A unifying model for non-adiabatic coupling at metallic surfaces beyond the local harmonic approximation: From vibrational relaxation to scanning tunneling microscopy

Abstract

A model for treating excitation and relaxation of adsorbates at metallic surfaces induced by non-adiabatic coupling is developed. The derivation is based on the concept of resonant electron transfer, where the adsorbate serves as a molecular bridge for the inelastic transition between an electron source and a sink. In this picture, energy relaxation and scanning tunneling microscopy (STM) at metallic surfaces are treated on an equal footing as a quasi-thermal process. The model goes beyond the local harmonic approximation and allows for an unbiased description of floppy systems with multiple potential wells. Further, the limitation of the product ansatz for the vibronic wave function to include the position-dependence of the non-adiabatic couplings is avoided by explicitly enforcing detailed balance. The theory is applied to the excitation of hydrogen on palladium, which has multiple local potential minima connected by low energy barriers. The main aspects investigated are the lifetimes of adsorbate vibrations in different adsorption sites, as well as the dependence of the excitation, response, and transfer rates on an applied potential bias. The excitation and relaxation simulations reveal intricate population dynamics that depart significantly from the simplistic tunneling model in a truncated harmonic potential. In particular, the population decay from an initially occupied local minimum induced by the contact with an STM tip is found to be better described by a double exponential. The two rates are interpreted as a response to the system perturbation and a transfer rate following the perturbation. The transfer rate is found to obey a power law, as was the case in previous experimental and theoretical work.

Diffusion Rates for Hydrogen on Pd(111) from Molecular Quantum Dynamics Calculations

“…Relevant life times from ref. [10] differ only little from the adopted value and if these are used instead of the generic one for the few states for which they are known, results change insignificantly. However, if the values for intrinsic life times change by a factor of 2 or more, so does the calculated diffusion rate [5].…”

“…Depopulation of vibrational eigenstates of adsorbates on metal substrates via formation of electron-hole pairs is expected to proceed on the picosecond time scale [7,8], or even faster [9,10]. This is about the time scale that can be reached with the 3 He spin-echo technique.…”

Manipulating interfacial hydrogens at palladium via STM

“…As in previous work, 21 the population evolution of the system states driven by the STM is studied using the Pauli master equation…”

“…[18][19][20] A perturbative model for computing rates associated with non-adiabatic coupling of an impurity embedded in a metallic environment was recently introduced. 21 The model includes both energy relaxation/excitation rates due to electronhole pair creation/annihilation in the metallic environment, as well as the STM excitation mechanism. It is based on the evaluation of the vibronic coupling induced by the nuclear kinetic energy operator in the basis of one-electron Kohn-Sham states.…”

Relaxation dynamics in quantum dissipative systems: The microscopic effect of intramolecular vibrational energy redistribution

“…By doing so, well-established expressions for the anharmonic vibrational relaxation rates can be obtained. 42,[44][45][46][47] It is important to note that the effects of IVR, i.e., of intermode coupling induced by the molecular potential, are here explicitly included in the definition of both the relaxation operators and the associate rates.…”