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Sah MK, Naskar K, Adhikari S, Smits B, Meyer J, Somers MF. On the quantum dynamical treatment of surface vibrational modes for reactive scattering of H2 from Cu(111) at 925 K. J Chem Phys 2024; 161:014306. [PMID: 38953445 DOI: 10.1063/5.0217639] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2024] [Accepted: 06/13/2024] [Indexed: 07/04/2024] Open
Abstract
We construct the effective Hartree potential for H2 on Cu(111) as introduced in our earlier work [Dutta et al., J. Chem. Phys. 154, 104103 (2021), and Dutta et al., J. Chem. Phys. 157, 194112 (2022)] starting from the same gas-metal interaction potential obtained for 0 K. Unlike in that work, we now explicitly account for surface expansion at 925 K and investigate different models to describe the surface vibrational modes: (i) a cluster model yielding harmonic normal modes at 0 K and (ii) slab models resulting in phonons at 0 and 925 K according to the quasi-harmonic approximation-all consistently calculated at the density functional theory level with the same exchange-correlation potential. While performing dynamical calculations for the H2(v = 0, j = 0)-Cu(111) system employing Hartree potential constructed with 925 K phonons and surface temperature, (i) the calculated chemisorption probabilities are the highest compared to the other approaches over the energy domain and (ii) the threshold for the reaction probability is the lowest, in close agreement with the experiment. Although the survival probabilities (v' = 0) depict the expected trend (lower in magnitude), the excitation probabilities (v' = 1) display a higher magnitude since the 925 K phonons and surface temperature are more effective for the excitation process compared to the phonons/normal modes obtained from the other approaches investigated to describe the surface.
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Affiliation(s)
- Mantu Kumar Sah
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Koushik Naskar
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Bauke Smits
- Leiden Institute of Chemistry, Gorlaeus Building, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Jörg Meyer
- Leiden Institute of Chemistry, Gorlaeus Building, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Mark F Somers
- Leiden Institute of Chemistry, Gorlaeus Building, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
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Formulation of temperature dependent effective Hartree potential incorporating quadratic over linear molecular DOFs-surface modes couplings and its effect on quantum dynamics of D2 (v = 0, j = 0)/D2 (v = 0, j = 2) on Cu(111) metal surface. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2021.111371] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Dutta J, Mandal S, Adhikari S, Spiering P, Meyer J, Somers MF. Effect of surface temperature on quantum dynamics of H 2 on Cu(111) using a chemically accurate potential energy surface. J Chem Phys 2021; 154:104103. [PMID: 33722025 DOI: 10.1063/5.0035830] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The effect of surface atom vibrations on H2 scattering from a Cu(111) surface at different temperatures is being investigated for hydrogen molecules in their rovibrational ground state (v = 0, j = 0). We assume weakly correlated interactions between molecular degrees of freedom and surface modes through a Hartree product type wavefunction. While constructing the six-dimensional effective Hamiltonian, we employ (a) a chemically accurate potential energy surface according to the static corrugation model [M. Wijzenbroek and M. F. Somers, J. Chem. Phys. 137, 054703 (2012)]; (b) normal mode frequencies and displacement vectors calculated with different surface atom interaction potentials within a cluster approximation; and (c) initial state distributions for the vibrational modes according to Bose-Einstein probability factors. We carry out 6D quantum dynamics with the so-constructed effective Hamiltonian and analyze sticking and state-to-state scattering probabilities. The surface atom vibrations affect the chemisorption dynamics. The results show physically meaningful trends for both reaction and scattering probabilities compared to experimental and other theoretical results.
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Affiliation(s)
- Joy Dutta
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Souvik Mandal
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Paul Spiering
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Jörg Meyer
- 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
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Serwatka T, Tremblay JC. Stochastic wave packet approach to nonadiabatic scattering of diatomic molecules from metals. J Chem Phys 2019; 150:184105. [PMID: 31091890 DOI: 10.1063/1.5092698] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this contribution, we present a quantum dynamical approach to study inelastic scattering of diatomic molecules from metal surfaces at normal incidence. The dissipative dynamics obeys a stochastic Schrödinger equation describing the time-evolution of the system as a piecewise deterministic process. Energy exchange between the molecular vibrational degrees of freedom and the metal electrons is represented using operators in tensor product form, which are coupled via anharmonic transition rates calculated from first-order perturbation theory. Full dimensional observables are obtained by averaging over simulations in 4D-including the internal stretch, the distance to the surface, and the orientation angles-at different surface sites. The method is applied to the state-resolved scattering of vibrationally excited NO from Au(111), revealing important channels for quantized energy relaxation.
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Affiliation(s)
- T Serwatka
- Institut für Chemie und Biochemie, Freie Universität Berlin, D-14195 Berlin, Germany
| | - J C Tremblay
- Institut für Chemie und Biochemie, Freie Universität Berlin, D-14195 Berlin, Germany
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Mandal S, Ghosh S, Sardar S, Adhikari S. The TDDVR approach for molecular photoexcitation, molecule–surface and triatomic reactive scattering processes. INT REV PHYS CHEM 2018. [DOI: 10.1080/0144235x.2018.1548103] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Souvik Mandal
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, India
| | - Sandip Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, India
| | | | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, India
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Kroes GJ, Díaz C. Quantum and classical dynamics of reactive scattering of H2 from metal surfaces. Chem Soc Rev 2016; 45:3658-700. [DOI: 10.1039/c5cs00336a] [Citation(s) in RCA: 120] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
State-of-the-art theoretical models allow nowadays an accurate description of H2/metal surface systems and phenomena relative to heterogeneous catalysis. Here we review the most relevant ones investigated during the last 10 years.
