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Energy-related descriptors in machine learning are a promising strategy to predict adsorption properties of metal–organic frameworks (MOFs) in the low-pressure regime. Interactions between hosts and guests in these systems are typically expressed as a sum of dispersion and electrostatic potentials. The energy landscape of dispersion potentials plays a crucial role in defining Henry's constants for simple probe molecules in MOFs. To incorporate more information about this energy landscape, we introduce the Gaussian-approximated Lennard-Jones (GALJ) potential, which fits pairwise Lennard-Jones potentials with multiple Gaussians by varying their heights and widths. The GALJ approach is capable of replicating information that can be obtained from the original LJ potentials and enables efficient development of Gaussian integral (GI) descriptors that account for spatial correlations in the dispersion energy environment. GI descriptors would be computationally inconvenient to compute using the usual direct evaluation of the dispersion potential energy surface. We show that these new GI descriptors lead to improvement in ML predictions of Henry's constants for a diverse set of adsorbates in MOFs compared to previous approaches to this task. [ABSTRACT FROM AUTHOR]

Alkanethiolate monolayers are one of the most comprehensively studied self-assembled systems due to their ease of preparation, their ability to be functionalized, and the opportunity to control their thickness perpendicular to the surface. However, these systems suffer from degradation due to oxidation and defects caused by surface etching and adsorbate rotational boundaries. Thioethers offer a potential alternative to thiols that overcome some of these issues and allow dimensional control of self-assembly parallel to the surface. Thioethers have found uses in surface modification of nanoparticles, and chiral thioethers tethered to catalytically active surfaces have been shown to enable enantioselective hydrogenation. However, the effect of structural, chemical, and chiral modifications of the alkyl chains of thioethers on their self-assembly has remained largely unstudied. To elucidate how molecular structure, particularly alkyl branching and chirality, affects molecular self-assembly, we compare four related thioethers, including two pairs of structural isomers. The self-assembly of structural isomers N-butyl methyl sulfide and tert-butyl methyl sulfide was studied with high resolution scanning tunneling microscopy (STM); our results indicate that both molecules form highly ordered arrays despite the bulky tert-butyl group. We also investigated the effect of intrinsic chirality in the alkyl tails on the adsorption and self-assembly of butyl sec-butyl sulfide (BSBS) with STM and density functional theory and contrast our results to its structural isomer, dibutyl sulfide. Calculations provide the relative stability of the four stereoisomers of BSBS and STM imaging reveals two prominent monomer forms. Interestingly, the racemic mixture of BSBS is the only thioether we have examined to date that does not form highly ordered arrays; we postulate that this is due to weak enantiospecific intermolecular interactions that lead to the formation of energetically similar but structurally different assemblies. Furthermore, we studied all of the molecules in their monomeric molecular rotor form, and the surface-adsorbed chirality of the three asymmetric thioethers is distinguishable in STM images. [ABSTRACT FROM AUTHOR]

KTaO3 (KTO) is a useful prototypical perovskite for examining the mechanisms of proton transport in perovskites. Previously, Gomez et al. [J. Chem. Phys. 126, 194701 (2007)] reported density functional theory (DFT) calculations describing proton hopping in defect-free KTO. We use DFT calculations to extend that work in two directions, namely, understanding isotope effects in low and high temperature proton transport and the role of native point defects in KTO. At cryogenic temperatures, quantum tunneling plays a vital role in the net hopping of protons in KTO. At the elevated temperature characteristic of applications involving proton-conducting perovskites, tunneling is negligible but zero point energy effects still lead to non-negligible isotope effects for H+, D+, and T+. We also use DFT to characterize the populations of relevant point defects in KTO as a function of experimental conditions, and to examine the migration of protons that are close in proximity to these defects. This information gives useful insight into the overall transport rates of protons through KTO under a variety of external environments. We also assess the overall diffusivity of protons in KTO at various ranges of oxygen vacancy concentrations by performing kinetic Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Detailed density functional theory calculations have been performed to investigate the adsorption and diffusion of the Rh and Au adatom on the graphene moiré superstructure on Ru(0001). The adsorption energies of each adatom in all of the non-equivalent C-top and C6 ring center sites on the graphene moiré have been calculated. The resulting potential energy surfaces encompass the entire graphene moiré unit cell and shows that the adsorption of both Rh1 and Au1 is most stable in the fcc region on the graphene moiré. The minimum-energy diffusion path between adjacent moiré cells is identified to run mostly directly between the fcc and hcp regions for Au1, but deviates toward the mound region for Rh1. The global diffusion barrier is estimated to be 0.53 eV for Rh1 and 0.71 eV for Au1, corresponding to a hopping rate between adjacent moiré cells of ∼103 s-1 and ∼1 s-1 at 298 K, respectively. The consequences of different hopping rates to cluster nucleation have been explored by performing Monte Carlo-based statistical analysis, which suggests that diffusing species other than adatoms need to be taken into account to develop an accurate description of cluster nucleation and growth on this surface. [ABSTRACT FROM AUTHOR]

