Path integral calculation of hydrogen diffusion rates on metal surfaces

Path integral quantum transition state theory is implemented to calculate the diffusion constant for atomic hydrogen on metal surfaces at low coverage. The path integral theory provides a unified computational methodology to study the influence on the diffusion constant from multidimensional tunneling, vibrational mode quantization, surface distortion, and phonon thermal fluctuations. An approximate technique has also been employed to incorporate the dissipative effect from the electron-hole pair excitations of the metal. The hydrogen diffusion rates on two model metal surfaces are calculated. These surface models are (1) a simple rigid model of the Cu(100) surface allowing a comparison with previous theoretical results, and (2) a more realistic moving model of the Cu(100) surface to examine the effects of surface atom motion. The quantum diffusion constant for hydrogen is calculated over a temperature range of 100-300 K. The largest effect from the moving lattice atoms is found to be the surface distortion effect, leading to a 5% modification of the activation free energy for site-to-site hopping. The phonon thermal fluctuations are not found to significantly enhance or dissipate the tunneling at low temperatures. The electron-hole pair dissipation is, however, estimated to have an effect on the tunneling behavior at the lowest temperature studied (100 K).