Assessment of Two Problems of Specific Reaction Parameter Density Functional Theory: Sticking and Diffraction of H2 on Pt(111)

Simulating Highly Activated Sticking of H2 on Al(110): Quantum versus Quasi-Classical Dynamics

We evaluate the importance of quantum effects on the sticking of H₂ 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 H₂ + Al(110) on the basis of the standard procedure for comparing results of theory with molecular beam experiments.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

GGA-Level Subsystem DFT Achieves Sub-kcal/mol Accuracy Intermolecular Interactions by Mimicking Nonlocal Functionals

The key feature of nonlocal kinetic energy functionals is their ability to reduce to the Thomas-Fermi functional in the regions of high density and to the von Weizsäcker functional in the region of low-density/high reduced density gradient. This behavior is crucial when these functionals are employed in subsystem DFT simulations to approximate the nonadditive kinetic energy. We propose a GGA nonadditive kinetic energy functional which mimics the good behavior of nonlocal functionals, retaining the computational complexity of typical semilocal functionals. Crucially, this functional depends on the inter-subsystem density overlap. The new functional reproduces Kohn-Sham DFT and benchmark CCSD(T) interaction energies of weakly interacting dimers in the S22-5 and S66 test sets with a mean absolute deviation well below 1 kcal/mol.

Performance of Made Simple Meta-GGA Functionals with rVV10 Nonlocal Correlation for H2 + Cu(111), D2 + Ag(111), H2 + Au(111), and D2 + Pt(111)

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 (H2) + Cu(111), deuterium (D2) + Ag(111), H2 + Au(111), and D2 + 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 D2 + Ag(111) and D2 + 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 H2 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 H2 (D2) interacting with late transition metals.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

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 CH₄. 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. O₂, H₂O, NH₃, CO₂, and CH₃OH. 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.

Normal and off-normal incidence dissociative dynamics of O2(v,J) on ultrathin Cu films grown on Ru(0001)

The dissociative adsorption of molecular oxygen on metal surfaces has long been controversial, mostly due to the spin-triplet nature of its ground state, to possible non-adiabatic effects, such as an abrupt charge transfer from the metal to the molecule, or even to the role played by the surface electronic state. Here, we have studied the dissociative adsorption of O₂ on Cu_ML/Ru(0001) at normal and off-normal incidence, from thermal to super-thermal energies, using quasi-classical dynamics, in the framework of the generalized Langevin oscillator model, and density functional theory based on a multidimensional potential energy surface. Our simulations reveal a rather intriguing behavior of dissociative adsorption probabilities, which exhibit normal energy scaling at incidence energies below the reaction barriers and total energy scaling above, irrespective of the reaction channel, either direct dissociation, trapping dissociation, or molecular adsorption. We directly compare our results with existing scanning tunneling spectroscopy and microscopy measurements. From this comparison, we infer that the observed experimental behavior at thermal energies may be due to ligand and strain effects, as already found for super-thermal incidence energies.

Designing new SRP density functionals including non-local vdW-DF2 correlation for H2 + Cu(111) and their transferability to H2 + Ag(111), Au(111) and Pt(111)

Specific reaction parameter density functionals (SRP-DFs) that can describe dissociative chemisorption molecular beam experiments of hydrogen (H₂) 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 H₂ + Cu(111) system, and evaluate their transferability to the highly activated H₂ + Ag(111) and H₂ + Au(111) systems and the non-activated H₂ + Pt(111) system. We design our functionals for the H₂ + 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 H₂ + Cu(111) with chemical accuracy can also describe such experiments for H₂ + 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 H₂ 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 H₂ + 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 H₂ on Cu(111) is still well described quasi-classically.