Experimental studies have reported that glycine is adsorbed on the Cu(110) and Cu(100) surfaces in its deprotonated form at room temperature, but in its zwitterionic form on Pd(111) and Pt(111). In contrast, recent density functional theory (DFT) calculations indicated that the deprotonated molecules are thermodynamically favored on Cu(110), Cu(100), and Pd(111). To explore the source of this disagreement, we have tested three possible hypotheses. Using DFT calculations, we first show that the kinetic barrier for the deprotonation reaction of glycine on Pd(111) is larger than on Cu(110) or Cu(100). We then report that the presence of excess hydrogen would have little influence on the experimentally observed results, especially for Pd(111). Lastly, we perform Monte Carlo simulations to demonstrate that the aggregates of zwitterionic species on Pt(111) are energetically preferred to those of neutral species. Our results strongly suggest that the formation of aggregates with relatively large numbers of adsorbed molecules is favored under experimentally relevant conditions and that the adsorbate-adsorbate interactions in these aggregates stabilize the zwitterionic species. [ABSTRACT FROM AUTHOR]

Osmotic framework adsorbed solution theory is a useful molecular simulation method to predict the evolution of structural transitions upon adsorption of guest molecules in flexible nanoporous solids. One challenge with previous uses of this approach has been the estimation of free energy differences between the solid phases of interest in the absence of adsorbed molecules. Here we demonstrate that these free energy differences can be calculated without reference to experimental data via the vibrational density of states of each phase, a quantity that can be obtained from molecular dynamics simulations. We show the applicability of this method through case studies of the swelling behaviors of two representative systems in which swelling upon adsorption of water is of importance: single-walled aluminosilicate nanotube bundles and cesium montmorillonite. The resulting predictions show that the aluminosilicate nanotube bundles swell significantly with increasing interstitial adsorption and that the layer spacing of cesium montmorillonite expands up to about 12.5 Å, giving good agreement with experiments. The method is applicable to a wide range of flexible nanoporous materials, such as zeolites, metal-organic frameworks, and layered oxide materials, when candidate structures can be defined and a force field to describe the material is available. [ABSTRACT FROM AUTHOR]

Chemical interactions of H2O, CO, NO, pyridine, C2H2, H2S, and NH3 with open metal sites in the metal-organic framework (MOF) Cu3(benzenetricarboxylate)2 are examined using plane wave periodic density functional theory (DFT). In the case of single molecule adsorption on a Cu dimer, NH3 and pyridine have the strongest binding, while NO binds weakly. Binding of pairs of molecules on a Cu dimer shows significant interaction energies, that is, the binding energy of the pair of molecules is not a simple summation of the binding energies of each molecule. The effect of molecular adsorption on the magnetic moments of Cu atoms in the MOF is also examined. Using the binding energies from DFT calculations, the effects of the pressure and temperature on the chemisorbed species are investigated. Finally the effect of water adsorption on the elastic behavior of Cu3(BTC)2 is described. [ABSTRACT FROM AUTHOR]

Diffusion of interstitial hydrogen plays a key role in potential uses for amorphous metals as membranes for hydrogen purification. We show how first principles-based methods can be used to characterize diffusion of interstitial H in amorphous metals using amorphous Fe3B as an example. Net transport of interstitial H is governed by the transport diffusion coefficient that appears in Fick’s law. This diffusion coefficient is strongly dependent on the interstitial concentration, and is not equal to the self-diffusion coefficient except at dilute interstitial concentrations. Under conditions of practical interest, the concentrations of interstitial H in amorphous metals are nondilute so methods to determine the transport diffusion coefficient must be used if net mass transport is to be described. We show how kinetic Monte Carlo simulations of interstitial H diffusion that use rates derived from first-principles calculations can be used to assess both self- and transport diffusion coefficients of H in amorphous metals. These methods will be helpful in efforts to screen amorphous metal alloys as potential membranes for hydrogen purification. [ABSTRACT FROM AUTHOR]