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Affiliation(s)
- Geert-Jan Kroes
- Leiden Institute of Chemistry
- Gorlaeus Laboratories
- Leiden University
- 2300 RA Leiden
- The Netherlands
| | - Cristina Díaz
- Departamento de Química
- Módulo 13
- Universidad Autónoma de Madrid
- 28049 Madrid
- Spain
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Mandal S, Sahoo T, Ghosh S, Adhikari S. The effect of surface temperature on H2/D2(v= 0,j= 0)–Ni(100) scattering processes. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1074741] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Mandal S, Sahoo T, Ghosh S, Adhikari S. The effect of phonon modes and electron–hole pair couplings on molecule–surface scattering processes. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2015. [DOI: 10.1142/s0219633615500285] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The effect of phonon modes and electron–hole pair (elhp) couplings at different surface temperature on D 2(v = 0, 1; j = 0)– Cu (111) collision has been explored by assuming weakly correlated interactions between molecular Degrees of Freedoms (DOFs) with surface modes and elhp excitations through a Hartree product type wavefunction, where the initial state distributions for the phonon modes and the elhp couplings are incorporated by using Bose–Einstein and Fermi–Dirac probability factors, respectively. We carry out four (4D⊗2D)- and six (6D)- dimensional quantum dynamics on such an effective Hamiltonian, and depict the calculated sticking/transition probabilities and energy transfer from molecule to the surface. The phonon modes slightly affect the sticking probability by broadening the profile, but the transition probability are substantially changed with respect to the rigid surface. On the contrary, the inclusion of elhp coupling along with phonon modes does not change the results much compared to the only phonon case.
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Affiliation(s)
- Souvik Mandal
- Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Tapas Sahoo
- Department of Chemical Physics, Wiseman Institute of Science, Rehovot 76100, Israel
| | - Sandip Ghosh
- Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Satrajit Adhikari
- Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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Wang W, Zhao Y. The direct and precursor mediated dissociation rates of H2 on a Ni(111) surface. Phys Chem Chem Phys 2015; 17:5901-12. [PMID: 25630487 DOI: 10.1039/c4cp05624h] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The dissociation and recombination rates of physisorbed H2, and the direct and steady state dissociation (i.e., the precursor mediated dissociation) rates of gas phase H2 on Ni(111), as well as the corresponding kinetic isotope effects, are calculated using the quantum instanton method, together with path integral Monte Carlo and adaptive umbrella sampling techniques. All these rates except the recombination one first decrease and then increase with the increasing temperature, and their minimum values appear at about 250, 300 and 250 K, respectively. These non-monotonic behaviors reveal that the quantum effect of H2 should be very remarkable at low temperatures. The steady state rates are smaller than the direct rates at low temperatures, however, they become larger than the direct ones at high temperatures, these two kinds of rates become equal at about 400 and 300 K on the rigid and quantum lattices, respectively. The quantum motion of the lattice can enhance the direct and steady state rates, and it increases the steady state rate much more than the direct one, for instance, the direct and steady state rates on the quantum lattice are 1.30 and 2.08 times larger than that on the rigid one at 300 K. The calculated kinetic isotope effects are much larger than 1, which reveals that H2 always has a larger rate than that of D2, and the direct process predicts much larger kinetic isotope effects than the steady state process at low temperatures. In addition, the kinetic isotope effects are not affected by the lattice motion.
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Affiliation(s)
- Wenji Wang
- College of Science, Northwest A&F University, Yangling, 712100, Shaanxi Province, P. R. China.
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Wang W, Zhao Y. Dissociation rates of H2on a Ni(100) surface: the role of the physisorbed state. Phys Chem Chem Phys 2014; 16:13318-28. [DOI: 10.1039/c4cp01705f] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Sementa L, Wijzenbroek M, van Kolck BJ, Somers MF, Al-Halabi A, Busnengo HF, Olsen RA, Kroes GJ, Rutkowski M, Thewes C, Kleimeier NF, Zacharias H. Reactive scattering of H2 from Cu(100): Comparison of dynamics calculations based on the specific reaction parameter approach to density functional theory with experiment. J Chem Phys 2013; 138:044708. [DOI: 10.1063/1.4776224] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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Muzas AS, Juaristi JI, Alducin M, Muiño RD, Kroes GJ, Díaz C. Vibrational deexcitation and rotational excitation of H2 and D2 scattered from Cu(111): Adiabatic versus non-adiabatic dynamics. J Chem Phys 2012; 137:064707. [DOI: 10.1063/1.4742907] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sahoo T, Mukherjee S, Adhikari S. Surface temperature effect on the scattering of D2(v = 0, j = 0)-Cu(111) system. J Chem Phys 2012; 136:084306. [DOI: 10.1063/1.3687175] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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