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Density functional theory (DFT) at the generalized gradient approximation (GGA) level is often considered the best compromise between feasibility and accuracy for reactions of molecules on metal surfaces. Recent work, however, strongly suggests that density functionals (DFs) based on GGA exchange are not able to describe molecule-metal surface reactions for which the work function of the metal surface minus the electron affinity of the molecule is less than 7 eV. Systems for which this is true exhibit an increased charge transfer from the metal to the molecule at the transition state, increasing the delocalisation of the electron density. This enlarged delocalisation can cause GGA-DFT to underestimate energy values relative to the gas-phase and thus underestimate the barrier height, similar to what has been observed for several gas-phase reactions. An example of such a molecule-metal surface system is O 2 + Al(111). Following a similar strategy as for gas-phase reactions, previous work showed results of increased accuracy when using a screened hybrid DF for O 2 + Al(111). However, even screened hybrid DFs are computationally expensive to use for metal surfaces. To resolve this, we test a non-self-consistent field (NSCF) screened hybrid DF approach. This approach computes screened hybrid DFT energies based on self-consistent-field (SCF) GGA electronic densities. Here, we explore the accuracy of the NSCF screened hybrid DF approach by implementing the NSCF HSE03-1/3x@RPBE DF for O 2 + Al(111). We compute and analyse molecular beam sticking probabilities as well as a set of sticking probabilities for rotationally aligned O 2 . Our results show that the NSCF approach results in reaction probability curves that reproduce SCF results with near-chemical accuracy, suggesting that the NSCF approach can be used advantageously for exploratory purposes. An analysis of the potential energy surface and the barriers gives insight into the cause of the disagreement between the SCF and NSCF reaction probabilities and into the changes needed in theoretical modelling to further improve the description of the O 2 + Al(111) system. Finally, the hole model yields fair agreement with dynamics results for the reaction probability curve, but results in an increased slope of the reaction probability curve compared to the molecular dynamics, with a shift to lower or higher energies depending on whether the vibrational energy of the molecule is included in the initial energy of the molecule or not.

Predictive capability, accuracy, and affordability are essential features of a theory that is capable of describing dissociative chemisorption on a metal surface. This type of reaction is important for heterogeneous catalysis. Here we present an approach in which we use diffusion Monte Carlo (DMC) to pin the minimum barrier height and construct a density functional that reproduces this value. This predictive approach allows the construction of a potential energy surface at the cost of density functional theory while retaining near DMC accuracy. Scrutinizing effects of energy dissipation and quantum tunneling, dynamics calculations suggest the approach to be of near chemical accuracy, reproducing molecular beam sticking experiments for the showcase H 2 + Al(110) system to ∼1.4 kcal/mol.

The production of a majority of chemicals involves heterogeneous catalysis at some stage, and the rates of many heterogeneously catalyzed processes are governed by transition states for dissociative chemisorption on metals. Accurate values of barrier heights for dissociative chemisorption on metals are therefore important to benchmarking electronic structure theory in general and density functionals in particular. Such accurate barriers can be obtained using the semiempirical specific reaction parameter (SRP) approach to density functional theory. However, this approach has thus far been rather ad hoc in its choice of the generic expression of the SRP functional to be used, and there is a need for better heuristic approaches to determining the mixing parameters contained in such expressions. Here we address these two issues. We investigate the ability of several mixed, parametrized density functional expressions combining exchange at the generalized gradient approximation (GGA) level with either GGA or nonlocal correlation to reproduce barrier heights for dissociative chemisorption on metal surfaces. For this, seven expressions of such mixed density functionals are tested on a database consisting of results for 16 systems taken from a recently published slightly larger database called SBH17. Three expressions are derived that exhibit high tunability and use correlation functionals that are either of the PBE GGA form or of one of two limiting nonlocal forms also describing the attractive van der Waals interaction in an approximate way. We also find that, for mixed density functionals incorporating GGA correlation, the optimum fraction of repulsive RPBE GGA exchange obtained with a specific GGA density functional is correlated with the charge-transfer parameter, which is equal to the difference in the work function of the metal surface and the electron affinity of the molecule. However, the correlation is generally not large and not large enough to obtain accurate guesses of the mixing parameter for the systems considered, suggesting that it does not give rise to a very effective search strategy.

We evaluate the importance of quantum effects on the sticking of H 2 on Al(110) for conditions that are close to those of molecular beam experiments that have been done on this system. Calculations with the quasi-classical trajectory (QCT) method and with quantum dynamics (QD) are performed using a model in which only motion in the six molecular degrees of freedom is allowed. The potential energy surface used has a minimum barrier height close to the value recently obtained with the quantum Monte Carlo method. Monte Carlo averaging over the initial rovibrational states allowed the QD calculations to be done with an order of magnitude smaller computational expense. The sticking probability curve computed with QD is shifted to lower energies relative to the QCT curve by 0.21 to 0.05 kcal/mol, with the highest shift obtained for the lowest incidence energy. Quantum effects are therefore expected to play a small role in calculations that would evaluate the accuracy of electronic structure methods for determining the minimum barrier height to dissociative chemisorption for H 2 + Al(110) on the basis of the standard procedure for comparing results of theory with molecular beam experiments., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)

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 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.

The probability for dissociation of molecules on metal surfaces, which often controls the rate of industrially important catalytic processes, can depend strongly on how energy is partitioned in the incident molecule. There are many example systems where the addition of vibrational energy promotes reaction more effectively than the addition of translational energy, but for rotational pre-excitation similar examples have not yet been discovered. Here, we make an experimentally testable theoretical prediction that adding energy to the rotation of HCl can promote its dissociation on Au(111) 20 times more effectively than increasing its translational energy. In the underlying mechanism, the molecule's initial rotational motion allows it to pass through a critical region of the reaction path, where this path shows a strong and nonmonotonic dependence on the molecular orientation.

