Accurate barriers for rate controlling elementary reactions on metal surfaces are key to understanding, controlling, and predicting the rate of heterogeneously catalyzed processes. While barrier... Show moreAccurate barriers for rate controlling elementary reactions on metal surfaces are key to understanding, controlling, and predicting the rate of heterogeneously catalyzed processes. While barrier heights for gas phase reactions have been extensively benchmarked, dissociative chemisorption barriers for the reactions of molecules on metal surfaces have received much less attention. The first database called SBH10 and containing 10 entries was recently constructed based on the specific reaction parameter approach to density functional theory (SRP-DFT) and experimental results. We have now constructed a new and improved database (SBH17) containing 17 entries based on SRP-DFT and experiments. For this new SBH17 benchmark study, we have tested three algorithms (high, medium, and light) for calculating barrier heights for dissociative chemisorption on metals, which we have named for the amount of computational effort involved in their use. We test the performance of 14 density functionals at the GGA, GGA+vdW-DF, and meta-GGA rungs. Our results show that, in contrast with the previous SBH10 study where the BEEF-vdW-DF2 functional seemed to be most accurate, the workhorse functional PBE and the MS2 density functional are the most accurate of the GGA and meta-GGA functionals tested. Of the GGA+vdW functionals tested, the SRP32-vdW-DF1 functional is the most accurate. Additionally, we found that the medium algorithm is accurate enough for assessing the performance of the density functionals tested, while it avoids geometry optimizations of minimum barrier geometries for each density functional tested. The medium algorithm does require metal lattice constants and interlayer distances that are optimized separately for each functional. While these are avoided in the light algorithm, this algorithm is found not to give a reliable description of functional performance. The combination of relative ease of use and demonstrated reliability of the medium algorithm will likely pave the way for incorporation of the SBH17 database in larger databases used for testing new density functionals and electronic structure methods. Show less
Metals surfaces form a group of effective catalysts for the reaction of small molecules such as hydrogen (H2). In order to improve the predictive power of theory with respect to the catalytic... Show moreMetals surfaces form a group of effective catalysts for the reaction of small molecules such as hydrogen (H2). In order to improve the predictive power of theory with respect to the catalytic activity of small molecules reacting at metal surfaces, the way in which metal surfaces modify the potential energy of molecules needs to be understood at a fundamental level. Currently density functional theory (DFT) is the only electronic structure method that is accurate enough to achieve chemical accuracy while being cheap enough to make large comparative studies feasible. The work in this thesis is concerned with the creation of highly accurate density functionals that can give a simultaneously good description of the metal surface, the molecule, and the molecule interacting with the metal surface, as well as the description and simulation of supersonic molecular beam experiments and associative desorption experiments needed to validate the obtained results. Show less
Reactions on stepped surfaces are relevant to heterogeneous catalysis, in which a reaction often takes place at the edges of nanoparticles where the edges resemble steps on single-crystal stepped... Show moreReactions on stepped surfaces are relevant to heterogeneous catalysis, in which a reaction often takes place at the edges of nanoparticles where the edges resemble steps on single-crystal stepped surfaces. Previous results on H2 + Cu(211) showed that, in this system, steps do not enhance the reactivity and raised the question of whether this effect could be, in any way, related to the neglect of quantum dynamical effects in the theory. To investigate this, we present full quantum dynamical molecular beam simulations of sticking of H2 on Cu(211), in which all important rovibrational states populated in a molecular beam experiment are taken into account. We find that the reaction of H2 with Cu(211) is very well described with quasi-classical dynamics when simulating molecular beam sticking experiments, in which averaging takes place over a large number of rovibrational states and over translational energy distributions. Our results show that the stepped Cu(211) surface is distinct from its component Cu(111) terraces and Cu(100) steps and cannot be described as a combination of its component parts with respect to the reaction dynamics when considering the orientational dependence. Specifically, we present evidence that, at translational energies close to the reaction threshold, vibrationally excited molecules show a negative rotational quadrupole alignment parameter on Cu(211), which is not found on Cu(111) and Cu(100). The