Hydrogen atom scattering on metal surfaces is investigated based on a simplified Newns–Anderson model. Both the nuclear and electronic degrees of freedom are treated quantum mechanically. By partitioning all the surface electronic states as the bath, the hierarchical equations of motion method for the fermionic bath is employed to simulate the scattering dynamics. It is found that, with a reasonable set of parameters, the main features of the recent experimental studies of hydrogen atom scattering on metal surfaces can be reproduced. Vibrational states on the chemisorption state whose energies are close to the incident energy are found to play an important role, and the scattering process is dominated by a single-pass electronic transition forth and back between the diabatic physisorption and chemisorption states. Further study on the effects of the atom-surface coupling strength reveals that, upon increasing the atom-surface coupling strength, the scattering mechanism changes from typical nonadiabatic transitions to dynamics in the electronic friction regime.
REFERENCES
1.
A.
Nitzan
, Chemical Dynamics in Condensed Phases
(Oxford University Press
, New York
, 2006
).2.
M.
Head-Gordon
and J. C.
Tully
, “Molecular dynamics with electronic frictions
,” J. Chem. Phys.
103
, 10137
–10145
(1995
).3.
C. T.
Rettner
, D. J.
Auerbach
, J. C.
Tully
, and A. W.
Kleyn
, “Chemical dynamics at the gas–surface interface
,” J. Phys. Chem.
100
, 13021
–13033
(1996
).4.
K.
Golibrzuch
, N.
Bartels
, D. J.
Auerbach
, and A. M.
Wodtke
, “The dynamics of molecular interactions and chemical reactions at metal surfaces: Testing the foundations of theory
,” Annu. Rev. Phys. Chem.
66
, 399
–425
(2015
).5.
B.
Jiang
, M.
Yang
, D.
Xie
, and H.
Guo
, “Quantum dynamics of polyatomic dissociative chemisorption on transition metal surfaces: Mode specificity and bond selectivity
,” Chem. Soc. Rev.
45
, 3621
–3640
(2016
).6.
M. M.
Montemore
, M. A.
van Spronsen
, R. J.
Madix
, and C. M.
Friend
, “O2 activation by metal surfaces: Implications for bonding and reactivity on heterogeneous catalysts
,” Chem. Rev.
118
, 2816
–2862
(2018
).7.
S. P.
Rittmeyer
, V. J.
Bukas
, and K.
Reuter
, “Energy dissipation at metal surfaces
,” Adv. Phys.: X
3
, 1381574
(2018
).8.
O.
Bünermann
, H.
Jiang
, Y.
Dorenkamp
, A.
Kandratsenka
, S. M.
Janke
, D. J.
Auerbach
, and A. M.
Wodtke
, “Electron–hole pair excitation determines the mechanism of hydrogen atom adsorption
,” Science
350
, 1346
–1349
(2015
).9.
Y.
Dorenkamp
, H.
Jiang
, H.
Köckert
, N.
Hertl
, M.
Kammler
, S. M.
Janke
, A.
Kandratsenka
, A. M.
Wodtke
, and O.
Bünermann
, “Hydrogen collisions with transition metal surfaces: Universal electronically nonadiabatic adsorption
,” J. Chem. Phys.
148
, 034706
(2018
).10.
C.
Steinsiek
, P. R.
Shirhatti
, J.
Geweke
, J. A.
Lau
, J.
Altschäffel
, A.
Kandratsenka
, C.
Bartels
, and A. M.
Wodtke
, “Translational inelasticity of NO and CO in scattering from ultrathin metallic films of Ag/Au(111)
,” J. Phys. Chem. C
122
, 18942
–18948
(2018
).11.
Y.
Huang
, C. T.
Rettner
, D. J.
Auerbach
, and A. M.
Wodtke
, “Vibrational promotion of electron transfer
,” Science
290
, 111
–114
(2000
).12.
C.
Bartels
, R.
Cooper
, D. J.
Auerbach
, and A. M.
Wodtke
, “Energy transfer at metal surfaces: The need to go beyond the electronic friction picture
,” Chem. Sci.
2
, 1647
–1655
(2011
).13.
S.
Kumar
, H.
Jiang
, M.
Schwarzer
, A.