Accurately modeling heterogeneous catalysis requires accurate descriptions of rate-controlling elementary reactions of molecules on metal surfaces, but standard density functionals (DFs) are not accurate enough for this. The problem can be solved with the specific reaction parameter approach to density functional theory (SRP-DFT), but the transferability of SRP DFs among chemically related systems is limited. We combine the MS-PBEl, MS-B86bl, and MS-RPBEl semilocal made simple (MS) meta-generalized gradient approximation (GGA) (mGGA) DFs with rVV10 nonlocal correlation, and we evaluate their performance for the hydrogen (H 2 ) + Cu(111), deuterium (D 2 ) + Ag(111), H 2 + Au(111), and D 2 + Pt(111) gas-surface systems. The three MS mGGA DFs that have been combined with rVV10 nonlocal correlation were not fitted to reproduce particular experiments, nor has the b parameter present in rVV10 been reoptimized. Of the three DFs obtained the MS-PBEl-rVV10 DF yields an excellent description of van der Waals well geometries. The three original MS mGGA DFs gave a highly accurate description of the metals, which was comparable in quality to that obtained with the PBEsol DF. Here, we find that combining the three original MS mGGA DFs with rVV10 nonlocal correlation comes at the cost of a slightly less accurate description of the metal. However, the description of the metal obtained in this way is still better than the descriptions obtained with SRP DFs specifically optimized for individual systems. Using the Born-Oppenheimer static surface (BOSS) model, simulations of molecular beam dissociative chemisorption experiments yield chemical accuracy for the D 2 + Ag(111) and D 2 + Pt(111) systems. A comparison between calculated and measured E 1/2 (ν, J ) parameters describing associative desorption suggests chemical accuracy for the associative desorption of H 2 from Au(111) as well. Our results suggest that ascending Jacob's ladder to the mGGA rung yields increasingly more accurate results for gas-surface reactions of H 2 (D 2 ) interacting with late transition metals., Competing Interests: The authors declare no competing financial interest., (© 2021 The Authors. Published by American Chemical Society.)

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E b , which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol -1 . The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH 4 . We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O 2 , H 2 O, NH 3 , CO 2 , and CH 3 OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

Specific reaction parameter density functionals (SRP-DFs) that can describe dissociative chemisorption molecular beam experiments of hydrogen (H 2 ) on cold transition metal surfaces with chemical accuracy have so far been shown to be only transferable among different facets of the same metal, but not among different metals. We design new SRP-DFs that include non-local vdW-DF2 correlation for the H 2 + Cu(111) system, and evaluate their transferability to the highly activated H 2 + Ag(111) and H 2 + Au(111) systems and the non-activated H 2 + Pt(111) system. We design our functionals for the H 2 + Cu(111) system since it is the best studied system both theoretically and experimentally. Here we demonstrate that a SRP-DF fitted to reproduce molecular beam sticking experiments for H 2 + Cu(111) with chemical accuracy can also describe such experiments for H 2 + Pt(111) with chemical accuracy, and vice versa. Chemically accurate functionals have been obtained that perform very well with respect to reported van der Waals well geometries, and which improve the description of the metal over current generalized gradient approximation (GGA) based SRP-DFs. From a systematic comparison of our new SRP-DFs that include non-local correlation to previously developed SRP-DFs, for both activated and non-activated systems, we identify non-local correlation as a key ingredient in the construction of transferable SRP-DFs for H 2 interacting with transition metals. Our results are in excellent agreement with experiment when accurately measured observables are available. It is however clear from our analysis that, except for the H 2 + Cu(111) system, there is a need for more, more varied, and more accurately described experiments in order to further improve the design of SRP-DFs. Additionally, we confirm that, when including non-local correlation, the sticking of H 2 on Cu(111) is still well described quasi-classically.

While density functional theory (DFT) is perhaps the most used electronic structure theory in chemistry, many of its practical aspects remain poorly understood. For instance, DFT at the generalized gradient approximation (GGA) tends to fail miserably at describing gas-phase reaction barriers, while it performs surprisingly well for many molecule-metal surface reactions. GGA-DFT also fails for many systems in the latter category, and up to now it has not been clear when one may expect it to work. We show that GGA-DFT tends to work if the difference between the work function of the metal and the molecule's electron affinity is greater than ∼7 eV and to fail if this difference is smaller, with sticking of O 2 on Al(111) being a spectacular example. Using dynamics calculations we show that, for this system, the DFT problem may be solved as done for gas-phase reactions, i.e., by resorting to hybrid functionals, but using screening at long-range to obtain a correct description of the metal. Our results suggest the GGA error in the O 2 + Al(111) barrier height to be functional driven. Our results also suggest the possibility to compute potential energy surfaces for the difficult-to-treat systems with computationally cheap nonself-consistent calculations in which a hybrid functional is applied to a GGA density.

Reactions of molecules on metal surfaces are notoriously difficult to simulate accurately. Density functional theory can be utilized to generate a potential energy surface, but with presently available functionals, the results are not yet accurate enough. To provide benchmark barrier heights with a high-quality method, diffusion Monte Carlo (DMC) is applied to H 2 + Al(110). Barrier heights have been computed for six geometries. Our present goal is twofold: first, to provide accurate barrier heights for the two lowest lying transition states of the system, and second, to assess whether density functionals are capable of describing the variation of barrier height with molecular orientation and impact site through a comparison with DMC barriers. To this end, barrier heights computed with selected functionals at the generalized gradient approximation (GGA) and meta-GGA levels are compared to the DMC results. The comparison shows that all selected functionals yield a rather accurate description of the variation of barrier heights with impact site and orientation, although their absolute values may not be accurate. RPBE-vdW-DF and BEEF-vdW were found to perform quite well even in terms of absolute numbers. Both functionals provided barrier heights for the energetically lowest lying transition state that are within 1 kcal/mol of the DMC value.