effect arises because these molecules react with a site-specific reaction mechanism at the step, that is, inelastic rotational enhancement, which is only effective for molecules with a small absolute value of the magnetic rotation quantum number. From a comparison to recent associative desorption experiments as well as Born–Oppenheimer molecular dynamics calculations, it follows that the effects of surface atom motion and electron–hole pair excitation on the reactivity fall within chemical accuracy, that is, modeling these effect shifts extracted reaction probability curves by less than 1 kcal/mol translational energy. We found no evidence in our fully state-resolved calculations for the “slow” reaction channel that was recently reported for associative desorption of H2 from Cu(111) and Cu(211), but our results for the fast channel are in good agreement with the experiments on H2 + Cu(211). Show less
Accurate barriers for rate controlling elementary surface reactions are key to understanding, controlling, and predicting the rate of overall heterogeneously catalyzed processes. The specific... Show moreAccurate barriers for rate controlling elementary surface reactions are key to understanding, controlling, and predicting the rate of overall heterogeneously catalyzed processes. The specific reaction parameter approach to density functional theory (SRP-DFT) in principle allows chemically accurate barrier heights to be obtained for molecules dissociating on metal surfaces, and such accurate barriers are now available for four H2–metal and three CH4–metal systems. Also, there is some evidence that SRP density functionals (SRP-DFs) may be transferable among systems in which the same molecule interacts with a low-index face of metals belonging to the same group. To extend the SRP database, here we take a first step to obtain an SRP-DF for H2 + Ni(111) by comparing sticking probabilities (S0) computed with the quasi-classical trajectory method with S0 measured in several molecular beam experiments, using potential energy surfaces computed with several density functionals. We find that the SRP-DF for H2 + Pt(111) is not transferable to H2 + Ni(111). On the other hand, the PBE-vdW2 functional describes the molecular beam experiments on H2 + Ni(111), which we deem to be most accurate with chemical accuracy and may therefore be considered a candidate SRP-DF for this system, of which the quality still needs to be confirmed through comparison with an experiment to which it was not fitted. However, the different molecular beam sticking measurements that we considered showed discrepancies with one another and with the theory for incidence energies > 0.2 eV, and it would be good if better defined and more accurate experiments would be done for these energies to resolve these differences. Show less
Specific reaction parameter density functionals (SRP-DFs), which can describe dissociative chemisorption reactions on metals to within chemical accuracy, have so far been based on exchange... Show moreSpecific reaction parameter density functionals (SRP-DFs), which can describe dissociative chemisorption reactions on metals to within chemical accuracy, have so far been based on exchange functionals within the generalized gradient approximation (GGA) and on GGA correlation functionals or van der Waals correlation functionals. These functionals are capable of describing the molecule–metal surface interaction accurately, but they suffer from the general GGA problem that this can be done only at the cost of a rather poor description of the metal. Here, we show that it is possible also to construct SRP-DFs for H2 dissociation on Cu(111) based on meta-GGA functionals, introducing three new functionals based on the “made-simple” (MS) concept. The exchange parts of the three functionals (MS-PBEl, MS-B86bl, and MS-RPBEl) are based on the expressions for the PBE, B86b, and RPBE exchange functionals. Quasi-classical trajectory (QCT) calculations performed with potential energy surfaces (PESs) obtained with the three MS functionals reproduce molecular beam experiments on H2, D2 + Cu(111) with chemical accuracy. Therefore, these three non-empirical functionals themselves are also capable of describing H2 dissociation on Cu(111) with chemical accuracy. Similarly, QCT calculations performed on the MS-PBEl and MS-B86bl PESs reproduced molecular beam and associative desorption experiments on D2, H2 + Ag(111) more accurately than was possible with the SRP48 density functional for H2 + Cu(111). Also, the three new MS functionals describe the Cu, Ag, Au, and Pt metals more accurately than the all-purpose Perdew–Burke–Ernzerhof (PBE) functional. The only disadvantage we noted of the new MS functionals is that, as found for the example of H2 + Cu(111), the reaction barrier height obtained by taking weighted averages of the MS-PBEl and MS-RPBEl functionals is tunable over a smaller range (9 kJ/mol) than possible with the standard GGA PBE and RPBE functionals (33 kJ/mol). As a result of this restricted tunability, it is not possible to construct an SRP-DF for H2 + Ag(111) on the basis of the three examined MS meta-GGA functionals. Show less
