1
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Xiong L, Zhang L, Zhao B, Jiang B. Six-dimensional quantum dynamics of an Eley-Rideal reaction between gaseous and adsorbed hydrogen atoms on Cu(111). Faraday Discuss 2024; 251:457-470. [PMID: 38757528 DOI: 10.1039/d3fd00163f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/18/2024]
Abstract
In the form of direct abstraction of a surface adsorbate by a gaseous projectile, the Eley-Rideal (ER) reaction at the gas-surface interface manifests interesting dynamics. Unfortunately, high-dimensional quantum dynamical (QD) studies for ER reactions remain very challenging, which demands a large configuration space and the coordinate transformation of wavefunctions. Here, we report the first six-dimensional (6D) fully coupled quantum scattering method for studying the ER reaction between gas phase H(D) atoms and adsorbed D(H) atoms on a rigid Cu(111) surface. Reaction probabilities and product rovibrational state distributions obtained by this 6D model are found to be quite different from those obtained by reduced-dimensional QD models, demonstrating the high-dimensional nature of the ER reaction. Using two distinct potential energy surfaces (PESs), we further discuss the influence of the PES on the calculated product vibrational and rotational state distributions, in comparison with experimental results. The lateral corrugation and the exothermicity of the PES are found to play a critical role in controlling the energy disposal in the ER reaction.
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Affiliation(s)
- Longlong Xiong
- Department of Chemical Physics, Key Laboratory of Precision and Intelligent Chemistry, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Liang Zhang
- Department of Chemical Physics, Key Laboratory of Precision and Intelligent Chemistry, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Bin Zhao
- Department of Chemistry, Southern University of Science and Technology, Shenzhen, 518055, P. R. China.
| | - Bin Jiang
- Department of Chemical Physics, Key Laboratory of Precision and Intelligent Chemistry, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
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2
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Schatz GC, Wodtke AM, Yang X. Spiers Memorial Lecture: New directions in molecular scattering. Faraday Discuss 2024; 251:9-62. [PMID: 38764350 DOI: 10.1039/d4fd00015c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/21/2024]
Abstract
The field of molecular scattering is reviewed as it pertains to gas-gas as well as gas-surface chemical reaction dynamics. We emphasize the importance of collaboration of experiment and theory, from which new directions of research are being pursued on increasingly complex problems. We review both experimental and theoretical advances that provide the modern toolbox available to molecular-scattering studies. We distinguish between two classes of work. The first involves simple systems and uses experiment to validate theory so that from the validated theory, one may learn far more than could ever be measured in the laboratory. The second class involves problems of great complexity that would be difficult or impossible to understand without a partnership of experiment and theory. Key topics covered in this review include crossed-beams reactive scattering and scattering at extremely low energies, where quantum effects dominate. They also include scattering from surfaces, reactive scattering and kinetics at surfaces, and scattering work done at liquid surfaces. The review closes with thoughts on future promising directions of research.
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Affiliation(s)
- George C Schatz
- Dept of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
| | - Alec M Wodtke
- Institute for Physical Chemistry, Georg August University, Goettingen, Germany
- Max Planck Institute for Multidisciplinary Natural Sciences, Goettingen, Germany.