Highly stepped metal surfaces can define intrinsically chiral structures and these chiral surfaces can potentially be used to separate chiral molecules. The decoration of steps on these surfaces with additional metal atoms is one potential avenue for improving the enantiospecificity of these surfaces. For a successful step decoration, the additional metal atoms should ideally remain at the kinked step sites on the surface. We performed density functional theory (DFT) calculations to identify pairs of metal adatoms and metal surfaces where this kind of step decoration could be thermodynamically stable. These calculations have identified multiple stable examples of step decoration. Using our DFT results, we developed a model to predict surface segregation on a wide range of stepped metal surfaces. With this model, we have estimated the stability of step decoration without further DFT calculations for surface segregation for all combinations of the 3d, 4d, and 5d metals. [ABSTRACT FROM AUTHOR]

First-principles calculations offer a useful complement to experimental approaches for characterizing hydrogen permeance through dense metal membranes. A challenge in applying these methods to disordered alloys is to make quantitative predictions for the net solubility and diffusivity of interstitial H based on the spatially local information that can be obtained from first-principles calculations. In this study, we used a combination of density functional theory calculations and a cluster expansion method to describe interstitial H in alloys of composition Pd96M4, where M=Ag, Cu, and Rh. The cluster expansion approach highlights the shortcomings of simple lattice models that have been used in the past to study similar systems. We use Sieverts’ law to calculate H solubility and a kinetic Monte Carlo scheme to find the diffusivity of H in PdAg, PdCu, and PdRh alloys at a temperature range of 400≤=T≤=1200 K. From these results, we are able to predict the permeability of hydrogen through membranes made from these Pd-based binary alloys. [ABSTRACT FROM AUTHOR]

Surfaces of simple fcc metals such as Cu with nonzero and unequal Miller indices are intrinsically chiral. Density functional theory (DFT) calculations are a useful way to study the enantiospecific adsorption of small chiral molecules on these chiral metal surfaces. We report DFT calculations of seven chiral molecules on several structurally distinct chiral Cu surfaces. These surfaces include two surfaces with (111)-oriented terraces and one with (100)-oriented terraces. Calculations are also described on a surface that was modified to mimic the surface structures that typically appear on real metal surfaces following thermally driven fluctuations in step edges. Our results provide initial information on how variation in the surface structure of intrinsically chiral metal surfaces can affect the enantiospecific adsorption of small molecules on these surfaces. [ABSTRACT FROM AUTHOR]

Plane wave density functional theory calculations have been used to characterize the transition states for β-hydride elimination of ethyl on Cu(100), Cu(110), Cu(111), and Cu(221). The reaction rates predicted by these calculations have been compared to experiments by including tunneling corrections within harmonic transition state theory. Tunneling corrections are found to be important in describing the peak temperatures observed using temperature programed desorption experiments on Cu(110), Cu(111), and Cu(221). Once these corrections are included, the effective activation energies obtained from our calculations are in good agreement with previous experimental studies of this reaction on these four Cu surfaces. The transition states determined in our calculations are used to examine two general hypotheses that have been suggested to describe structure sensitivity in metal-catalyzed surface reactions. [ABSTRACT FROM AUTHOR]

Optimization of enantioselectivity in heterogeneous catalysis and chiral chromatography is a challenging task for the production of enantiopure chemicals. Enantioselective adsorbents usually consist of a surface with chiral receptors being either chiral molecules linked to the surface or chiral pockets formed by molecular templating of the surface. In both cases, the enantioselectivity is controlled mainly by the strength of the receptor-enantiomer interaction, such that one-to-one correspondence is usually preserved. The authors use Monte Carlo calculations to show that this steric requirement is not a necessary condition for the effective separation of chiral molecules. In particular, they propose a way in which a chiral surface can be constructed by a suitable spatial distribution of active sites for which the classical concept of a chiral receptor is no longer useful. Their calculations indicate that the effectiveness of the separation is affected mainly by the difference in shape of the adsorption energy distribution functions corresponding to the enantiomers. [ABSTRACT FROM AUTHOR]