Kandratsenka
, D.
Schwarzer
, and A. M.
Wodtke
, “Vibrational relaxation lifetime of a physisorbed molecule at a metal surface
,” Phys. Rev. Lett.
123
, 156101
(2019
).14.
G.-J.
Kroes
, A.
Gross
, E.-J.
Baerends
, M.
Scheffler
, and D. A.
McCormack
, “Quantum theory of dissociative chemisorption on metal surfaces
,” Acc. Chem. Res.
35
, 193
–200
(2002
).15.
B.
Gergen
, H.
Nienhaus
, W. H.
Weinberg
, and E. W.
McFarland
, “Chemically induced electronic excitations at metal surfaces
,” Science
294
, 2521
–2523
(2001
).16.
D.
Diesing
and E.
Hasselbrink
, “Chemical energy dissipation at surfaces under UHV and high pressure conditions studied using metal–insulator–metal and similar devices
,” Chem. Soc. Rev.
45
, 3747
–3755
(2016
).17.
A. M.
Wodtke
, J. C.
Tully
, and D. J.
Auerbach
, “Electronically non-adiabatic interactions of molecules at metal surfaces: Can we trust the Born–Oppenheimer approximation for surface chemistry?
,” Int. Rev. Phys. Chem.
23
, 513
–539
(2004
).18.
J. D.
White
, J.
Chen
, D.
Matsiev
, D. J.
Auerbach
, and A. M.
Wodtke
, “Conversion of large-amplitude vibration to electron excitation at a metal surface
,” Nature
433
, 503
–505
(2005
).19.
S.
Roy
, N. A.
Shenvi
, and J. C.
Tully
, “Model Hamiltonian for the interaction of NO with the Au(111) surface
,” J. Chem. Phys.
130
, 174716
(2009
).20.
N.
Shenvi
, S.
Roy
, and J. C.
Tully
, “Nonadiabatic dynamics at metal surfaces: Independent-electron surface hopping
,” J. Chem. Phys.
130
, 174107
(2009
).21.
N.
Shenvi
, S.
Roy
, and J. C.
Tully
, “Dynamical steering and electronic excitation in NO scattering from a gold surface
,” Science
326
, 829
–832
(2009
).22.
S.
Li
and H.
Guo
, “Monte Carlo wave packet study of negative ion mediated vibrationally inelastic scattering of NO from the metal surface
,” J. Chem. Phys.
117
, 4499
–4508
(2002
).23.
W.
Dou
and J. E.
Subotnik
, “A broadened classical master equation approach for nonadiabatic dynamics at metal surfaces: Beyond the weak molecule-metal coupling limit
,” J. Chem. Phys.
144
, 024116
(2016
).24.
G.
Miao
, W.
Dou
, and J.
Subotnik
, “Vibrational relaxation at a metal surface: Electronic friction versus classical master equations
,” J. Chem. Phys.
147
, 224105
(2017
).25.
W.
Dou
, A.
Nitzan
, and J. E.
Subotnik
, “Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model
,” J. Chem. Phys.
142
, 084110
(2015
).26.
F.
Elste
, G.
Weick
, C.
Timm
, and F.
von Oppen
, “Current-induced conformational switching in single-molecule junctions
,” Appl. Phys. A
93
, 345
–354
(2008
).27.
V.
Krishna
and J. C.
Tully
, “Vibrational lifetimes of molecular adsorbates on metal surfaces
,” J. Chem. Phys.
125
, 054706
(2006
).28.
W.
Dou
and J. E.
Subotnik
, “Perspective: How to understand electronic friction
,” J. Chem. Phys.
148
, 230901
(2018
).29.
S. L.
Rudge
, Y.
Ke
, and M.
Thoss
, “Current-induced forces in nanosystems: A hierarchical equations of motion approach
,” Phys. Rev. B
107
, 115416
(2023
).30.
G.-J.
Kroes
, “Frontiers in surface scattering simulations
,” Science
321
, 794
–797
(2008
).31.
R. J.
Maurer
, M.
Askerka
, V. S.
Batista
, and J. C.
Tully
, “Ab initio tensorial electronic friction for molecules on metal surfaces: Nonadiabatic vibrational relaxation
,” Phys. Rev. B
94
, 115432
(2016
).32.
