^{1}and Yi Zhao

^{2,a)}

### Abstract

The diffusion coefficients for hydrogen on Ni(100) surface are calculated by using the quantum instanton approximation, together with path integral Monte Carlo and adaptive umbrella sampling techniques. The model includes 163 atoms in which the motions of the hydrogen and 25 Ni atoms are treated quantum mechanically and the left Ni atoms are considered classically. At high temperature, the predicted diffusion coefficients are in good agreement with experiments. As temperature decreases to 80 K the hydrogen tunneling begins to dominate the diffusive process and the transition temperature is found to be 70 K under which the diffusion coefficient is nearly independent of temperature. The calculations also indicate that the quantum motions of surface atoms hinder the diffusive process compared to the rigid surface and purely classical motions of surface atoms. The underlying mechanisms are extensively investigated.

We would like to thank Professor T. Yamamoto for useful discussions and suggestions. This work has been supported by the National Science Foundation of China (Grant Nos. 20773115 and 20833004) and National Key Basic Research Foundation Program of China (Grant No. 2007CB815204). The authors also acknowledge a generous allocation of supercomputer time from the Super Computing Center of CAS.

I. INTRODUCTION

II. THEORY

A. Quantum instanton approximation

B. Path integral evaluation of quantum instanton rates

C. Adaptive umbrella sampling for

III. MODEL AND COMPUTATIONAL DETAILS

A. Potential function of H/Ni(100) system

B. Computational details

IV. RESULTS

A. Probability distribution of paths

B. Rate constants

C. Diffusion coefficients

V. CONCLUDING REMARKS

### Key Topics

- Diffusion
- 44.0
- Nickel
- 37.0
- Tunneling
- 34.0
- Free energy
- 19.0
- Transition state theory
- 14.0

## Figures

Surface lattice (100) of Ni. Two minimum-energy sites of fourfold symmetry are marked by Ha and a saddle point of twofold symmetry by Hb. (b) is the hop length of diffusive process.

Surface lattice (100) of Ni. Two minimum-energy sites of fourfold symmetry are marked by Ha and a saddle point of twofold symmetry by Hb. (b) is the hop length of diffusive process.

The plan form and profile chart of H diffusion on Ni(100) lattice. The gray circles represent H atom on different surface sites and the orange circles represent the fixed Ni atoms. Blue circles are Ni atoms treated classically while the red ones are treated quantum mechanically.

The plan form and profile chart of H diffusion on Ni(100) lattice. The gray circles represent H atom on different surface sites and the orange circles represent the fixed Ni atoms. Blue circles are Ni atoms treated classically while the red ones are treated quantum mechanically.

Distribution of H and Ni quantum paths on the surface with two coordinate beads ( and ) of H path fixed at the two dividing surfaces. The probabilities are normalized for both H and Ni. The difference between two nearest contour lines for Ni is five times larger than that for H. Solid lines denote H and dotted lines denote Ni.

Distribution of H and Ni quantum paths on the surface with two coordinate beads ( and ) of H path fixed at the two dividing surfaces. The probabilities are normalized for both H and Ni. The difference between two nearest contour lines for Ni is five times larger than that for H. Solid lines denote H and dotted lines denote Ni.

Arrhenius plots of the rate constants in the range of 40–300 K. Solid line: the QI results for the quantized lattice. Dotted line: the QI results for the rigid lattice. Dot-dashed line: the CVT results for the rigid lattice. Dashed line: the CVT/SCSAG results for the rigid lattice. Dot-dot-dashed line: the CVT/SCSAG results for the quantized lattice.

Arrhenius plots of the rate constants in the range of 40–300 K. Solid line: the QI results for the quantized lattice. Dotted line: the QI results for the rigid lattice. Dot-dashed line: the CVT results for the rigid lattice. Dashed line: the CVT/SCSAG results for the rigid lattice. Dot-dot-dashed line: the CVT/SCSAG results for the quantized lattice.

Free energy profiles at 200 K. The solid, dotted, and dashed lines correspond to the quantized, classical, and rigid lattices, respectively.

Free energy profiles at 200 K. The solid, dotted, and dashed lines correspond to the quantized, classical, and rigid lattices, respectively.

Arrhenius plots of the diffusion coefficients in the range of 40–300 K. Solid line: the QI results for quantized lattice. Dotted line: the QI results for rigid lattice. Dashed line: the CVT/SCSAG results for the rigid lattice. Pluses, crosses, squares, and circles are experimental results of Lee *et al.*, Gomer *et al.*, Mullins *et al.* and George *et al.*, respectively.

Arrhenius plots of the diffusion coefficients in the range of 40–300 K. Solid line: the QI results for quantized lattice. Dotted line: the QI results for rigid lattice. Dashed line: the CVT/SCSAG results for the rigid lattice. Pluses, crosses, squares, and circles are experimental results of Lee *et al.*, Gomer *et al.*, Mullins *et al.* and George *et al.*, respectively.

## Tables

The positions of two dividing surfaces.

The positions of two dividing surfaces.

Rate constants (unit is , powers of 10 are in parentheses, and the rates are only for a one reaction path) for the H/Ni(100) system.

Rate constants (unit is , powers of 10 are in parentheses, and the rates are only for a one reaction path) for the H/Ni(100) system.

The free energy barriers (kcal/mol) and the prefactors (powers of 10 are in parentheses).

The free energy barriers (kcal/mol) and the prefactors (powers of 10 are in parentheses).

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