Adsorption of amino acids on Cu(100) is known experimentally to induce surface reconstructions featuring intrinsically chiral Cu(3,1,17) facets, but no information about the geometry of the molecules on these chiral facets is available. We present density-functional theory calculations for the structure of glycine and alanine at moderate coverages on Cu(3,1,17). As might be expected, molecules prefer to bind at the step edges on this surface rather than on the surface's (100)-oriented terraces. The adsorption of enantiopure alanine on Cu(3,1,17) is predicted to be weakly enantiospecific, with S-alanine being more stable on Cu(3,1,17)S than R-alanine. By comparing the surface energies of Cu(100) and Cu(3,1,17) in the presence of adsorbed glycine or alanine, our calculations provide insight into the driving force for chiral reconstructions of Cu(100) by amino acids. [ABSTRACT FROM AUTHOR]

We have used atomically detailed simulations to examine the adsorption and transport diffusion of CO2 and N2 in single-walled carbon nanotubes at room temperature as a function of nanotube diameter. Linear and spherical models for CO2 are compared, showing that representing this species as spherical has only a slight impact in the computed diffusion coefficients. Our results support previous predictions that transport diffusivities of molecules inside carbon nanotubes are extremely rapid when compared with other porous materials. By examining carbon nanotubes as large as the (40,40) nanotube, we are able to compare the transport rates predicted by our calculations with recent experimental measurements. The predicted transport rates are in reasonable agreement with experimental observations. [ABSTRACT FROM AUTHOR]

Plane-wave density functional theory calculations were performed to investigate the binding and diffusion of hydrogen on three flat Ni surfaces, Ni(100), Ni(110), and Ni(111), and two stepped Ni surfaces, Ni(210) and Ni(531). On each surface, the favored adsorption sites were identified by considering the energy and stability of various binding sites and zero-point energy corrections were computed. Binding energies are compared with experimental and theoretical results from the literature. Good agreement with experimental and previous theoretical data is found. At surface coverages where adsorbate-adsorbate interactions are relatively weak, the binding energy of H is similar on the five Ni surfaces studied. Favorable binding energies are observed for stable surface sites, while subsurface sites have unfavorable values relative to the gas phase molecular hydrogen. Minimum energy paths for hydrogen diffusion on Ni surfaces and into subsurface sites were constructed. [ABSTRACT FROM AUTHOR]

The adsorption of atomic oxygen and carbon was studied with plane wave density functional theory on four Ni surfaces, Ni(110), Ni(111), Ni(210), and Ni(531). Various adsorption sites on these surfaces are examined in order to identify the most favorable adsorption site for each atomic species. The dependence of surface bonding on adsorbate coverage is also investigated. Adsorption energies and structural information are obtained and compared with existing experimental results for Ni(110) and Ni(111). In addition, activation barriers to CO dissociation have been determined on Ni(111) and Ni(531) by locating the transition states for these processes. Our results indicate that the binding energies of C are comparatively stronger on stepped surfaces than on flat surfaces, and the energy barriers associated with CO dissociation strongly favor reactions occurring near surface steps. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We use density functional theory to investigate Pt growth on SrTiO[sub 3](100) surfaces. We have determined the favored monolayer arrangement for Pt on both terminations of SrTiO[sub 3](100). The work of separation as a function of the number of monolayers of Pt has been determined for Pt films of up to 5 monolayers. To examine which surface growth mode will dominate Pt film growth on this substrate, we have also examined isolated Pt clusters on each termination of SrTiO[sub 3](100). Our results indicate that the TiO[sub 2]-terminated surface is more favorable for epitaxial growth of (100) oriented Pt films than the SrO-terminated surface. [ABSTRACT FROM AUTHOR]