The specific reaction parameter (SRP) approach to density functional theory has been shown to model reactions of polyatomic molecules with metal surfaces important for heterogeneous catalysis in the industry with chemical accuracy. However, transferability of the SRP functional among systems in which methane interacts with group 10 metals remains unclear for methane + Pd(111). Therefore, in this work, predictions have been made for the reaction of CHD 3 on Pd(111) using Born-Oppenheimer molecular dynamics while also performing a rough comparison with experimental data for CH 4 + Pd(111) obtained for lower incidence energies. Hopefully, future experiments can test the transferability of the SRP functional among group 10 metals also for Pd(111). We found that the reactivity of CHD 3 on Pd(111) is intermediate between and similar to either Pt(111) or Ni(111), depending on the incidence energy and the initial vibrational state distribution. This is surprising because the barrier height and experiments performed at lower incidence energies than investigated here suggest that the reactivity of Pd(111) should be similar to that of Pt(111) only. The relative decrease in the reactivity of Pd(111) at high incidence energies is attributed to site specificity of the reaction and to dynamical effects such as the bobsled effect and energy transfer from methane to the surface., Competing Interests: The authors declare no competing financial interest., (Copyright © 2019 American Chemical Society.)

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 surfaces. Previous results on H 2 + 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 H 2 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 H 2 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 H 2 from Cu(111) and Cu(211), but our results for the fast channel are in good agreement with the experiments on H 2 + Cu(211)., Competing Interests: The authors declare no competing financial interest., (Copyright © 2019 American Chemical Society.)

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 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 H 2 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 H 2 , D 2 + Cu(111) with chemical accuracy. Therefore, these three non-empirical functionals themselves are also capable of describing H 2 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 D 2 , H 2 + Ag(111) more accurately than was possible with the SRP48 density functional for H 2 + 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 H 2 + 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 H 2 + Ag(111) on the basis of the three examined MS meta-GGA functionals.

Electron-hole pair (ehp) excitation is thought to substantially affect the dynamics of molecules on metal surfaces, but it is not clear whether this can be better addressed by orbital-dependent friction (ODF) or the local density friction approximation (LDFA). We investigate the effect of ehp excitation on the dissociative chemisorption of N 2 on and its inelastic scattering from Ru(0001), which is the benchmark system of highly activated dissociation, with these two different models. ODF is in better agreement with the best experimental estimates for the reaction probabilities than LDFA, yields results for vibrational excitation in better agreement with experiment, but slightly overestimates the translational energy loss during scattering. N 2 on Ru(0001) is thus the first system for which the ODF and LDFA approaches are shown to yield substantially different results for easily accessible experimental observables, including reaction probabilities.

It is important that theory is able to accurately describe dissociative chemisorption reactions on metal surfaces, as such reactions are often rate-controlling in heterogeneously catalyzed processes. Chemically accurate theoretical descriptions have recently been obtained on the basis of the specific reaction parameter (SRP) approach to density functional (DF) theory (DFT), allowing reaction barriers to be obtained with chemical accuracy. However, being semiempirical, this approach suffers from two basic problems. The first is that sticking probabilities (to which SRP density functionals (DFs) are usually fitted) might show differences across experiments, of which the origins are not always clear. The second is that it has proven hard to use experiments on diffractive scattering of H 2 from metals for validation purposes, as dynamics calculations using a SRP-DF may yield a rather poor description of the measured data, especially if the potential used contains a van der Waals well. We address the first problem by performing dynamics calculations on three sets of molecular beam experiments on D 2 + Pt(111), using four sets of molecular beam parameters to obtain sticking probabilities, and the SRP-DF recently fitted to one set of experiments on D 2 + Pt(111). It is possible to reproduce all three sets of experiments with chemical accuracy with the aid of two sets of molecular beam parameters. The theoretical simulations with the four different sets of beam parameters allow one to determine for which range of incidence conditions the experiments should agree well and for which conditions they should show specific differences. This allows one to arrive at conclusions about the quality of the experiments and about problems that might affect the experiments. Our calculations on diffraction of H 2 scattering from Pt(111) show both quantitative and qualitative differences with previously measured diffraction probabilities, which were Debye-Waller (DW)-extrapolated to 0 K. We suggest that DW extrapolation, which is appropriate for direct scattering, might fail if the scattering is affected by the presence of a van der Waals well and that theory should attempt to model surface atom motion for reproducing diffraction experiments performed for surface temperatures of 500 K and higher., Competing Interests: The authors declare no competing financial interest.

An accurate description of reactive scattering of molecules on metal surfaces often requires the modeling of energy transfer between the molecule and the surface phonons. Although ab initio molecular dynamics (AIMD) can describe this energy transfer, AIMD is at present untractable for reactions with reaction probabilities smaller than 1%. Here, we show that it is possible to use a neural network potential to describe a polyatomic molecule reacting on a mobile metal surface with considerably reduced computational effort compared to AIMD. The highly activated reaction of CHD 3 on Cu(111) is used as a test case for this method. It is observed that the reaction probability is influenced considerably by dynamical effects such as the bobsled effect and surface recoil. A special dynamical effect for CHD 3 + Cu(111) is that a higher vibrational efficacy is obtained for two quanta in the CH stretch mode than for a single quantum.

Stepped transition metal surfaces, including the reconstructed Pt(110)-(2 × 1) surface, can be used to model the effect of line defects on catalysts. We present a combined experimental and theoretical study of CHD 3 dissociation on this surface. Theoretical predictions for the initial sticking coefficients, S 0 , are obtained from ab initio molecular dynamics calculations using the specific reaction parameter (SRP) approach to density functional (DF) theory, while the measured sticking coefficients were obtained using the King and Wells method. The SRP DF used here had been previously derived for methane dissociation on Pt(111) so that the experiments test the transferability of this SRP DF to methane + Pt(110)-(2 × 1). The agreement between the experimental and calculated S 0 is poor, with the average energy shift between the theoretical and measured reactivities being 20 kJ/mol. There are two factors which may contribute to this difference, the first of which is that there is a large uncertainty in the calculated sticking coefficients due to a large number of molecules being trapped on the surface at the end of the 1 ps propagation time. The second is that the SRP32-vdW functional may not accurately describe the Pt(110)-(2 × 1) surface. At the lowest incident energies considered here, Pt(110)-(2 × 1) is more reactive than the flat Pt(111) surface, but the situation is reversed at incident energies above 100 kJ/mol.