- International Center for the Advanced Studies of Energy Conversion, Georg August University, Goettingen, Germany
| | - Xueming Yang
- Dalian Institute for Chemical Physics, Chinese Academy of Sciences, Dalian, China
- Department of Chemistry, College of Science, Southern University of Science and Technology, Shenzhen, China
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3
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Hasecke L, Mata RA. Optimization of Quantum Nuclei Positions with the Adaptive Nuclear-Electronic Orbital Approach. J Phys Chem A 2024; 128:3205-3211. [PMID: 38619054 PMCID: PMC11056972 DOI: 10.1021/acs.jpca.4c00096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2024] [Revised: 03/08/2024] [Accepted: 03/08/2024] [Indexed: 04/16/2024]
Abstract
The use of multicomponent methods has become increasingly popular over the last years. Under this framework, nuclei (commonly protons) are treated quantum mechanically on the same footing as the electronic structure problem. Under the use of atomic-centered orbitals, this can lead to some complications as the ideal location of the nuclear basis centers must be optimized. In this contribution, we propose a straightforward approach to determine the position of such centers within the self-consistent cycle of a multicomponent calculation, making use of individual proton charge centroids. We test the method on model systems including the water dimer, a protonated water tetramer, and a porphine system. Comparing to numerical gradient calculations, the adaptive nuclear-electronic orbital (NEO) procedure is able to converge the basis centers to within a few cents of an Ångström and with less than 0.1 kcal/mol differences in absolute energies. This is achieved in one single calculation and with a small added computational effort of up to 80% compared to a regular NEO- self-consistent field run. An example application for the human transketolase proton wire is also provided.
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Affiliation(s)
- Lukas Hasecke
- Institute of Physical Chemistry, University
of Göttingen, Tammannstrasse 6, 37077 Göttingen, Germany
| | - Ricardo A. Mata
- Institute of Physical Chemistry, University
of Göttingen, Tammannstrasse 6, 37077 Göttingen, Germany
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4
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Arribas D, Villalobos-Vilda V, Tosi E, Lacovig P, Baraldi A, Bignardi L, Lizzit S, Martínez JI, de Andres PL, Gutiérrez A, Martín-Gago JÁ, Merino P. In situ observation of the on-surface thermal dehydrogenation of n-octane on Pt(111). NANOSCALE 2023; 15:14458-14467. [PMID: 37458500 DOI: 10.1039/d3nr02564k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/26/2023]
Abstract
The catalytic dehydrogenation of alkanes constitutes a key step for the industrial conversion of these inert sp3-bonded carbon chains into other valuable unsaturated chemicals. To this end, platinum-based materials are among the most widely used catalysts. In this work, we characterize the thermal dehydrogenation of n-octane (n-C8H18) on Pt(111) under ultra-high vacuum using synchrotron-radiation X-ray photoelectron spectroscopy, temperature-programmed desorption and scanning tunneling microscopy, combined with ab initio calculations. At low activation temperatures, two different dehydrogenation stages are observed. At 330 K, n-C8H18 effectively undergoes a 100% regioselective single C-H bond cleavage at one methyl end. At 600 K, the chemisorbed molecules undergo a double dehydrogenation, yielding double bonds in their carbon skeletons. Diffusion of the dehydrogenated species leads to the formation of carbon molecular clusters, which represents the first step towards poisoning of the catalyst. Our results reveal the chemical mechanisms behind the first stages of alkane dehydrogenation on a platinum model surface at the atomic scale, paving the way for designing more efficient dehydrogenation catalysts.
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Affiliation(s)
- Daniel Arribas
- Instituto de Ciencia de Materiales de Madrid, c/Sor Juana Inés de la Cruz, 3, Spain.
| | | | - Ezequiel Tosi
- Instituto de Ciencia de Materiales de Madrid, c/Sor Juana Inés de la Cruz, 3, Spain.
- Elettra-Sincrotrone Trieste S.C.p.A., S.S. 14 km 163.5, Trieste, Italy
| | - Paolo Lacovig
- Elettra-Sincrotrone Trieste S.C.p.A., S.S. 14 km 163.5, Trieste, Italy
| | - Alessandro Baraldi
- Elettra-Sincrotrone Trieste S.C.p.A., S.S. 14 km 163.5, Trieste, Italy
- Physics Department, University of Trieste, Via Valerio 2, 34127 Trieste, Italy
| | - Luca Bignardi
- Elettra-Sincrotrone Trieste S.C.p.A., S.S. 14 km 163.5, Trieste, Italy
| | - Silvano Lizzit
- Elettra-Sincrotrone Trieste S.C.p.A., S.S. 14 km 163.5, Trieste, Italy
| | - José Ignacio Martínez
- Instituto de Ciencia de Materiales de Madrid, c/Sor Juana Inés de la Cruz, 3, Spain.
| | - Pedro Luis de Andres
- Instituto de Ciencia de Materiales de Madrid, c/Sor Juana Inés de la Cruz, 3, Spain.
