Origin of Power Laws for Reactions at Metal Surfaces Mediated by Hot Electrons

A wide range of experiments have established that certain chemical reactions at metal surfaces can be driven by multiple hot-electron-mediated excitations of adsorbates. A high transient density of hot electrons is obtained by means of femtosecond laser pulses and a characteristic feature of such experiments is the emergence of a power law dependence of the reaction yield on the laser fluence $Y\sim F^n$. We propose a model of multiple inelastic scattering by hot electrons which reproduces this power law and the observed exponents of several experiments. All parameters are calculated within density functional theory and the delta self-consistent field method. With a simplifying assumption, the power law becomes exact and we obtain a simple physical interpretation of the exponent $n$, which represents the number of adsorbate vibrational states participating in the reaction.

Figure 1

The difference between excited and ground state densities for CO adsorbed on Cu(111). Black balls are carbon atoms and red balls are oxygen atoms. Blue contours is excess density in excited state and green contours is excess density in ground state. The excited state is constructed by occupying a ${\pi }^{*}$ orbital of CO. For clarity we only show the density difference in a single supercell.

Figure 2

The reaction yield of CO on Cu(111) as a function of hot-electron flux for four reaction energies. Note the initial linear dependence corresponding to single electron reactions.

Figure 3

The yield as a function of electron flux obtained using the transition probabilities in Eq. (6) for different parameters (see text).