifunctional catalyst). All subsequent steps occur at an oxide-metal interface at a reasonable speed. Results show that an extended gold surface or a gold nanoparticle can become a very good catalyst when combined with oxide.
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The Solar Hydrogen Source—Splitting Water
Finding new and efficient ways to use solar energy is important. In the pursuit of hydrogen, a portable and clean form of energy, one technique under investigation is using sunlight to split water into hydrogen and oxygen. |
| Many attempts have been made to find a catalyst that can split water under illumination of sunlight. K. Domen's group in Japan recently discovered a promising new catalyst: a solid solution of gallium nitride (GaN) and zinc oxide (ZnO). GaN and ZnO have the same crystal lattice structure and similar lattice parameters, and both are colorless materials that only absorb ultraviolet light. As solids, both are yellow powders that absorb visible light, which is important for solar energy because the solar spectrum contains more energy in the visible light region. Under the microscope, the yellow powder shows irregularly shaped crystals the size of hundreds of nanometers. When loaded on the surface with core-shell nanoparticles of ruthenium-chro-mium oxide (Ru/CrO3), this solid solution can split water into H2 and O2 under irradiation of visible light. H2 is generated on the surface of the Ru/CrO3 nanoparticles, and O2 is generated on the surface of the GaN/ZnO. |
The computing power came from a Linux cluster that contains 60 nodes and belongs to CFN's theory division and from NewYorkBlue, an IBM Blue Gene/L,P supercomputer located at Brookhaven National Laboratory. |
| The process that forms O2 is a research focus because it is not as well understood as H2 formation. To improve the efficiency of these new photo-catalysts (GaN/ZnO and Ru/CrO3), it is important to understand the microscopic process of both H2 and O2 formation. |
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| Illustration: A. Tovey; Source: Theory and Computation Group, CFN, BNL |
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| Figure 4. Adsorption geometry of a monolayer of water on a gallium nitride surface. |
| Theoretical modeling is helping to illuminate O2 formation. It is known that H2O molecules are oxidized into O2 molecules by accepted photo-holes from the GaN/ZnO crystal. What is unknown, however, is where and how this process happens at the atomic level. The geometries and compositions of the alloy surfaces are complicated. Current experiments are unclear regarding on which surface site the reaction happens. As with gold catalysts, theoretical modeling can reveal more about this system. |
| When DFT is implemented in scientific software on supercomputers or computer clusters, researchers can study hundreds of atoms at the quantum mechanical level. Although DFT does not give an exact treatment of electronic quantum effects, it usually predicts the ground state geometries and binding energies with reasonable accuracy. |
| However, even with DFT and powerful supercomputers, it is still impossible to simulate the real system because of size (much more than thousands of atoms) and complexity. The problem, therefore, must be simplified. CFN researchers have studied a model system of GaN surface covered by a layer of water molecules (figure 4, p43). The surface in this model is the most stable surface of the GaN crystal. Several possible adsorption geometries of water molecules were considered, and DFT was used to optimize the structures and obtain the binding energies of water molecule on the surface. The computing power came from a Linux cluster that contains 60 nodes and belongs to CFN's theory division and from NewYorkBlue (sidebar "NewYorkBlue—An Energy Efficient Supercomputer"), an IBM Blue Gene/L,P supercomputer located at Brookhaven National Laboratory (BNL). |
Because nanoscale gold clusters can catalyze the reaction of CO to CO2 despite the well known inertness of bulk gold, there has been a huge outpouring of computational studies of gold clusters in recent years following the discovery of its chemical reactivity.
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| The H2O molecules are totally dissociated into OH and hydrogen pairs on the surface of GaN. The OH is attached to a surface gallium atom, and the hydrogen is attached to a surface nitrogen atom. Other groups have studied a similar model system with ZnO, where half of the H2O molecules are dissociated into OH and hydrogen, while half are adsorbed as a whole H2O molecule. |
| The GaN surface may have already been realized in experiments. Non-polar GaN films have been grown as a potential building block of photoelectronic devices. If no surface reconstructions happen, the exposed surface of these films should be the one to study. When these films are in contact with air, a question emerges: are the water molecules adsorb onto the film? Current research directly answers that question. |
Scientists have only scratched the surface of photo-catalysis. The charge transfer reaction
(GaN)+N + H2O → (GaN)NOH+H+
is not yet understood, nor the chemistry for clearing the system for further oxidations
4OH → 2H2O+O2
Other areas open for study are the effect of liquid water beyond the surface, non-zero temperature, special alloy configurations, surface defects, and alternative surfaces. These areas present a worthy challenge for modern computational theory.