- On leave of absence at nanoteeche@surfaces Laboratory, Swiss Federal Laboratories for Materials Science and Technology, 8600-Dübendorf, Switzerland
| | - Alejandro Gutiérrez
- Applied Physics Department, Universidad Autónoma de Madrid, Calle Francisco Tomás y Valiente, 7, 28049 Madrid, Spain
- Instituto Nicolás Cabrera, Cantoblanco, Calle Francisco Tomás y Valiente, 7, 28049 Madrid, Spain
| | | | - Pablo Merino
- Instituto de Ciencia de Materiales de Madrid, c/Sor Juana Inés de la Cruz, 3, Spain.
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5
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Zhang L, Zuo J, Suleimanov YV, Guo H. Ring Polymer Molecular Dynamics Approach to Quantum Dissociative Chemisorption Rates. J Phys Chem Lett 2023; 14:7118-7125. [PMID: 37531595 DOI: 10.1021/acs.jpclett.3c01848] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/04/2023]
Abstract
A ring polymer molecular dynamics (RPMD) method is proposed for the calculation of the dissociative chemisorption rate coefficient on surfaces. The RPMD rate theory is capable of handling quantum effects such as the zero-point energy and tunneling in dissociative chemisorption, while it relies on classical trajectories for the simulation. Applications to H2 dissociative chemisorption are demonstrated. For the highly activated process on Ag(111), strong deviations from Arrhenius behavior are found at low temperatures and attributed to tunneling. On Pt(111), where the dissociation has a barrierless pathway, the RPMD rate coefficient is found to agree with the experimentally derived thermal sticking coefficient within a factor of 2 over a large temperature range. Significant quantum effects are also found.
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Affiliation(s)
- Liang Zhang
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
| | - Junxiang Zuo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
| | - Yury V Suleimanov
- American Association for the Advancement of Science, 1200 New York Ave NW, Washington, D.C. 20005, United States
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
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6
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Zhao Z, Wang Y, Yang X, Quan J, Krüger BC, Stoicescu P, Nieman R, Auerbach DJ, Wodtke AM, Guo H, Park GB. Spin-dependent reactivity and spin-flipping dynamics in oxygen atom scattering from graphite. Nat Chem 2023:10.1038/s41557-023-01204-2. [PMID: 37217785 DOI: 10.1038/s41557-023-01204-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2022] [Accepted: 04/14/2023] [Indexed: 05/24/2023]
Abstract
The formation of two-electron chemical bonds requires the alignment of spins. Hence, it is well established for gas-phase reactions that changing a molecule's electronic spin state can dramatically alter its reactivity. For reactions occurring at surfaces, which are of great interest during, among other processes, heterogeneous catalysis, there is an absence of definitive state-to-state experiments capable of observing spin conservation and therefore the role of electronic spin in surface chemistry remains controversial. Here we use an incoming/outgoing correlation ion imaging technique to perform scattering experiments for O(3P) and O(1D) atoms colliding with a graphite surface, in which the initial spin-state distribution is controlled and the final spin states determined. We demonstrate that O(1D) is more reactive with graphite than O(3P). We also identify electronically nonadiabatic pathways whereby incident O(1D) is quenched to O(3P), which departs from the surface. With the help of molecular dynamics simulations carried out on high-dimensional machine-learning-assisted first-principles potential energy surfaces, we obtain a mechanistic understanding for this system: spin-forbidden transitions do occur, but with low probabilities.
