Constructing High-Dimensional Neural Network Potential Energy

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Constructing High-Dimensional Neural Network Potential Energy Surfaces for Gas-Surface Scattering and Reactions Qinghua Liu, Xueyao Zhou, Linsen Zhou, Yaolong Zhang, Xuan Luo, Hua Guo, and Bin Jiang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12064 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 4, 2018

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The Journal of Physical Chemistry

Submitted to J. Phys. Chem. C, 12/07/2017

Constructing High-dimensional Neural Network Potential Energy Surfaces for Gas-Surface Scattering and Reactions

Qinghua Liu,1,# Xueyao Zhou,1,# Linsen Zhou,2 Yaolong Zhang,1 Xuan Luo,1 Hua Guo,2,* and Bin Jiang1,* 1

Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 2

Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States

#: These authors contribute equally to this work

*: Corresponding authors, [email protected], [email protected] 1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract While the ab initio molecular dynamics (AIMD) approach to gas-surface interaction has been instrumental in exploring important issues such as energy transfer and reactivity, it is only amenable to short-time events and a limited number of trajectories because of the on-the-fly nature of the density functional theory (DFT) calculations. Here, we report a high-dimensional global reactive potential energy surface (PES) constructed with high fidelity from judiciously placed DFT points, using a machine learning method; and it is orders-of-magnitude more efficient than AIMD in dynamical calculations and can be employed in various simulations without performing additional electronic structure calculations. Importantly, the surface atoms are included in such a PES, which provides a unique platform for studying energy transfer and scattering/reaction of the impinging molecule on the solid surface on an equal footing.

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I.

INTRODUCTION Heterogeneous catalytic processes are necessarily initiated by molecule-surface

collisions, which can lead to chemical bond rupture and/or formation, often accompanied by energy transfer.1 An in-depth understanding of the dynamics of these gas-surface processes at the atomic level is therefore highly desirable. Experimentally, the scattering and reactive processes have been investigated using laser and molecular beam techniques on clean crystalline surfaces in ultrahigh vacuum. These studies have succeeded in probing quantum state-resolved dynamics of molecule-surface encounters and provided stringent tests for theory.2-5 Theoretically,

the

dynamics

of

molecular

scattering

and

dissociative

chemisorption have been studied using quantum and classical models, both requiring information about electronic energies. To this end, the electronic Schrödinger equation is solved at given nuclear configurations within the Born-Oppenheimer (BO) approximation using a first-principles method, such as density functional theory (DFT).6 Dynamical calculations can be performed with a direct approach, which computes the energy and forces acting on the nuclei on the fly using DFT. This so-called Ab Initio Molecular Dynamics (AIMD) approach7 is quite versatile in handling both reaction and energy exchange between the impinging molecule and the surface. Consequently, there has recently been an increasing interest in AIMD simulations of molecular scattering and dissociation on metal surfaces, some of which have successfully reproduced experimental sticking coefficients within chemical

3



accuracy8,

9

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(i.e., H + H2S reaction, Phys. Chem. Chem. Phys. 2016, 18, 29113-29121. (43) Kolb, B.; Luo, X.; Zhou, X.; Jiang, B.; Guo, H., High-dimensional atomistic neural network potentials for molecule–surface interactions: HCl scattering from Au(111), J. Phys. Chem. Lett. 2017, 8, 666-672. (44) Shakouri, K.; Behler, J.; Meyer, J.; Kroes, G. J., Accurate neural network description of surface phonons in reactive gas-surface dynamics: N2 + Ru(0001), J. Phys. Chem. Lett. 2017, 8, 2131-2136.

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Table 1. Parameters used in QCT calculations to simulate exactly experimental conditions in Ref. 50 for HCl dissociation and Ref. 46 for HCl inelastic scattering, and AIMD conditions in Ref. 14, respectively.

a

Simulation

〈Ei〉 (eV)

ࢻ (m/s)a

Tn (K)

Ts (K)

Ntotal

HCl dissociation

0.94 1.18 1.29 1.55 1.80 2.12 2.56

158 245 207 292 323 364 371

296 400 500 620 740 910 1060

170 170 170 170 170 170 170

100000 50000 25000 10000 10000 5000 5000

DCl dissociation

1.6~2.5

-

300

300

5000

HCl inelastic scattering

0.99 1.12 1.37

-

ν=0, j=0 ν=0, j=0 ν=0, j=0

323, 593, 953 323, 593, 953 323, 593, 953

100000 100000 100000

The velocity distribution is given by f (v ) = v 3 exp(− [ (v − v0 ) / α ] ) and Ei=mv2/2 2

28


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Table 2 Vibrational excitation probabilities for HCl(ν=0→1) on Au(111).a Adiabatic PES Ei (eV)

0.99

1.12

1.37

a

Ts (K)

b

LDFA b

Expt.c

GB

HB

GB

HB

323

8.95E-4

1.33E-2

9.80E-4

9.42E-3

6.00E-4

593

1.65E-3

1.51E-2

1.96E-3

1.56E-2

6.87E-4

953

2.15E-3

1.89E-2

3.90E-3

2.32E-2

1.83E-3

323

2.75E-3

2.47E-2

2.00E-3

1.70E-2

8.10E-4

593

3.28E-3

2.61E-2

3.05E-3

2.27E-2

8.91E-4

953

4.59E-3

2.75E-2

4.91E-3

2.96E-2

1.95E-3

323

8.46E-3

5.00E-2

6.55E-3

3.75E-2

1.80E-3

593

8.90E-3

4.79E-2

8.36E-3

4.12E-2

1.91E-3

953

8.79E-3

4.39E-2

1.01E-2

4.19E-2

3.33E-3

Vibrational excitation probability is defined as P0,1 =

N0→1 measured in N0→0 + N0→1

experiment. b

The full width at half-maximum of the Gaussian weighting function is 0.1.

c

The experiment data are taken from Eq. (5) and TABLE II in Ref. 46.