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Gold Nanoparticles—Structures Galore
Because nanoscale gold clusters can catalyze the reaction of CO to CO2 despite the well known inertness of bulk gold, there has been a huge outpouring of computational studies of gold clusters in recent years following the discovery of its chemical reactivity. But, as with other atomic clusters, there is not yet a complete understanding of the factors that control structure and reactivity at the nanoscale. Clearly, the properties are different and markedly dependent on cluster size. Crystalline gold adopts the face-centered cubic (fcc) structure with 12 neighbors. Based on DFT and other studies, clusters with fewer than 8-10 atoms are expected to be planar. Larger clusters may adopt icosahedral structures, a symmetry that is forbidden in infinite crystals. For example, models employing the Lennard-Jones 6-12 potential show a preference for icosahedral symmetry up to 1,000atoms and do not adopt fcc structure until approximately 105 atoms. Although crystalline gold is non-magnetic, small clusters may retain a magnetic moment, for example those with an odd number of electrons. |
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| Source: Theory and Computation Group, CFN, BNL |
| Figure 5. NewYorkBlue, a 100 teraflops IBM Blue Gene/L which is part of the New York Center for Computational Sciences (NYCCS). NYCCS is a joint project of Stony Brook University and Brookhaven National Laboratory. |
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| For gold, the situation is even more complex. Gold is the most malleable and ductile of all metals. It can be rolled into gold leaf that is approximately 100 nm thick. It is expected that there would be many structures, including amorphous structures, lying close in energy to the ground state. Also, transformations among these structures could easily occur because of adsorbed atoms or molecules. Indeed, recent calculations illustrate these effects, making structure determinations all the more difficult. |
| Cluster structures are often described in terms of "magic numbers," which relate to the filling of nearly free electron shells or the completion of geometrical shells of atoms surrounding a central atom. This description provides only a rough guide to the structures that are actually expected. Studies of Lennard-Jones models suggest that the number of structures grows exponentially as a function of size, although clearly at some point the number must decline, as there are relatively few crystal structures that are energetically accessible. |
| BNL has studied a number of small gold (and palladium) clusters using NWChem (developed at Pacific Northwest National Laboratory) and GAMESS (developed by the Gordon group at Ames Laboratory). Both are open source Gaussian-based electronic structure codes. The Gaussian basis sets contain 35 functions/atom representing 5s, 5p, 5d, and 6s electrons with the balance described by an effective core potential. BNL used the gradient-corrected density functional method. Calculations were performed on NewYorkBlue (sidebar "NewYorkBlue—An Energy Efficient Supercomputer") with up to 2,048 processors. |
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| Source: Theory and Computation Group, CFN, BNL |
| Figure 6. Two- and three-dimensional structures for eight-atom gold clusters: (a) planar, lowest energy; (b) capped tetrahedron, 0.53 eV higher; (c) simple cube, 1.11 eV higher than (a). |
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| Figure 6 shows several structures for Au8. Consistent with previous work by the Gordon group and others, the lowest energy structure is planar. The two three-dimensional structures that might have been thought to be the most stable are the capped tetrahedron (0.53 eV higher in energy) and a simple cube (1.11 eV higher). |
There is a pressing need to extend accurate quantum mechanical calculations to nanoscale particles, which will require the petascale computational resources at the National Leadership Computing facilities. |
| Studies have begun of larger clusters. As mentioned previously, Lennard-Jones clusters adopt an icosahedral structure, and there have been a number of studies comparing icosahedral gold with a cubo-octahedral structure that can be viewed as cut out from an fcc lattice. Figure 7 shows examples of icosahedral structures of 13 and 55 atoms. Results indicate that for Au13, the icosahedral structure is not favored over the cubic structure. The energy difference is approximately 0.20 eV/atom. |
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| Illustration: A. Tovey; Source: Theory and Computation Group, CFN, BNL |
| Figure 7. Icosahedral gold clusters with 13 and 55 atoms. |
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Summary and Future Challenges
There is a pressing need to extend accurate quantum mechanical calculations to nanoscale particles, which will require the petascale computational resources at the National Leadership Computing facilities. Reorganizing and rewriting standard codes in the quantum chemistry community will be required, as will the development of new, more accurate approximation schemes for the many-particle Coulomb interaction. |
Nanoparticles are the intermediate between small molecules and crystalline solids with many unique properties. There is no guarantee that approximations such as the current implementation of DFT will be adequate. Their accuracy cannot be assessed until larger systems are able to be studied in a routine fashion.
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Contributors: Dr. Philip B. Allen, Dr. James W. Davenport, Dr. Ping Liu, Dr. Michael McGuigan, Dr. James Muckerman, Dr. Mark Hybertsen, Dr. Altaf Karim, Mr. Xiao Shen, and Dr. Yolanda Small
Acknowledgments: This work was performed at Brookhaven National Laboratory and supported by the U.S. Department of Energy, Office of Basic Energy Sciences and Laboratory Directed Research and Development, under contract DE-AC02-98CH10886
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| Further Reading
S. Chaudhuri, J. Graetz, A. Ignatov, J.J. Reilly and J.T. Muckerman. 2006. Understanding the Role of Ti in Reversible Hydrogen Storage as Sodium Alanate: A Combined Experimental and Density Functional Theoretical Approach. J. Am. Chem. Soc. 128: 11404.
C. L. Janssen and I. M. B. Nielsen. 2008. Parallel Computing in Quantum Chemistry. CRC Press, Boca Raton, FL.
J.A. Rodriguez, S. Ma, P. Liu, J. Hrbek, J. Evans, M. Perez. 2007. Activity of CeOx and TiOx Nanoparticles Grown on Au(111) in the Water-Gas Shift Reaction. Science 318: 1757.
D. J. Wales. 2003. Energy Landscapes, with Applications to Clusters, Biomolecules, and Glasses. Cambridge University Press, Cambridge, UK.
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