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Affiliation(s)
- Zibo Zhao
- Max-Planck-Institut für Multidisziplinäre Naturwissenschaften, Göttingen, Germany
| | - Yingqi Wang
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM, USA
| | - Ximei Yang
- Max-Planck-Institut für Multidisziplinäre Naturwissenschaften, Göttingen, Germany
| | - Jiamei Quan
- Max-Planck-Institut für Multidisziplinäre Naturwissenschaften, Göttingen, Germany
| | - Bastian C Krüger
- Max-Planck-Institut für Multidisziplinäre Naturwissenschaften, Göttingen, Germany
| | - Paula Stoicescu
- Georg-August-Universität Göttingen, Institut für physikalische Chemie, Göttingen, Germany
| | - Reed Nieman
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM, USA
| | - Daniel J Auerbach
- Max-Planck-Institut für Multidisziplinäre Naturwissenschaften, Göttingen, Germany
| | - Alec M Wodtke
- Max-Planck-Institut für Multidisziplinäre Naturwissenschaften, Göttingen, Germany
- Georg-August-Universität Göttingen, Institut für physikalische Chemie, Göttingen, Germany
- International Center for Advanced Studies of Energy Conversion, University of Goettingen, Göttingen, Germany
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM, USA.
| | - G Barratt Park
- Max-Planck-Institut für Multidisziplinäre Naturwissenschaften, Göttingen, Germany.
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, TX, USA.
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7
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Li C, Li Y, Jiang B. First-principles surface reaction rates by ring polymer molecular dynamics and neural network potential: role of anharmonicity and lattice motion. Chem Sci 2023; 14:5087-5098. [PMID: 37206404 PMCID: PMC10189860 DOI: 10.1039/d2sc06559b] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 04/05/2023] [Indexed: 08/04/2023] Open
Abstract
Elementary gas-surface processes are essential steps in heterogeneous catalysis. A predictive understanding of catalytic mechanisms remains challenging due largely to difficulties in accurately characterizing the kinetics of such steps. Experimentally, thermal rates for elementary surface reactions can now be measured using a novel velocity imaging technique, providing a stringent testing ground for ab initio rate theories. Here, we propose to combine ring polymer molecular dynamics (RPMD) rate theory with state-of-the-art first-principles-determined neural network potential to calculate surface reaction rates. Taking NO desorption from Pd(111) as an example, we show that the harmonic approximation and the neglect of lattice motion in the commonly-used transition state theory overestimates and underestimates the entropy change during the desorption process, respectively, leading to opposite errors in rate coefficient predictions and artificial error cancellations. Including anharmonicity and lattice motion, our results reveal a generally neglected surface entropy change due to significant local structural change during desorption and obtain the right answer for the right reasons. Although quantum effects are found to be less important in this system, the proposed approach establishes a more reliable theoretical benchmark for accurately predicting the kinetics of elementary gas-surface processes.
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Affiliation(s)
- Chen Li
- Key Laboratory of Precision and Intelligent Chemistry, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China Hefei Anhui 230026 China
| | - Yongle Li
- Department of Physics, International Center of Quantum and Molecular Structures, Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University Shanghai 200444 China
| | - Bin Jiang
- Key Laboratory of Precision and Intelligent Chemistry, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China Hefei Anhui 230026 China
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8
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Garashchuk S, Stetzler J, Rassolov V. Factorized Electron-Nuclear Dynamics with an Effective Complex Potential. J Chem Theory Comput 2023; 19:1393-1408. [PMID: 36795898 DOI: 10.1021/acs.jctc.2c01019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023]
Abstract
We present a quantum dynamics approach for molecular systems based on wave function factorization into components describing the light and heavy particles, such as electrons and nuclei. The dynamics of the nuclear subsystem can be viewed as motion of the trajectories defined in the nuclear subspace, evolving according to the average nuclear momentum of the full wave function. The probability density flow between the nuclear and electronic subsystems is facilitated by the imaginary potential, derived to ensure a physically meaningful normalization of the electronic wave function for each configuration of the nuclei, and conservation of the probability density associated with each trajectory in the Lagrangian frame of reference. The imaginary potential, defined in the nuclear subspace, depends on the momentum variance in the nuclear coordinates averaged over the electronic component of the wave function. An effective real potential, driving the dynamics of the nuclear subsystem, is defined to minimize motion of the electronic wave function in the nuclear degrees of freedom. Illustration and the analysis of the formalism are given for a two-dimensional model system of vibrationally nonadiabatic dynamics.