The accurate description of heterogeneously catalyzed reactions may require chemically accurate evaluation of barriers for reactions of molecules at the edges of metal nanoparticles. It was recently shown that a semiempirical density functional describing the interaction of a molecule dissociating on a flat metal surface (CHD 3 + Pt(111)) is transferable to the same molecule reacting on a stepped surface of the same metal (Pt(211)). However, validation of the method for additional systems is desirable. To address the question whether the specific reaction parameter (SRP) functional that describes H 2 + Pt(111) with chemical accuracy is also capable of accurately describing H 2 + Pt(211), we have performed molecular beam simulations with the quasi-classical trajectory (QCT) method, using the SRP functional developed for H 2 + Pt(111). Our calculations used the Born-Oppenheimer static surface model. The accuracy of the QCT method was assessed by comparison with quantum dynamics results for reaction of the ro-vibrational ground state of H 2 . The theoretical results for sticking of H 2 and D 2 on Pt(211) are in quite good agreement with the experiment, but uncertainties remain because of a lack of accuracy of the QCT simulations at low incidence energies and possible inaccuracies in the reported experimental incidence energies at high energies. We also investigated the nonadiabatic effect of electron-hole pair excitation on the reactivity using the molecular dynamics with the electron friction (MDEF) method, employing the local density friction approximation (LDFA). Only small effects of electron-hole pair excitation on sticking are found., Competing Interests: The authors declare no competing financial interest.

The HCl + Au(111) system has recently become a benchmark for highly activated dissociative chemisorption, which presumably is strongly affected by electron-hole pair excitation. Previous dynamics calculations, which were based on density functional theory at the generalized gradient approximation level (GGA-DFT) for the molecule-surface interaction, have all overestimated measured reaction probabilities by at least an order of magnitude. Here, we perform ab initio molecular dynamics (AIMD) and AIMD with electronic friction (AIMDEF) calculations employing a density functional that includes the attractive van der Waals interaction. Our calculations model the simultaneous and possibly synergistic effects of surface temperature, surface atom motion, electron-hole pair excitation, the molecular beam conditions of the experiments, and the van der Waals interaction on the reactivity. We find that reaction probabilities computed with AIMDEF and the SRP32-vdW functional still overestimate the measured reaction probabilities, by a factor 18 for the highest incidence energy at which measurements were performed (≈2.5 eV). Even granting that the experiment could have underestimated the sticking probability by about a factor three, this still translates into a considerable overestimation of the reactivity by the current theory. Likewise, scaled transition probabilities for vibrational excitation from ν = 1, j = 1 to ν = 2 are overestimated by the AIMDEF theory, by factors 3-8 depending on the initial conditions modeled. Energy losses to the surface and translational energy losses are, however, in good agreement with experimental values., Competing Interests: The authors declare no competing financial interest.

An important industrial process is methanol steam reforming, which is typically used in conjunction with copper catalysts. However, little agreement exists on the reaction mechanisms involved on a copper catalyst. Therefore, we have performed research yielding additional insight into the reaction mechanism for dissociative chemisorption of methanol on Cu(111) using ab initio molecular dynamics, supported by static calculations of the molecule-surface interaction with density functional theory. Our work predicts that after the initial dissociation, formaldehyde is formed through three different mechanisms. Additionally, it is observed that at high energy, CH cleavage is the dominant pathway instead of the formerly presumed OH cleavage pathway. Finally, in order to describe the interaction of methanol with the metal surface, the SRP32-vdW functional is used, which has been previously developed and tested for CHD 3 on Ni(111), Pt(111), and Pt(211) using the Specific Reaction Parameter (SRP) approach. In this work, the SRP32-vdW functional is applied to methanol on Cu(111) as well, in the hope that future experiments can validate the transferability of the SRP32-vdW functional to chemically related molecule-metal surface systems.

The dissociation of water on a transition-metal catalyst is a fundamental step in relevant industrial processes such as the water-gas shift reaction and steam reforming. Although many theoretical studies have been performed, quantitative agreement between theoretical simulations and molecular beam experiments has not yet been achieved. In this work, we present a predictive ab initio molecular dynamics study on the dissociation of mono-deuterated water (HOD) on Ni(111). The analysis of the trajectories gives useful insight into the full-dimensional dynamics of the process and suggests that rotational steering plays a key role in the dissociation. The computed reaction probability suggests that, in combination with accurate molecular beam experiments, the specific reaction parameter density functional developed for CHD 3 (SRP32-vdW) represents a good starting point for developing a semi-empirical functional able to achieve chemical accuracy for HOD on Ni(111).

In order to model accurately reactions of polyatomic molecules with metal surfaces important for heterogeneous catalysis in industry, the Specific Reaction Parameter (SRP) approach to density functional theory has been developed. This approach has been shown to describe the dissociation of CHD 3 on Ni(111), Pt(111), and Pt(211) with chemical accuracy. In this work, predictions have been made for the reaction of CHD 3 on Cu(111) and Cu(211) using barriers, elbow plots, and ab initio molecular dynamics. Future experiments could hopefully prove the transferability of the SRP functional to systems in which methane reacts with flat and stepped surfaces of adjacent groups of the periodic table, by comparison with our predictions. Moreover, the effect of a so-called single atom alloy on the reactivity of methane is investigated by making predictions for CHD 3 on Pt-Cu(111) and Pd-Cu(111). It is found that the reactivity is only increased for Pt-Cu(111) near the alloyed atom, which is not only caused by the lowering of the barrier height but also by changes in the dynamical pathway and reduction of energy transfer from methane to the surface.