A. M.
Wodtke
, “Electronically non-adiabatic influences in surface chemistry and dynamics
,” Chem. Soc. Rev.
45
, 3641
–3657
(2016
).33.
P.
Spiering
and J.
Meyer
, “Testing electronic friction models: Vibrational de-excitation in scattering of H2 and D2 from Cu(111)
,” J. Phys. Chem. Lett.
9
, 1803
–1808
(2018
).34.
R.
Martin-Barrios
, N.
Hertl
, O.
Galparsoro
, A.
Kandratsenka
, A. M.
Wodtke
, and P.
Larrégaray
, “H atom scattering from W(110): A benchmark for molecular dynamics with electronic friction
,” Phys. Chem. Chem. Phys.
24
, 20813
–20819
(2022
).35.
J. I.
Juaristi
, M.
Alducin
, R.
Díez Muiño
, H. F.
Busnengo
, and A.
Salin
, “Role of electron-hole pair excitations in the dissociative adsorption of diatomic molecules on metal surfaces
,” Phys. Rev. Lett.
100
, 116102
(2008
).36.
S. M.
Janke
, D. J.
Auerbach
, A. M.
Wodtke
, and A.
Kandratsenka
, “An accurate full-dimensional potential energy surface for H–Au(111): Importance of nonadiabatic electronic excitation in energy transfer and adsorption
,” J. Chem. Phys.
143
, 124708
(2015
).37.
A.
Kandratsenka
, H.
Jiang
, Y.
Dorenkamp
, S. M.
Janke
, M.
Kammler
, A. M.
Wodtke
, and O.
Bünermann
, “Unified description of H-atom–induced chemicurrents and inelastic scattering
,” Proc. Natl. Acad. Sci. U. S. A.
115
, 680
–684
(2018
).38.
K.
Krüger
, Y.
Wang
, S.
Tödter
, F.
Debbeler
, A.
Matveenko
, N.
Hertl
, X.
Zhou
, B.
Jiang
, H.
Guo
, A. M.
Wodtke
, and O.
Bünermann
, “Hydrogen atom collisions with a semiconductor efficiently promote electrons to the conduction band
,” Nat. Chem.
15
, 326
–331
(2023
).39.
N.
Shenvi
, S.
Roy
, P.
Parandekar
, and J.
Tully
, “Vibrational relaxation of NO on Au(111) via electron-hole pair generation
,” J. Chem. Phys.
125
, 154703
(2006
).40.
Y.
Tanimura
and R.
Kubo
, “Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath
,” J. Phys. Soc. Jpn.
58
, 101
–114
(1989
).41.
Y.
Tanimura
, “Stochastic Liouville, Langevin, Fokker–Planck, and master equation approaches to quantum dissipative systems
,” J. Phys. Soc. Jpn.
75
, 082001
(2006
).42.
J.
Jin
, S.
Welack
, J.
Luo
, X.-Q.
Li
, P.
Cui
, R.-X.
Xu
, and Y.
Yan
, “Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach
,” J. Chem. Phys.
126
, 134113
(2007
).43.
J.
Jin
, X.
Zheng
, and Y.
Yan
, “Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach
,” J. Chem. Phys.
128
, 234703
(2008
).44.
Z.
Li
, N.
Tong
, X.
Zheng
, D.
Hou
, J.
Wei
, J.
Hu
, and Y.
Yan
, “Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems
,” Phys. Rev. Lett.
109
, 266403
(2012
).45.
R.
Härtle
, G.
Cohen
, D.
Reichman
, and A.
Millis
, “Transport through an Anderson impurity: Current ringing, nonlinear magnetization, and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations
,” Phys. Rev. B
92
, 085430
(2015
).46.
Q.
Shi
, Y.
Xu
, Y.
Yan
, and M.
Xu
, “Efficient propagation of the hierarchical equations of motion using the matrix product state method
,” J. Chem. Phys.
148
, 174102
(2018
).47.
A.
Erpenbeck
, L.
Götzendörfer
, C.
Schinabeck
, and M.
Thoss
, “Hierarchical quantum master equation approach to charge transport in molecular junctions with time-dependent molecule-lead coupling strengths
,” Eur. Phys. J.: Spec. Top.