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Affiliation(s)
- Sophya Garashchuk
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Julian Stetzler
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Vitaly Rassolov
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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9
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Chen BW. Equilibrium and kinetic isotope effects in heterogeneous catalysis: A density functional theory perspective. CATAL COMMUN 2023. [DOI: 10.1016/j.catcom.2023.106654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023] Open
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10
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Fingerhut J, Lecroart L, Borodin D, Schwarzer M, Hörandl S, Kandratsenka A, Auerbach DJ, Wodtke AM, Kitsopoulos TN. Binding Energy and Diffusion Barrier of Formic Acid on Pd(111). J Phys Chem A 2022; 127:142-152. [PMID: 36583672 PMCID: PMC9841570 DOI: 10.1021/acs.jpca.2c07414] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Velocity-resolved kinetics is used to measure the thermal rate of formic acid desorption from Pd(111) between 228 and 273 K for four isotopologues: HCOOH, HCOOD, DCOOH, DCOOD. Upon molecular adsorption, formic acid undergoes decomposition to CO2 and H2 and thermal desorption. To disentangle the contributions of individual processes, we implement a mass-balance-based calibration procedure from which the branching ratio between desorption and decomposition for formic acid is determined. From experimentally derived elementary desorption rate constants, we obtain the binding energy 639 ± 8 meV and the diffusion barrier 370 ± 130 meV using the detailed balance rate model (DBRM). The DBRM explains the observed kinetic isotope effects.
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Affiliation(s)
- Jan Fingerhut
- Institute
for Physical Chemistry, Georg-August University
of Goettingen, Goettingen 37077, Germany
| | - Loïc Lecroart
- Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Goettingen 37077, Germany
| | - Dmitriy Borodin
- Institute
for Physical Chemistry, Georg-August University
of Goettingen, Goettingen 37077, Germany,Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Goettingen 37077, Germany,Email
| | - Michael Schwarzer
- Institute
for Physical Chemistry, Georg-August University
of Goettingen, Goettingen 37077, Germany
| | - Stefan Hörandl
- Institute
for Physical Chemistry, Georg-August University
of Goettingen, Goettingen 37077, Germany
| | - Alexander Kandratsenka
- Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Goettingen 37077, Germany
| | - Daniel J. Auerbach
- Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Goettingen 37077, Germany
| | - Alec M. Wodtke
- Institute
for Physical Chemistry, Georg-August University
of Goettingen, Goettingen 37077, Germany,Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Goettingen 37077, Germany,International
Center for Advanced Studies of Energy Conversion, Georg-August University of Goettingen, Goettingen 37077, Germany
| | - Theofanis N. Kitsopoulos
- Institute
for Physical Chemistry, Georg-August University
of Goettingen, Goettingen 37077, Germany,Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Goettingen 37077, Germany,Department
of Chemistry, University of Crete, Heraklion 715 00, Greece,Institute
of Electronic Structure and Laser − FORTH, Heraklion 70013, Greece,Email
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11
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Borodin D, Galparsoro O, Rahinov I, Fingerhut J, Schwarzer M, Hörandl S, Auerbach DJ, Kandratsenka A, Schwarzer D, Kitsopoulos TN, Wodtke AM. Steric Hindrance of NH 3 Diffusion on Pt(111) by Co-Adsorbed O-Atoms. J Am Chem Soc 2022; 144:21791-21799. [DOI: 10.1021/jacs.2c10458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Dmitriy Borodin
- Institute for Physical Chemistry, Georg-August University of Goettingen, Tammannstraße 6, Goettingen37077, Germany
- Department of Dynamics at Surfaces, Max Planck Institute for Multidisciplinary Sciences, Am Fassberg 11, Goettingen37077, Germany
| | - Oihana Galparsoro
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, Donostia-San Sebastián20018, Spain
- Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072Donostia-San Sebastián20018, Spain
