1
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Nakajima Y, Ohmura T, Seino J. Using atomic clustering based on structural and electronic descriptors that consider surrounding environment to evaluate local properties of DFT functionals. J Comput Chem 2024; 45:1870-1879. [PMID: 38686778 DOI: 10.1002/jcc.27375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2023] [Revised: 04/01/2024] [Accepted: 04/03/2024] [Indexed: 05/02/2024]
Abstract
We developed a method for evaluating the accuracies of the local properties of DFT functionals in detail using a clustering method based on machine learning and structural/electronic descriptors. We generated 36 clusters consistent with human intuition using 30,436 carbon atoms from the QM9 dataset. The results were used to evaluate 13C NMR chemical shifts calculated using 84 DFT functionals. Carbon atoms were grouped based on their similar environments, reducing errors within these groups. This enables more accurate assessment of the accuracy using a specific DFT functional. Therefore, the present atomic clustering provides more detailed insight into accuracy verification.
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Affiliation(s)
- Yuya Nakajima
- Waseda Research Institute for Science and Engineering, Tokyo, Japan
| | - Takuto Ohmura
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, Japan
| | - Junji Seino
- Waseda Research Institute for Science and Engineering, Tokyo, Japan
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, Japan
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2
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Voss J. Machine learning for accuracy in density functional approximations. J Comput Chem 2024; 45:1829-1845. [PMID: 38668453 DOI: 10.1002/jcc.27366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Revised: 02/16/2024] [Accepted: 03/25/2024] [Indexed: 07/21/2024]
Abstract
Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.
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Affiliation(s)
- Johannes Voss
- SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, Menlo Park, California, USA
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3
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Cai Y, Michiels R, De Luca F, Neyts E, Tu X, Bogaerts A, Gerrits N. Improving Molecule-Metal Surface Reaction Networks Using the Meta-Generalized Gradient Approximation: CO 2 Hydrogenation. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2024; 128:8611-8620. [PMID: 38835935 PMCID: PMC11145648 DOI: 10.1021/acs.jpcc.4c01110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/20/2024] [Revised: 05/07/2024] [Accepted: 05/09/2024] [Indexed: 06/06/2024]
Abstract
Density functional theory is widely used to gain insights into molecule-metal surface reaction networks, which is important for a better understanding of catalysis. However, it is well-known that generalized gradient approximation (GGA) density functionals (DFs), most often used for the study of reaction networks, struggle to correctly describe both gas-phase molecules and metal surfaces. Also, GGA DFs typically underestimate reaction barriers due to an underestimation of the self-interaction energy. Screened hybrid GGA DFs have been shown to reduce this problem but are currently intractable for wide usage. In this work, we use a more affordable meta-GGA (mGGA) DF in combination with a nonlocal correlation DF for the first time to study and gain new insights into a catalytically important surface reaction network, namely, CO2 hydrogenation on Cu. We show that the mGGA DF used, namely, rMS-RPBEl-rVV10, outperforms typical GGA DFs by providing similar or better predictions for metals and molecules, as well as molecule-metal surface adsorption and activation energies. Hence, it is a better choice for constructing molecule-metal surface reaction networks.
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Affiliation(s)
- Yuxiang Cai
- Research
Group PLASMANT, Department of Chemistry, University of Antwerp, Universiteitsplein 1, Antwerp, Wilrijk BE-2610, Belgium
- Department
of Electrical Engineering and Electronics, University of Liverpool, Liverpool L69 3GJ, U.K.
| | - Roel Michiels
- Research
Group PLASMANT, Department of Chemistry, University of Antwerp, Universiteitsplein 1, Antwerp, Wilrijk BE-2610, Belgium
| | - Federica De Luca
- Research
Group PLASMANT, Department of Chemistry, University of Antwerp, Universiteitsplein 1, Antwerp, Wilrijk BE-2610, Belgium
- Department
of ChiBioFarAM (Industrial Chemistry), ERIC aisbl and INSTM/CASPE, University of Messina, V.le F. Stagno d’Alcontres 31, Messina 98166, Italy
| | - Erik Neyts
- Research
Group PLASMANT, Department of Chemistry, University of Antwerp, Universiteitsplein 1, Antwerp, Wilrijk BE-2610, Belgium
| | - Xin Tu
- Department
of Electrical Engineering and Electronics, University of Liverpool, Liverpool L69 3GJ, U.K.
| | - Annemie Bogaerts
- Research
Group PLASMANT, Department of Chemistry, University of Antwerp, Universiteitsplein 1, Antwerp, Wilrijk BE-2610, Belgium
| | - Nick Gerrits
- Research
Group PLASMANT, Department of Chemistry, University of Antwerp, Universiteitsplein 1, Antwerp, Wilrijk BE-2610, Belgium
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, Leiden 2300 RA, The Netherlands
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4
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van Bree RAB, Gerrits N, Kroes GJ. Dissociative chemisorption of O 2 on Al(111): dynamics on a potential energy surface computed with a non-self-consistent screened hybrid density functional approach. Faraday Discuss 2024. [PMID: 38787655 DOI: 10.1039/d3fd00165b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
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 O2 + 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 O2 + 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 O2 + Al(111). We compute and analyse molecular beam sticking probabilities as well as a set of sticking probabilities for rotationally aligned O2. 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 O2 + 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.