Adsorption isotherms of hydrogen isotopes from molecular simulations in carbon nanotubes and interstices are presented. The adsorption of pure isotopes follows Henry’s law up to moderate coverages. A modified path integral grand canonical Monte Carlo (PI-GCMC) technique for mixture adsorption is presented and applied to adsorption of isotope mixtures in carbon nanotubes. Adsorption isotherms of H[sub 2]–T[sub 2] mixtures in nanotubes and interstices are determined at 20 and 77 K. Selectivities for T[sub 2] over H[sub 2] are calculated over a range of pressures. Selectivity in the nanotubes and interstices increases with pressure until the nanotube is saturated. Comparison of simulation results with predictions based on ideal adsorbed solution theory (IAST) shows good agreement up to moderate loadings. At higher loadings, selectivities determined from multicomponent simulations remain roughly constant, whereas IAST predicts continued increase in selectivities. Isotherms for H[sub 2]–D[sub 2] and the selectivities of D[sub 2] over H[sub 2] are determined for adsorption in (10,10) nanotubes and in the interstitial channels of closed (10,10) nanotubes. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines the generalized surface hopping method for the simulation of mixed quantum-classical dynamics. Numerical parameters used in simulations of the scattering problems; Effects on mean-field dynamics; Application of the Hellman-Feynman theorem.

Examines the adsorption kinetics of chemisorption by surface abstraction and dissociative adsorption. Use of a lattice gas (LG) model in the study of adsorption kinetics involving surface abstraction; Effect of surface diffusion; Effect of lateral interactions.

Uses molecular simulations to examine the diffusion of binary adsorbate chemical mixtures in the molecular sieve, AIPO4-5. Transition of single adsorbed species from normal to single-file diffusion; Diffusion mode exhibited by the coadsorbed mixtures.

We examine an approximate theory for the A+1/2B2→O surface reaction presented by Mai et al. [J. Chem. Phys. 98, 10017 (1993)]. This theory predicts kinetic oscillations in the vicinity of a kinetic phase transition. We show, using Monte Carlo simulations, that these oscillations are an artifact of the approximations in the theory. We demonstrate that these approximations fail near the phase transition. The theoretically predicted onset of oscillations actually corresponds to the position of the kinetic phase transition. [ABSTRACT FROM AUTHOR]

Comments on a proposed algorithm for performing constant temperature molecular dynamics (MD) simulations. Application of the algorithm to an ensemble of harmonic oscillators; Gaussian asymptotic position and velocity distributions; Intercollision dynamics of the system studied.

Total Internal Reflection Microscopy (TIRM) is an experimental technique that allows the potential energy profile of a colloidal particle above a plate to be determined from the particle's observed Brownian motion. We have used Brownian Dynamics (BD) simulations to numerically simulate TIRM experiments. We show that a careful treatment of the position dependence of the colloidal particle's mobility near the plate is vital to performing realistic simulations. These simulations enable us to systematically study the effect of experiment duration, data sampling methods, and physical parameters of the suspended colloid on the accuracy of potential energy profiles determined via TIRM. We also present an analytical theory to predict the range of energies reliably probed by TIRM experiments. This theory provides simple guidelines for the design and optimization of future TIRM experiments. Finally, we have used BD simulations to investigate the use of radiation pressure and the effects of experimental noise in TIRM experiments. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Transport of molecules through microporous crystals can be influenced by transport limitations at the mouths of pores. In the limit of high temperatures, the kinetics of adsorption into micropores is dominated by steric effects. To assess the role of molecular shape and pore size on pore mouth adsorption kinetics, discontinuous molecular dynamics has been used to simulate a variety of hard-sphere molecules adsorbing into slit, circular, and elliptical pores. Particular attention has been given to pores with length scales similar to zeolites. By simulating a range of straight chain, branched, and cyclic molecules, the selectivities that can arise due to differences in adsorption kinetics as functions of molecular size and shape have been probed. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Traditional models of single-file diffusion in zeolites assume that adsorbate diffusion mechanisms at high and dilute pore loadings are identical. Atomistic models of single file systems, in contrast, have shown that clusters of adsorbed molecules can diffuse via concerted motions that are not available to individual adsorbates. We report molecular dynamics simulations of CF[sub 4] clusters in AlPO[sub 4]-5 and Xe clusters in AlPO[sub 4]-31. We have used these simulations to characterize the diffusion and dissociation mechanisms and rates of these clusters as a function of temperature and cluster size. We have also used our MD results to parametrize coarse-grained models of adsorbed cluster dynamics. Using kinetic Monte Carlo simulations of our coarse-grained models, we have simulated pores containing hundreds of interacting clusters on microsecond time scales. These simulations offer the first opportunity to examine single-file diffusion in models that accurately account for the existence of concerted cluster diffusion. Our simulations show that concerted cluster motions make large contributions to single-file mobilities. The deviations of the computed single-file mobilities from the well-known result for hard sphere diffusion are discussed, as are the implications of using the latter model to interpret experimental measurements of single-file diffusion. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Chemical interactions of H(2)O, CO, NO, pyridine, C(2)H(2), H(2)S, and NH(3) with open metal sites in the metal-organic framework (MOF) Cu(3)(benzenetricarboxylate)(2) are examined using plane wave periodic density functional theory (DFT). In the case of single molecule adsorption on a Cu dimer, NH(3) and pyridine have the strongest binding, while NO binds weakly. Binding of pairs of molecules on a Cu dimer shows significant interaction energies, that is, the binding energy of the pair of molecules is not a simple summation of the binding energies of each molecule. The effect of molecular adsorption on the magnetic moments of Cu atoms in the MOF is also examined. Using the binding energies from DFT calculations, the effects of the pressure and temperature on the chemisorbed species are investigated. Finally the effect of water adsorption on the elastic behavior of Cu(3)(BTC)(2) is described.