| | - Igor Rahinov
- Department of Natural Sciences, The Open University of Israel, Raanana4353701, Israel
| | - Jan Fingerhut
- Institute for Physical Chemistry, Georg-August University of Goettingen, Tammannstraße 6, Goettingen37077, Germany
| | - Michael Schwarzer
- Institute for Physical Chemistry, Georg-August University of Goettingen, Tammannstraße 6, Goettingen37077, Germany
| | - Stefan Hörandl
- Institute for Physical Chemistry, Georg-August University of Goettingen, Tammannstraße 6, Goettingen37077, Germany
| | - Daniel J. Auerbach
- Department of Dynamics at Surfaces, Max Planck Institute for Multidisciplinary Sciences, Am Fassberg 11, Goettingen37077, Germany
| | - Alexander Kandratsenka
- Department of Dynamics at Surfaces, Max Planck Institute for Multidisciplinary Sciences, Am Fassberg 11, Goettingen37077, Germany
| | - Dirk Schwarzer
- Department of Dynamics at Surfaces, Max Planck Institute for Multidisciplinary Sciences, Am Fassberg 11, Goettingen37077, Germany
| | - Theofanis N. Kitsopoulos
- Institute for Physical Chemistry, Georg-August University of Goettingen, Tammannstraße 6, Goettingen37077, Germany
- Department of Dynamics at Surfaces, Max Planck Institute for Multidisciplinary Sciences, Am Fassberg 11, Goettingen37077, Germany
- Department of Chemistry, University of Crete, Heraklion71500, Greece
- Institute of Electronic Structure and Laser − FORTH, Heraklion70013, Greece
| | - Alec M. Wodtke
- Institute for Physical Chemistry, Georg-August University of Goettingen, Tammannstraße 6, Goettingen37077, Germany
- Department of Dynamics at Surfaces, Max Planck Institute for Multidisciplinary Sciences, Am Fassberg 11, Goettingen37077, Germany
- International Center for Advanced Studies of Energy Conversion, Georg-August University of Goettingen, Tammannstraße 6, Goettingen37077, Germany
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12
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Schmid M, Parkinson GS, Diebold U. Analysis of Temperature-Programmed Desorption via Equilibrium Thermodynamics. ACS PHYSICAL CHEMISTRY AU 2022; 3:44-62. [PMID: 36718262 PMCID: PMC9881163 DOI: 10.1021/acsphyschemau.2c00031] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Revised: 10/10/2022] [Accepted: 10/12/2022] [Indexed: 11/16/2022]
Abstract
Temperature-programmed desorption (TPD) experiments in surface science are usually analyzed using the Polanyi-Wigner equation and/or transition-state theory. These methods are far from straightforward, and the determination of the pre-exponential factor is often problematic. We present a different method based on equilibrium thermodynamics, which builds on an approach previously used for TPD by Kreuzer et al. (Surf. Sci. 1988). Equations for the desorption rate are presented for three different types of surface-adsorbate interactions: (i) a 2D ideal hard-sphere gas with a negligible diffusion barrier, (ii) an ideal lattice gas, that is, fixed adsorption sites without interaction between the adsorbates, and (iii) a lattice gas with a distribution of (site-dependent) adsorption energies. We show that the coverage dependence of the sticking coefficient for adsorption at the desorption temperature determines whether the desorption process can be described by first- or second-order kinetics. The sticking coefficient at the desorption temperature must also be known for a quantitative determination of the adsorption energy, but it has a rather weak influence (like the pre-exponential factor in a traditional TPD analysis). Quantitative analysis is also influenced by the vibrational contributions to the energy and entropy. For the case of a single adsorption energy, we provide equations to directly convert peak temperatures into adsorption energies. These equations also provide an approximation of the desorption energy in cases that cannot be described by a fixed pre-exponential factor. For the case of a distribution of adsorption energies, the desorption spectra cannot be considered a superposition of desorption spectra corresponding to the different energies. Nevertheless, we present a method to extract the distribution of adsorption energies from TPD spectra, and we rationalize the energy resolution of TPD experiments. The analytical results are complemented by a program for simulation and analysis of TPD data.