The excitation of electron-hole pairs in reactive scattering of molecules at metal surfaces often affects the physical and dynamical observables of interest, including the reaction probability. Here, we study the influence of electron-hole pair excitation on the dissociative chemisorption of N 2 on Ru(0001) using the local density friction approximation method. The effect of surface atom motion has also been taken into account by a high-dimensional neural network potential. Our nonadiabatic molecular dynamics simulations with electronic friction show that the reaction of N 2 is more strongly affected by the energy transfer to surface phonons than by the energy loss to electron-hole pairs. The discrepancy between the computed reaction probabilities and experimental results is within the experimental error both with and without friction; however, the incorporation of electron-hole pairs yields somewhat better agreement with experiments, especially at high collision energies. We also calculate the vibrational efficacy for the N 2 + Ru(0001) reaction and demonstrate that the N 2 reaction is more enhanced by exciting the molecular vibrations than by adding an equivalent amount of energy into translation., Competing Interests: The authors declare no competing financial interest.

The accurate description of the dissociative chemisorption of a molecule on a metal surface requires a chemically accurate description of the molecule-surface interaction. Previously, it was shown that the specific reaction parameter approach to density functional theory (SRP-DFT) enables accurate descriptions of the reaction of dihydrogen with metal surfaces in, for instance, H 2 + Pt(111), H 2 + Cu(111), and H 2 + Cu(100). SRP-DFT likewise allowed a chemically accurate description of dissociation of methane on Ni(111) and Pt(111), and the SRP functional for CH 4 + Ni(111) was transferable to CH 4 + Pt(111), where Ni and Pt belong to the same group. Here, we investigate whether the SRP density functional derived for H 2 + Cu(111) also gives chemically accurate results for H 2 + Ag(111), where Ag belongs to the same group as Cu. To do this, we have performed quasi-classical trajectory calculations using the six-dimensional potential energy surface of H 2 + Ag(111) within the Born-Oppenheimer static surface approximation. The computed reaction probabilities are compared with both state-resolved associative desorption and molecular beam sticking experiments. Our results do not yet show transferability, as the computed sticking probabilities and initial-state selected reaction probabilities are shifted relative to experiment to higher energies by about 2-3 kcal/mol. The lack of transferability may be due to the different character of the SRP functionals for H 2 + Cu and CH 4 + group 10 metals, the latter containing a van der Waals correlation functional and the former not., Competing Interests: The authors declare no competing financial interest.

The simulation of the dissociation of molecules on metal surfaces is a cornerstone for the understanding of heterogeneously catalyzed processes. However, due to high computational demand, the accurate dynamical simulation of the dissociative chemisorption of polyatomic molecules has been limited mostly to flat low-index metal surfaces. The study of surfaces that feature "defected" sites, such as steps, is crucial to improve the understanding of the overall catalytic process due to the high reactivity of under-coordinated sites for this kind of reaction. In this work, we have extensively analyzed more than 10 000 ab initio molecular dynamics trajectories where a CHD 3 molecule is impinging either on the flat Pt(111) surface or on the stepped Pt(211) surface for different initial rovibrational states and collision energies. The results have been compared in order to get insight into the effect of the step in the dissociation of methane. We have found that, despite a large difference in the activation barrier and consequently in reactivity, the geometry of the lowest transition states is very similar on the two surfaces and this results in a similar dissociation dynamics. Furthermore, the trapping observed on the Pt(211) surface can be explained with energy transfer to parallel translational motion induced by the geometry of the slab and by a larger energy transfer to phonons for the stepped Pt(211) surface.

The dissociation of methane on transition metal surfaces is not only of fundamental interest but also of industrial importance as it represents a rate-controlling step in the steam-reforming reaction used commercially to produce hydrogen. Recently, a specific reaction parameter functional (SRP32-vdW) has been developed, which describes the dissociative chemisorption of CHD 3 at normal incidence on Ni(111), Pt(111), and Pt(211) within chemical accuracy (4.2 kJ/mol). Here, we further test the validity of this functional by comparing the initial sticking coefficients ( S 0 ), obtained from ab-initio molecular dynamics calculations run using this functional, with those measured with the King and Wells method at different angles of incidence for CHD 3 dissociation on Pt(211). The two sets of data are in good agreement, demonstrating that the SRP32-vdW functional also accurately describes CHD 3 dissociation at off-normal angles of incidence. When the direction of incidence is perpendicular to the step edges, an asymmetry is seen in the reactivity with respect to the surface normal, with S 0 being higher when the molecule is directed toward the (100) step rather than the (111) terrace. Although there is a small shadowing effect, the trends in S 0 can be attributed to different activation barriers for different surface sites, which in turn is related to the generalized co-ordination numbers of the surface atom to which the dissociating molecule is adsorbed in the transition state. Consequently, most reactivity is seen on the least co-ordinated step atoms at all angles of incidence., Competing Interests: The authors declare no competing financial interest.

We present a comparison of ab initio molecular dynamics calculations for CHD 3 dissociation on Pt(111) using the Perdew, Burke and Ernzerhof (PBE) functional and a specific reaction parameter (SRP) functional. Despite the two functionals predicting approximately the same activation barrier for the reaction, the calculations using the PBE functional consistently overestimate the experimentally determined dissociation probability, whereas the SRP functional reproduces the experimental values within a chemical accuracy (4.2 kJ/mol). We present evidence that suggests that this difference in reactivity can at least in part be attributed to the presence of a van der Waals well in the potential of the SRP functional which is absent from the PBE description. This leads to the CHD 3 molecules being accelerated and spending less time near the surface for the trajectories run with the SRP functional, as well as more energy being transferred to the surface atoms. We suggest that both these factors reduce the reactivity observed in the SRP calculations compared to the PBE calculations.

Stepped metal surfaces are usually assumed to exhibit an increased catalytic activity for bond cleavage of small molecules over their flat single-crystal counterparts. We present experimental and theoretical data on the dissociative adsorption of molecular hydrogen on copper that contradicts this notion. We observe hydrogen molecules to be more reactive on the flat Cu(111) than on the stepped Cu(211) surface. We suggest that this exceptional behavior is due to a geometric effect, that is, that bond cleavage on the flat surface does not occur preferentially over a top site.