Diffusion of interstitial hydrogen plays a key role in potential uses for amorphous metals as membranes for hydrogen purification. We show how first principles-based methods can be used to characterize diffusion of interstitial H in amorphous metals using amorphous Fe(3)B as an example. Net transport of interstitial H is governed by the transport diffusion coefficient that appears in Fick's law. This diffusion coefficient is strongly dependent on the interstitial concentration, and is not equal to the self-diffusion coefficient except at dilute interstitial concentrations. Under conditions of practical interest, the concentrations of interstitial H in amorphous metals are nondilute so methods to determine the transport diffusion coefficient must be used if net mass transport is to be described. We show how kinetic Monte Carlo simulations of interstitial H diffusion that use rates derived from first-principles calculations can be used to assess both self- and transport diffusion coefficients of H in amorphous metals. These methods will be helpful in efforts to screen amorphous metal alloys as potential membranes for hydrogen purification.

Highly stepped metal surfaces can define intrinsically chiral structures and these chiral surfaces can potentially be used to separate chiral molecules. The decoration of steps on these surfaces with additional metal atoms is one potential avenue for improving the enantiospecificity of these surfaces. For a successful step decoration, the additional metal atoms should ideally remain at the kinked step sites on the surface. We performed density functional theory (DFT) calculations to identify pairs of metal adatoms and metal surfaces where this kind of step decoration could be thermodynamically stable. These calculations have identified multiple stable examples of step decoration. Using our DFT results, we developed a model to predict surface segregation on a wide range of stepped metal surfaces. With this model, we have estimated the stability of step decoration without further DFT calculations for surface segregation for all combinations of the 3d, 4d, and 5d metals.

First-principles calculations offer a useful complement to experimental approaches for characterizing hydrogen permeance through dense metal membranes. A challenge in applying these methods to disordered alloys is to make quantitative predictions for the net solubility and diffusivity of interstitial H based on the spatially local information that can be obtained from first-principles calculations. In this study, we used a combination of density functional theory calculations and a cluster expansion method to describe interstitial H in alloys of composition Pd96M4, where M=Ag, Cu, and Rh. The cluster expansion approach highlights the shortcomings of simple lattice models that have been used in the past to study similar systems. We use Sieverts' law to calculate H solubility and a kinetic Monte Carlo scheme to find the diffusivity of H in PdAg, PdCu, and PdRh alloys at a temperature range of 400

Plane wave density functional theory calculations have been used to characterize the transition states for beta-hydride elimination of ethyl on Cu(100), Cu(110), Cu(111), and Cu(221). The reaction rates predicted by these calculations have been compared to experiments by including tunneling corrections within harmonic transition state theory. Tunneling corrections are found to be important in describing the peak temperatures observed using temperature programmed desorption experiments on Cu(110), Cu(111), and Cu(221). Once these corrections are included, the effective activation energies obtained from our calculations are in good agreement with previous experimental studies of this reaction on these four Cu surfaces. The transition states determined in our calculations are used to examine two general hypotheses that have been suggested to describe structure sensitivity in metal-catalyzed surface reactions.