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Affiliation(s)
- Robert A B van Bree
- Leiden Institute of Chemisty, Leiden University, Gorlaeus Labaratories, P.O. Box 9502 2300 RA, Leiden, The Netherlands.
| | - Nick Gerrits
- Leiden Institute of Chemisty, Leiden University, Gorlaeus Labaratories, P.O. Box 9502 2300 RA, Leiden, The Netherlands.
| | - Geert-Jan Kroes
- Leiden Institute of Chemisty, Leiden University, Gorlaeus Labaratories, P.O. Box 9502 2300 RA, Leiden, The Netherlands.
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5
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Sheldon C, Paier J, Usvyat D, Sauer J. Hybrid RPA:DFT Approach for Adsorption on Transition Metal Surfaces: Methane and Ethane on Platinum (111). J Chem Theory Comput 2024; 20:2219-2227. [PMID: 38330551 PMCID: PMC10938501 DOI: 10.1021/acs.jctc.3c01308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2023] [Revised: 01/17/2024] [Accepted: 01/18/2024] [Indexed: 02/10/2024]
Abstract
The hybrid QM:QM approach is extended to adsorption on transition metal surfaces. The random phase approximation (RPA) as the high-level method is applied to cluster models and, using the subtractive scheme, embedded in periodic models which are treated with density functional theory (DFT) that is the low-level method. The PBE functional, both without dispersion and augmented with the many-body dispersion (MBD), is employed. Adsorption of methane and ethane on the Pt(111) surface is studied. For methane in a 2 × 2 surface cell, the hybrid RPA:PBE and RPA:PBE+MBD results, -14.3 and -16.0 kJ mol-1, respectively, are in close agreement with the periodic RPA value of -13.8 kJ mol-1 at significantly reduced computational cost (factor of ∼50). For methane and ethane, the RPA:PBE results (-14.3 and -17.8 kJ mol-1, respectively) indicate underbinding relative to energies derived from experimental desorption barriers for relevant loadings (-15.6 ± 1.6 and -27.2 ± 2.9 kJ mol-1, respectively), whereas the hybrid RPA:PBE+MBD results (-16.0 and -24.9 kJ mol-1, respectively) agree with the experiment well within experimental uncertainty limits (deviation of -0.4 ± 1.5 and +2.3 ± 2.9 kJ mol-1, respectively). Finding a cluster that adequately and robustly represents the adsorbate at the bulk surface is important for the success of the RPA-based QM:QM scheme for metals.
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Affiliation(s)
- Christopher Sheldon
- Institut
für Chemie, Humboldt-Universität
zu Berlin, Unter den Linden 6, Berlin 10099, Germany
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft, Faradayweg 4, Berlin 14195, Germany
| | - Joachim Paier
- Institut
für Chemie, Humboldt-Universität
zu Berlin, Unter den Linden 6, Berlin 10099, Germany
- Lehrstuhl
für Theoretische Chemie, Friedrich-Alexander-Universität
Erlangen-Nürnberg, Egerlandstrasse 3, Erlangen 91058, Germany
| | - Denis Usvyat
- Institut
für Chemie, Humboldt-Universität
zu Berlin, Unter den Linden 6, Berlin 10099, Germany
| | - Joachim Sauer
- Institut
für Chemie, Humboldt-Universität
zu Berlin, Unter den Linden 6, Berlin 10099, Germany
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6
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Powell A, Gerrits N, Tchakoua T, Somers MF, Busnengo HF, Meyer J, Kroes GJ, Doblhoff-Dier K. Best-of-Both-Worlds Predictive Approach to Dissociative Chemisorption on Metals. J Phys Chem Lett 2024; 15:307-315. [PMID: 38169287 PMCID: PMC10788952 DOI: 10.1021/acs.jpclett.3c02972] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2023] [Revised: 12/21/2023] [Accepted: 12/28/2023] [Indexed: 01/05/2024]
Abstract
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 H2 + Al(110) system to ∼1.4 kcal/mol.