Specific features of diffractive scattering of H 2 from metal surfaces can serve as fingerprints of the reactivity of the metal towards H 2 , and in principle theory-experiment comparisons for molecular diffraction can help with the validation of semi-empirical functionals fitted to experiments of sticking of H 2 on metals. However, a recent comparison of calculated and Debye-Waller (DW) extrapolated experimental diffraction probabilities, in which the theory was done on the basis of a potential energy surface (PES) accurately describing sticking to Ru(0001), showed substantial discrepancies, with theoretical and experimental probabilities differing by factors of 2 and 3. We demonstrate that assuming a particular amount of random static disorder to be present in the positions of the surface atoms, which can be characterized through a single parameter, removes most of the discrepancies between experiment and theory. Further improvement might be achievable by improving the accuracy of the DW extrapolation, the model of the H 2 rotational state distribution in the experimental beams, and by fine-tuning the PES. However, the question of whether the DW model is applicable to attenuation of diffractive scattering in the presence of a sizable van der Waals well (depth ≈ 50 meV) should also receive attention, in addition to the question of whether the amount of static surface disorder effectively assumed in the modeling by us could have been present in the experiments.

A fifteen-dimensional global potential energy surface for the dissociative chemisorption of methane on the rigid Ni(111) surface is developed by a high fidelity fit of ∼200 000 DFT energy points computed using a specific reaction parameter density functional designed to reproduce experimental data. The permutation symmetry and surface periodicity are rigorously enforced using the permutation invariant polynomial-neural network approach. The fitting accuracy of the potential energy surface is thoroughly investigated by examining both static and dynamical attributes of CHD 3 dissociation on the frozen surface. This potential energy surface is expected to be chemically accurate as after correction for surface temperature effects it reproduces the measured initial sticking probabilities of CHD 3 on Ni(111) for various incidence conditions.

Accurately simulating heterogeneously catalyzed reactions requires reliable barriers for molecules reacting at defects on metal surfaces, such as steps. However, first-principles methods capable of computing these barriers to chemical accuracy have yet to be demonstrated. We show that state-resolved molecular beam experiments combined with ab initio molecular dynamics using specific reaction parameter density functional theory (SRP-DFT) can determine the molecule-metal surface interaction with the required reliability. Crucially, SRP-DFT exhibits transferability: the functional devised for methane reacting on a flat (111) face of Pt (and Ni) also describes its reaction on stepped Pt(211) with chemical accuracy. Our approach can help bridge the materials gap between fundamental surface science studies on regular surfaces and heterogeneous catalysis in which defected surfaces are important.

Accurate modeling of heterogeneous catalysis requires the availability of highly accurate potential energy surfaces. Within density functional theory, these can-unfortunately-depend heavily on the exchange-correlation functional. High-level ab initio calculations, on the other hand, are challenging due to the system size and the metallic character of the metal slab. Here, we present a quantum Monte Carlo (QMC) study for the benchmark system H 2 + Cu(111), focusing on the dissociative chemisorption barrier height. These computationally extremely challenging ab initio calculations agree to within 1.6 ± 1.0 kcal/mol with a chemically accurate semiempirical value. Remaining errors, such as time-step errors and locality errors, are analyzed in detail in order to assess the reliability of the results. The benchmark studies presented here are at the cutting edge of what is computationally feasible at the present time. Illustrating not only the achievable accuracy but also the challenges arising within QMC in such a calculation, our study presents a clear picture of where we stand at the moment and which approaches might allow for even more accurate results in the future.

In scattering of H 2 from Cu(111), vibrational excitation has so far defied an accurate theoretical description. To expose the causes of the large discrepancies with experiment, we investigate how the feature due to vibrational excitation (the "gain peak") in the simulated time-of-flight spectrum of ( v = 1, j = 3) H 2 scattering from Cu(111) depends on the surface temperature ( T s ) and the possibility of energy exchange with surface phonons and electron-hole pairs (ehp's). Quasi-classical dynamics calculations are performed on the basis of accurate semiempirical density functionals for the interaction with H 2 + Cu(111). The methods used include the quasi-classical trajectory method within the Born-Oppenheimer static surface model, the generalized Langevin oscillator (GLO) method incorporating energy transfer to surface phonons, the GLO + friction (GLO+F) method also incorporating energy exchange with ehp's, and ab initio molecular dynamics with electronic friction (AIMDEF). Of the quasi-classical methods tested, comparison with AIMDEF suggests that the GLO+F method is accurate enough to describe vibrational excitation as measured in the experiments. The GLO+F calculations also suggest that the promoting effect of raising T s on the measured vibrational excitation is due to an electronically nonadiabatic mechanism. However, by itself, enabling energy exchange with the surface by modeling surface phonons and ehp's leads to reduced vibrational excitation, further decreasing the agreement with experiment. The simulated gain peak is quite sensitive to energy shifts in calculated vibrational excitation probabilities and to shifts in a specific experimental parameter (the chopper opening time). While the GLO+F calculations allow important qualitative conclusions, comparison to quantum dynamics results suggests that, with the quasi-classical way of describing nuclear motion and the present box quantization method for assigning the final vibrational state, the gain peak is not yet described with quantitative accuracy. Ways in which this problem might be resolved in the future are discussed.

Atomic diffraction by surfaces under fast grazing incidence conditions has been used for almost a decade to characterize surface properties with more accuracy than with more traditional atomic diffraction methods. From six-dimensional solutions of the time-dependent Schrödinger equation, we show that diffraction of H 2 molecules under fast grazing incidence conditions could be even more informative for the characterization of ionic surfaces, due to the large anisotropic electrostatic interaction between the quadrupole moment of the molecule and the electric field created by the ionic crystal. Using the LiF(001) surface as a benchmark, we show that fast grazing incidence diffraction of H 2 strongly depends on the initial rotational state of the molecule, while rotationally inelastic processes are irrelevant. We demonstrate that, as a result of the anisotropy of the impinging projectile, initial rotational excitation leads to an increase in intensity of high-order diffraction peaks at incidence directions that satisfy precise symmetry constraints, thus providing a more detailed information on the surface characteristics than that obtained from low-order atomic diffraction peaks under fast grazing incidence conditions. As quadrupole-ion surface potentials are expected to accurately represent the interaction between H 2 and any surface with a marked ionic character, our analysis should be of general applicability to any of such surfaces. Finally, we show that a density functional theory description of the molecule-ion surface potential catches the main features observed experimentally.