227
, 1981
–1994
(2019
).48.
H.-D.
Zhang
, L.
Cui
, H.
Gong
, R.-X.
Xu
, X.
Zheng
, and Y.
Yan
, “Hierarchical equations of motion method based on Fano spectrum decomposition for low temperature environments
,” J. Chem. Phys.
152
, 064107
(2020
).49.
C.
Schinabeck
, A.
Erpenbeck
, R.
Härtle
, and M.
Thoss
, “Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems
,” Phys. Rev. B
94
, 201407
(2016
).50.
C.
Schinabeck
, R.
Härtle
, and M.
Thoss
, “Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities
,” Phys. Rev. B
97
, 235429
(2018
).51.
C.
Schinabeck
and M.
Thoss
, “Hierarchical quantum master equation approach to current fluctuations in nonequilibrium charge transport through nanosystems
,” Phys. Rev. B
101
, 075422
(2020
).52.
C.
Kaspar
, A.
Erpenbeck
, J.
Bätge
, C.
Schinabeck
, and M.
Thoss
, “Nonadiabatic vibronic effects in single-molecule junctions: A theoretical study using the hierarchical equations of motion approach
,” Phys. Rev. B
105
, 195435
(2022
).53.
A.
Erpenbeck
, C.
Schinabeck
, U.
Peskin
, and M.
Thoss
, “Current-induced bond rupture in single-molecule junctions
,” Phys. Rev. B
97
, 235452
(2018
).54.
A.
Erpenbeck
and M.
Thoss
, “Hierarchical quantum master equation approach to vibronic reaction dynamics at metal surfaces
,” J. Chem. Phys.
151
, 191101
(2019
).55.
A.
Erpenbeck
, Y.
Ke
, U.
Peskin
, and M.
Thoss
, “Current-induced dissociation in molecular junctions beyond the paradigm of vibrational heating: The role of antibonding electronic states
,” Phys. Rev. B
102
, 195421
(2020
).56.
Y.
Ke
, A.
Erpenbeck
, U.
Peskin
, and M.
Thoss
, “Unraveling current-induced dissociation mechanisms in single-molecule junctions
,” J. Chem. Phys.
154
, 234702
(2021
).57.
Y.
Ke
, R.
Borrelli
, and M.
Thoss
, “Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
,” J. Chem. Phys.
156
, 194102
(2022
).58.
M.
Xu
, Y.
Liu
, K.
Song
, and Q.
Shi
, “A non-perturbative approach to simulate heterogeneous electron transfer dynamics: Effective mode treatment of the continuum electronic states
,” J. Chem. Phys.
150
, 044109
(2019
).59.
P. W.
Anderson
, “Localized magnetic states in metals
,” Phys. Rev.
124
, 41
–53
(1961
).60.
D. M.
Newns
, “Self-consistent model of hydrogen chemisorption
,” Phys. Rev.
178
, 1123
–1135
(1969
).61.
W.
Schmickler
, “A theory of adiabatic electron-transfer reactions
,” J. Electroanal. Chem. Interfacial Electrochem.
204
, 31
–43
(1986
).62.
W.
Schmickler
and J.
Mohr
, “The rate of electrochemical electron-transfer reactions
,” J. Chem. Phys.
117
, 2867
–2872
(2002
).63.
A.
Nitzan
, “Electron transmission through molecules and molecular interfaces
,” Annu. Rev. Phys. Chem.
52
, 681
–750
(2001
).64.
W.
Dou
and J. E.
Subotnik
, “Electronic friction near metal surfaces: A case where molecule-metal couplings depend on nuclear coordinates
,” J. Chem. Phys.
146
, 092304
(2017
).65.
R.
Härtle
, G.
Cohen
, D. R.
Reichman
, and A. J.
Millis
, “Decoherence and lead-induced interdot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach
,” Phys. Rev. B
88
, 235426
(2013
).66.
K. L.
Sebastian
, “Electrochemical electron transfer: Accounting for electron–hole excitations in the metal electrode
,” J. Chem. Phys.
90
, 5056
–5067
(1989
).67.