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Affiliation(s)
- Andrew
D. Powell
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Nick Gerrits
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Theophile Tchakoua
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Mark F. Somers
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Heriberto F. Busnengo
- Instituto
de Física Rosario (IFIR), CONICET-UNR, 2000 Rosario, Argentina
- Facultad
de Ciencias Exatas, Ingeniería y
Agrimensura, UNR, 2000 Rosario, Argentina
| | - Jörg Meyer
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Geert-Jan Kroes
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Katharina Doblhoff-Dier
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
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7
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Tchakoua T, Jansen T, van Nies Y, van den Elshout RFA, van Boxmeer BAB, Poort SP, Ackermans MG, Beltrão GS, Hildebrand SA, Beekman SEJ, van der Drift T, Kaart S, Šantić A, Spuijbroek EE, Gerrits N, Somers MF, Kroes GJ. Constructing Mixed Density Functionals for Describing Dissociative Chemisorption on Metal Surfaces: Basic Principles. J Phys Chem A 2023; 127:10481-10498. [PMID: 38051300 PMCID: PMC10726370 DOI: 10.1021/acs.jpca.3c01932] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
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.
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Affiliation(s)
- Théophile Tchakoua
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Tim Jansen
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Youri van Nies
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | | | - Bart A B van Boxmeer
- Faculty of Applied Engineering, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerpen, Belgium
| | - Saskia P Poort
- Department of Chemical Engineering, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Michelle G Ackermans
- Department of Chemical Engineering, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Gabriel Spiller Beltrão
- Department of Chemical Engineering, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Stefan A Hildebrand
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Steijn E J Beekman
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Thijs van der Drift
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Sam Kaart
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Anthonie Šantić
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Esmee E Spuijbroek
- Department of Chemical Engineering, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Nick Gerrits
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Mark F Somers
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Geert-Jan Kroes
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
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8
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Boychuk BTA, Wetmore SD. Assessment of Density Functional Theory Methods for the Structural Prediction of Transition and Post-Transition Metal-Nucleic Acid Complexes. J Chem Theory Comput 2023. [PMID: 37399186 DOI: 10.1021/acs.jctc.3c00127] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/05/2023]
Abstract
Understanding the structure of metal-nucleic acid systems is important for many applications such as the design of new pharmaceuticals, metal detection platforms, and nanomaterials. Herein, we explore the ability of 20 density functional theory (DFT) functionals to reproduce the crystal structure geometry of transition and post-transition metal-nucleic acid complexes identified in the Protein Data Bank and Cambridge Structural Database. The environmental extremes of the gas phase and implicit water were considered, and analysis focused on the global and inner coordination geometry, including the coordination distances. Although gas-phase calculations were unable to describe the structure of 12 out of the 53 complexes in our test set regardless of the DFT functional considered, accounting for the broader environment through implicit solvation or constraining the model truncation points to crystallographic coordinates generally afforded agreement with the experimental structure, suggesting that functional performance for these systems is likely due to the models rather than the methods. For the remaining 41 complexes, our results show that the reliability of functionals depends on the metal identity, with the magnitude of error varying across the periodic table. Furthermore, minimal changes in the geometries of these metal-nucleic acid complexes occur upon use of the Stuttgart-Dresden effective core potential and/or inclusion of an implicit water environment. The overall top three performing functionals are ωB97X-V, ωB97X-D3(BJ), and MN15, which reliably describe the structure of a broad range of metal-nucleic acid systems. Other suitable functionals include MN15-L, which is a cheaper alternative to MN15, and PBEh-3c, which is commonly used in QM/MM calculations of biomolecules. In fact, these five methods were the only functionals tested to reproduce the coordination sphere of Cu2+-containing complexes. For metal-nucleic acid systems that do not contain Cu2+, ωB97X and ωB97X-D are also suitable choices. These top-performing methods can be utilized in future investigations of diverse metal-nucleic acid complexes of relevance to biology and material science.
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Affiliation(s)
- Briana T A Boychuk
- Department of Chemistry and Biochemistry, University of Lethbridge, 4401 University Drive West, Lethbridge, AB T1K 3M4, Canada
| | - Stacey D Wetmore
- Department of Chemistry and Biochemistry, University of Lethbridge, 4401 University Drive West, Lethbridge, AB T1K 3M4, Canada
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9
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Tchakoua T, Powell AD, Gerrits N, Somers MF, Doblhoff-Dier K, Busnengo HF, Kroes GJ. Simulating Highly Activated Sticking of H 2 on Al(110): Quantum versus Quasi-Classical Dynamics. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2023; 127:5395-5407. [PMID: 36998253 PMCID: PMC10041643 DOI: 10.1021/acs.jpcc.3c00426] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/18/2023] [Revised: 02/28/2023] [Indexed: 06/19/2023]
Abstract
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.
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Affiliation(s)
- Theophile Tchakoua
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Andrew D. Powell
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Nick Gerrits
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Mark F. Somers
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Katharina Doblhoff-Dier
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Heriberto F. Busnengo
- Instituto
de Física Rosario (IFIR), CONICET-UNR, Bv. 27 de Febrero 210 bis, 2000 Rosario, Argentina
- Facultad
de Ciencias Exactas, Ingeniería y
Agrimensura, UNR, Av.
Pellegrini 250, 2000 Rosario, Argentina
| | - Geert-Jan Kroes
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
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