Ab initio molecular dynamics (AIMD) simulations enable the accurate description of reactive molecule-surface scattering especially if energy transfer involving surface phonons is important. However, presently, the computational expense of AIMD rules out its application to systems where reaction probabilities are smaller than about 1%. Here we show that this problem can be overcome by a high-dimensional neural network fit of the molecule-surface interaction potential, which also incorporates the dependence on phonons by taking into account all degrees of freedom of the surface explicitly. As shown for N 2 + Ru(0001), which is a prototypical case for highly activated dissociative chemisorption, the method allows an accurate description of the coupling of molecular and surface atom motion and accurately accounts for vibrational properties of the employed slab model of Ru(0001). The neural network potential allows reaction probabilities as low as 10 -5 to be computed, showing good agreement with experimental results.

The outcome of molecule-surface collisions can be modified by pre-aligning the molecule; however, experiments accomplishing this are rare because of the difficulty of preparing molecules in aligned quantum states. Here we present a general solution to this problem based on magnetic manipulation of the rotational magnetic moment of the incident molecule. We apply the technique to the scattering of H 2 from flat and stepped copper surfaces. We demonstrate control of the molecule's initial quantum state, allowing a direct comparison of differences in the stereodynamic scattering from the two surfaces. Our results show that a stepped surface exhibits a much larger dependence of the corrugation of the interaction on the alignment of the molecule than the low-index surface. We also demonstrate an extension of the technique that transforms the set-up into an interferometer, which is sensitive to molecular quantum states both before and after the scattering event.

We have performed calculations on the dissociative chemisorption of H 2 on un-reconstructed and reconstructed Au(111) with density functional theory, and dynamics calculations on this process on un-reconstructed Au(111). Due to a very late barrier for dissociation, H 2 + Au(111) is a candidate H 2 -metal system for which the dissociative chemisorption could be considerably affected by the energy transfer to electron-hole pairs. Minimum barrier geometries and potential energy surfaces were computed for six density functionals. The functionals tested yield minimum barrier heights in the range of 1.15-1.6 eV, and barriers that are even later than found for the similar H 2 + Cu(111) system. The potential energy surfaces have been used in quasi-classical trajectory calculations of the initial (v,J) state resolved reaction probability for several vibrational states v and rotational states J of H 2 and D 2 . Our calculations may serve as predictions for state-resolved associative desorption experiments, from which initial state-resolved dissociative chemisorption probabilities can be extracted by invoking detailed balance. The vibrational efficacy η v=0→1 reported for D 2 dissociating on un-reconstructed Au(111) (about 0.9) is similar to that found in earlier quantum dynamics calculations on H 2 + Ag(111), but larger than found for D 2 + Cu(111). With the two functionals tested most extensively, the reactivity of H 2 and D 2 exhibits an almost monotonic increase with increasing rotational quantum number J. Test calculations suggest that, for chemical accuracy (1 kcal/mol), the herringbone reconstruction of Au(111) should be modeled.

In dynamics calculations of H2 dissociating on metal surfaces often clean, high-symmetry surfaces are used. Few such dynamics studies have been performed on surfaces with pre-adsorbed molecules, especially when also the motion of the surface and the adsorbate are considered. In this study, the dissociation of H2 on a carbon monoxide-covered Ru(0001) surface is considered. Ab initio molecular dynamics (AIMD) calculations are performed on this system using the PBE-vdW-DF2 functional, which accurately describes the reaction probability for H2 on Ru(0001). Using this functional, the reaction probability of H2 on the CO-covered Ru(0001) surface is found to be too low when compared to experiments. This suggests that exchange-correlation functionals that can describe the reaction of H2 on a bare metal surface are not in general able to describe the reaction of H2 on a CO-precovered surface of the same metal, with the same accuracy. However, it cannot be ruled out that the discrepancy between theory and experiment is partly due to an inhomogeneous coverage of the surface by CO in the experiments. The incorporation of the motion of the surface has only a small effect on the reaction probability. It is found that when including surface motion for this system, the size of the simulation cell can be important. Upon collision, a considerable amount of energy is transferred to the surface, causing the adsorbed CO molecules to move apart, which opens the surface for reaction. In order to obtain converged reaction probabilities with respect to the size of the simulation cell, at least a 3 × 3 simulation cell is needed, because in the smaller cell the CO molecules cannot be pushed apart as only a single independent CO molecule is present, also leading to less energy exchange with the surface.

Although important to heterogeneous catalysis, the ability to accurately model reactions of polyatomic molecules with metal surfaces has not kept pace with developments in gas phase dynamics. Partnering the specific reaction parameter (SRP) approach to density functional theory with ab initio molecular dynamics (AIMD) extends our ability to model reactions with metals with quantitative accuracy from only the lightest reactant, H2, to essentially all molecules. This is demonstrated with AIMD calculations on CHD3 + Ni(111) in which the SRP functional is fitted to supersonic beam experiments, and validated by showing that AIMD with the resulting functional reproduces initial-state selected sticking measurements with chemical accuracy (4.2 kJ/mol ≈ 1 kcal/mol). The need for only semilocal exchange makes our scheme computationally tractable for dissociation on transition metals.