G. D.
Mahan
, Many-Particle Physics
(Kluwer Academic/Plenum
, New York
, 2000
).68.
H.
Haug
, A.-P.
Jauho
et al, Quantum Kinetics in Transport and Optics of Semiconductors
(Springer
, 2008
), Vol. 2
.69.
M.
Pons
, B.
Juliá-Díaz
, A.
Polls
, A.
Rios
, and I.
Vidaña
, “The Hellmann–Feynman theorem at finite temperature
,” Am. J. Phys.
88
, 503
–510
(2020
).70.
W.
Ouyang
, W.
Dou
, A.
Jain
, and J. E.
Subotnik
, “Dynamics of barrier crossings for the generalized Anderson–Holstein model: Beyond electronic friction and conventional surface hopping
,” J. Chem. Theory Comput.
12
, 4178
–4183
(2016
).71.
W.
Dou
and J. E.
Subotnik
, “Nonadiabatic molecular dynamics at metal surfaces
,” J. Phys. Chem. A
124
, 757
–771
(2020
).72.
X.
Dan
, M.
Xu
, Y.
Yan
, and Q.
Shi
, “Generalized master equation for charge transport in a molecular junction: Exact memory kernels and their high order expansion
,” J. Chem. Phys.
156
, 134114
(2022
).73.
J. P.
Muscat
and D. M.
Newns
, “Chemisorption on metals
,” Prog. Surf. Sci.
9
, 1
–43
(1978
).74.
O.
Bünermann
, A.
Kandratsenka
, and A. M.
Wodtke
, “Inelastic scattering of H atoms from surfaces
,” J. Phys. Chem. A
125
, 3059
–3076
(2021
).75.
S.
Venkatachalam
and T.
Jacob
, “Hydrogen adsorption on Pd-containing Au(111) bimetallic surfaces
,” Phys. Chem. Chem. Phys.
11
, 3263
–3270
(2009
).76.
Y.
Santiago-Rodríguez
, J. A.
Herron
, M. C.
Curet-Arana
, and M.
Mavrikakis
, “Atomic and molecular adsorption on Au(111)
,” Surf. Sci.
627
, 57
–69
(2014
).77.
N. E.
Christensen
and B. O.
Seraphin
, “Relativistic band calculation and the optical properties of gold
,” Phys. Rev. B
4
, 3321
–3344
(1971
).78.
M. S.
Mizielinski
, D. M.
Bird
, M.
Persson
, and S.
Holloway
, “Newns–Anderson model of chemicurrents in H/Cu and H/Ag
,” Surf. Sci.
602
, 2617
–2622
(2008
).79.
X.
Dan
, M.
Xu
, J. T.
Stockburger
, J.
Ankerhold
, and Q.
Shi
, “Efficient low-temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model
,” Phys. Rev. B
107
, 195429
(2023
).80.
G.
Cohen
, E. Y.
Wilner
, and E.
Rabani
, “Generalized projected dynamics for non-system observables of non-equilibrium quantum impurity models
,” New J. Phys.
15
, 073018
(2013
).81.
Q.
Shi
, L.
Chen
, G.
Nan
, R.-X.
Xu
, and Y.
Yan
, “Efficient hierarchical Liouville space propagator to quantum dissipative dynamics
,” J. Chem. Phys.
130
, 084105
(2009
).82.
I. V.
Oseledets
, “Tensor-train decomposition
,” SIAM J. Sci. Comput.
33
, 2295
–2317
(2011
).83.
B.
Popescu
and U.
Kleinekathöfer
, “Treatment of time-dependent effects in molecular junctions
,” Phys. Status Solidi B
250
, 2288
–2297
(2013
).84.
V.
May
and O.
Kühn
, Charge and Energy Transfer Dynamics in Molecular Systems
, 3rd ed.
(Wiley-VCH
, Weinheim
, 2011
).85.
J. S.
Kretchmer
and G. K.-L.
Chan
, “The fate of atomic spin in atomic scattering off surfaces
,” J. Phys. Chem. Lett.
9
, 2863
–2868
(2018
).86.
D. M.
Newns
, “Electron-hole pair mechanism for excitation of intramolecular vibrations in molecule-surface scattering
,” Surf. Sci.
171
, 600
–614
(1986
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.