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Table 3. Mean total energy loss (in eV) in the vibrational elastic and inelastic scattering and relative percentages of the incidence energy in parentheses. Ei=0.99 eV Ts (K) Adiabatic

ν=0→0

ν=0→1

Ei=1.12 eV

Ei=1.37 eV

LDFA

Adiabatic

LDFA

Adiabatic

LDFA

323

0.30 (29.9%)

0.31 (30.8%)

0.35 (31.2%)

0.36 (32.1%)

0.45 (33.0%)

0.47 (33.9%)

593

0.28 (28.6%)

0.29 (28.9%)

0.34 (30.1%)

0.34 (30.5%)

0.44 (32.1%)

0.44 (32.5%)

953

0.26 (26.5%)

0.26 (26.3%)

0.31 (28.0%)

0.31 (27.7%)

0.42 (30.5%)

0.41 (30.3%)

323

0.22 (22.0%)

0.22 (22.3%)

0.28 (24.6%)

0.28 (25.1%)

0.38 (27.5%)

0.41 (29.8%)

593

0.19 (19.3%)

0.17 (17.1%)

0.25 (22.2%)

0.24 (21.0%)

0.36 (26.5%)

0.37 (26.9%)

953

0.14 (14.3%)

0.12 (12.0%)

0.21 (18.5%)

0.18 (16.3%)

0.33 (24.1%)

0.30 (22.1%)

30


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Figure captions: Fig. 1 (a) The six-dimensional dynamical coordinate system for HCl/Au(111). (b-d) two-dimensional cuts of the PES with the molecular center and orientation fixed at a top (T) site and θ=47°, ϕ=30° (b), bridge (B) site and θ=65°, ϕ=30° (c), and hcp (H) site and θ=47°, ϕ=90° (d), respectively, as a function of the HCl bond length (r) and the vertical distance of the HCl molecule (Z) above the frozen surface. The fcc (F) site shows roughly the same PES contour as the hcp site, so not displayed. The contours from the PES (solid lines) and DFT (dashed lines) have an interval of 0.1 eV. The Au, Cl, and H atoms are shown in yellow, green, and white, respectively. Fig. 2 (a) Transition-state geometry with upper two metal layers optimized with DFT. The displacements of Au atoms surrounding the HCl molecule (in Å) are marked in the figure. (b) The dependence of the barrier height (Eb) on the three-dimensional displacements (∆X, ∆Y, ∆Z) of surface atoms. ∆X and ∆Y are taken with respect to Au5 only, while ∆Z is taken on Au1, Au2, and Au5 synchronously. The barrier heights obtained from the PES (solid symbols) are compared with these calculated by DFT at the same geometries (open symbols). Fig. 3 (a) Comparison of initial dissociation sticking probabilities (S0) of DCl obtained from AIMD14 (red circles) and the PES (black squares). (b) Comparison of experimental50 and calculated S0 of HCl at various nozzle temperatures and a fixed surface temperature of 170 K. Previous QD55 and AIMD15 results are also shown for comparison. 31



Fig. 4 Distributions of total energy transfer to surface phonons and to EHPs (insets) for HCl(ν=0→0) (upper panel) and HCl(ν=0→1) (lower panel) scattering from Au(111) at the three incidence energies and a surface temperature of 593 K.

32


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Fig. 1.

33



Fig. 2.

34


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Fig. 3.

35



Fig. 4.

36


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TOC graphic

37



Fig. 1 (a) The six-dimensional dynamical coordinate system for HCl/Au(111). (b-d) two-dimensional cuts of the PES with the molecular center and orientation fixed at a top (T) site and θ=47°, ϕ=30° (b), bridge (B) site and θ=65°, ϕ=30° (c), and hcp (H) site and θ=47°, ϕ=90° (d), respectively, as a function of the HCl bond length (r) and the vertical distance of the HCl molecule (Z) above the frozen surface. The fcc (F) site shows roughly the same PES contour as the hcp site, so not displayed. The contours from the PES (solid lines) and DFT (dashed lines) have an interval of 0.1 eV. The Au, Cl, and H atoms are shown in yellow, green, and white, respectively. 527x506mm (150 x 150 DPI)


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Fig. 2 (a) Transition-state geometry with upper two metal layers optimized with DFT. The displacements of Au atoms surrounding the HCl molecule (in Å) are marked in the figure. (b) The dependence of the barrier height (Eb) on the three-dimensional displacements (∆X, ∆Y, ∆Z) of surface atoms. ∆X and ∆Y are taken with respect to Au5 only, while ∆Z is taken on Au1, Au2, and Au5 synchronously. The barrier heights obtained from the PES (solid symbols) are compared with these calculated by DFT at the same geometries (open symbols). 254x305mm (150 x 150 DPI)



Fig. 3 (a) Comparison of initial dissociation sticking probabilities (S0) of DCl obtained from AIMD12 (red circles) and the PES (black squares). (b) Comparison of experimental46 and calculated S0 of HCl at various nozzle temperatures and a fixed surface temperature of 170 K. Previous QD51 and AIMD13 results are also shown for comparison. 97x153mm (150 x 150 DPI)


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Fig. 4 Distributions of total energy transfer to surface phonons and to EHPs (insets) for HCl(ν=0→0) (upper panel) and HCl(ν=0→1) (lower panel) scattering from Au(111) at the three incidence energies and a surface temperature of 593 K. 500x730mm (150 x 150 DPI)


Constructing High-Dimensional Neural Network Potential Energy

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