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13
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Schwarzer M, Hertl N, Nitz F, Borodin D, Fingerhut J, Kitsopoulos TN, Wodtke AM. Adsorption and Absorption Energies of Hydrogen with Palladium. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2022; 126:14500-14508. [PMID: 36081903 PMCID: PMC9442642 DOI: 10.1021/acs.jpcc.2c04567] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Revised: 08/04/2022] [Indexed: 06/15/2023]
Abstract
Thermal recombinative desorption rates of HD on Pd(111) and Pd(332) are reported from transient kinetic experiments performed between 523 and 1023 K. A detailed kinetic model accurately describes the competition between recombination of surface-adsorbed hydrogen and deuterium atoms and their diffusion into the bulk. By fitting the model to observed rates, we derive the dissociative adsorption energies (E 0, ads H2 = 0.98 eV; E 0, ads D2 = 1.00 eV; E 0, ads HD = 0.99 eV) as well as the classical dissociative binding energy ϵads = 1.02 ± 0.03 eV, which provides a benchmark for electronic structure theory. In a similar way, we obtain the classical energy required to move an H or D atom from the surface to the bulk (ϵsb = 0.46 ± 0.01 eV) and the isotope specific energies, E 0, sb H = 0.41 eV and E 0, sb D = 0.43 eV. Detailed insights into the process of transient bulk diffusion are obtained from kinetic Monte Carlo simulations.
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Affiliation(s)
- Michael Schwarzer
- Institute
for Physical Chemistry, Georg-August University
Goettingen, Tammannstraße 6, Goettingen 37077, Germany
| | - Nils Hertl
- Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Am Fassberg 11, Goettingen 37077, Germany
| | - Florian Nitz
- Institute
for Physical Chemistry, Georg-August University
Goettingen, Tammannstraße 6, Goettingen 37077, Germany
| | - Dmitriy Borodin
- Institute
for Physical Chemistry, Georg-August University
Goettingen, Tammannstraße 6, Goettingen 37077, Germany
- Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Am Fassberg 11, Goettingen 37077, Germany
| | - Jan Fingerhut
- Institute
for Physical Chemistry, Georg-August University
Goettingen, Tammannstraße 6, Goettingen 37077, Germany
| | - Theofanis N. Kitsopoulos
- Institute
for Physical Chemistry, Georg-August University
Goettingen, Tammannstraße 6, Goettingen 37077, Germany
- Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Am Fassberg 11, Goettingen 37077, Germany
- Department
of Chemistry, University of Crete, Heraklion 71003, Greece
- Institute
of Electronic Structure and Laser − FORTH, Heraklion 71110, Greece
| | - Alec M. Wodtke
- Institute
for Physical Chemistry, Georg-August University
Goettingen, Tammannstraße 6, Goettingen 37077, Germany
- Department
of Dynamics at Surfaces, Max Planck Institute
for Multidisciplinary Sciences, Am Fassberg 11, Goettingen 37077, Germany
- International
Center for Advanced Studies of Energy Conversion, Georg-August University Goettingen, Tammannstraße 6, Goettingen 37077, Germany
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