Accurately modeling surface temperature and surface motion effects is necessary to study molecule-surface reactions in which the energy dissipation to surface phonons can largely affect the observables of interest. We present here a critical comparison of two methods that allow to model such effects, namely, the ab initio molecular dynamics (AIMD) method and the generalized Langevin oscillator (GLO) model, using the dissociation of N2 on W(110) as a benchmark. AIMD is highly accurate as the surface atoms are explicitly part of the dynamics, but this advantage comes with a large computational cost. The GLO model is much more computationally convenient, but accounts for lattice motion effects in a very approximate way. Results show that, despite its simplicity, the GLO model is able to capture the physics of the system to a large extent, returning dissociation probabilities which are in better agreement with AIMD than static-surface results. Furthermore, the GLO model and the AIMD method predict very similar energy transfer to the lattice degrees of freedom in the non-reactive events, and similar dissociation dynamics.

We review the state-of-the art in dynamics calculations on the reactive scattering of H2 from metal surfaces, which is an important model system of an elementary reaction that is relevant to heterogeneous catalysis. In many applications, quantum dynamics and classical trajectory calculations are performed within the Born-Oppenheimer static surface model. However, ab initio molecular dynamics (AIMD) is finding increased use in applications aimed at modeling the effect of surface phonons on the dynamics. Molecular dynamics with electronic friction has been used to model the effect of electron-hole pair excitation. Most applications are still based on potential energy surfaces (PESs) or forces computed with density functional theory (DFT), using a density functional within the generalized gradient approximation to the exchange-correlation energy. A new development is the use of a semi-empirical version of DFT (the specific reaction parameter (SRP) approach to DFT). We also discuss the accurate methods that have become available to represent electronic structure data for the molecule-surface interaction in global PESs. It has now become possible to describe highly activated H2 + metal surface reactions with chemical accuracy using the SRP-DFT approach, as has been shown for H2 + Cu(111) and Cu(100). However, chemical accuracy with SRP-DFT has yet to be demonstrated for weakly activated systems like H2 + Ru(0001) and non-activated systems like H2 + Pd(111), for which SRP DFs are not yet available. There is now considerable evidence that electron-hole pair (ehp) excitation does not need to be modeled to achieve the (chemically) accurate calculation of dissociative chemisorption and scattering probabilities. Dynamics calculations show that phonons can be safely neglected in the chemically accurate calculation of sticking probabilities on cold metal surfaces for activated systems, and in the calculation of a number of other observables. However, there is now sufficient evidence to suggest that the decision on whether or not to neglect phonons should be taken with care, with appropriate consideration of the observable to be computed and of the relevant surface temperature. AIMD calculations have provided valuable insights into the mechanisms that are operative in the dissociative adsorption and absorption of hydrogen on/in precovered metal surfaces. Classical and quantum dynamics calculations have shown that the reaction probability of H2 on Pt surfaces consisting of (100) steps and (111) terraces can to a very good approximation be computed as a weighted average of the reactivities on the steps and terraces. Progress obtained with dynamics calculations on the scattering of H2 from alloys and from simple low index metal surfaces is also reported. Insights that may be obtained on the reactivity of a metal surface from the prominent presence of out-of-plane diffraction or, conversely, the complete absence of diffraction, are discussed. A new field has been opened up by experiments on H2 scattering from surfaces at fast grazing incidence, and we discuss new predictions regarding diffraction and dissociative scattering of H2 under such conditions.

Transition metals and transition metal compounds are important to catalysis, photochemistry, and many superconducting systems. We study the performance of diffusion Monte Carlo (DMC) applied to transition metal containing dimers (TMCDs) using single-determinant Slater-Jastrow trial wavefunctions and investigate the possible influence of the locality and pseudopotential errors. We find that the locality approximation can introduce nonsystematic errors of up to several tens of kilocalories per mole in the absolute energy of Cu and CuH if Ar or Mg core pseudopotentials (PPs) are used for the 3d transition metal atoms. Even for energy differences such as binding energies, errors due to the locality approximation can be problematic if chemical accuracy is sought. The use of the Ne core PPs developed by Burkatzki et al. (J. Chem. Phys. 2008, 129, 164115), the use of linear energy minimization rather than unreweighted variance minimization for the optimization of the Jastrow function, and the use of large Jastrow parametrizations reduce the locality errors. In the second section of this article, we study the general performance of DMC for 3d TMCDs using a database of binding energies of 20 TMCDs, for which comparatively accurate experimental data is available. Comparing our DMC results to these data for our results that compare best with experiment, we find a mean unsigned error (MUE) of 4.5 kcal/mol. This compares well with the achievable accuracy in CCSDT(2)Q (MUE = 4.6 kcal/mol) and the best all-electron DFT results (MUE = 4.5 kcal/mol) for the same set of systems (Truhlar et al. J. Chem. Theory Comput. 2015, 11, 2036-2052). The mean errors in DMC depend less on the exchange-correlation functionals used to generate the trial wavefunction than the corresponding mean errors in the underlying DFT calculations. Furthermore, the QMC results obtained for each molecule individually vary less with the functionals used. These observations are relevant for systems such as molecules interacting with transition metal surfaces where the DFT functionals performing best for molecules (hybrids) do not yield improvements in DFT. Overall, the results presented in this article yield important guidelines for both the assessment of the achievable accuracy with DMC and the design of DMC calculations for systems including transition metal atoms.

Dissociation of methane on metal surfaces is of high practical and fundamental interest. Therefore there is currently a big push aimed at determining the simplest dynamical model that allows the reaction dynamics to be described with quantitative accuracy using quantum dynamics. Using five-dimensional quantum dynamical and full-dimensional ab initio molecular dynamics calculations, we show that the CD3 umbrella axis of CHD3 must reorient before the molecule reaches the barrier for C-H cleavage to occur in reaction on Pt(111). This rules out the application of the rotationally sudden approximation, as explicitly shown through a comparison with calculations using this approximation. Further, we suggest that the observed umbrella swing should strongly affect the sensitivity of C-H cleavage to the initial alignment of the molecule relative to the surface as found experimentally for closely related systems. We find very large differences in reactivity for molecules pre-excited to different rotational states, particularly if these states are associated with different orientations of the C-H bond.