Electronic damping of anharmonic adsorbate vibrations at metallic surfaces

The nonadiabatic coupling of an adsorbate close to a metallic surface leads to electronic damping of adsorbate vibrations and line broadening in vibrational spectroscopy. Here, a perturbative treatment of the electronic contribution to the lifetime broadening serves as a building block for a new approach, in which anharmonic vibrational transition rates are calculated from a position-dependent coupling function. Different models for the coupling function will be tested, all related to embedding theory. The first two are models based on a scattering approach with (i) a jellium-type and (ii) a density functional theory based embedding density, respectively. In a third variant a further refined model is used for the embedding density, and a semiempirical approach is taken in which a scaling factor is chosen to match harmonic, single-site, first-principles transition rates, obtained from periodic density functional theory. For the example of hydrogen atoms on (adsorption) and below (subsurface absorption) a Pd(111) surface, lifetimes of and transition rates between vibrational levels are computed. The transition rates emerging from different models serve as input for the selective subsurface adsorption of hydrogen in palladium starting from an adsorption site, by using sequences of infrared laser pulses in a laser distillation scheme.

Figure 1

(Color online) Schematic representation of the dynamical system. Panel (a): Cartoon of the H/Pd(111) system showing the three cartesian axes. Panel (b): Coordinates describing the hydrogen atom position on the surface. The $1\times 1$ unit cell is represented by balls, triangles, and inverted triangles for the first, second and third palladium atom layer, respectively. See text for more details.

Figure 2

Ground and first excited vibrational states of the full-dimensional Hamiltonian sorted according to the site where they are localized. The labels ${}^{\left(b\right)}$ and ${}^{\left(s\right)}$, refer to the bulk and subsurface octahedral site, and the labels ${}^{\left(h\right)}$ and ${}^{\left(f\right)}$ to the hcp and fcc adsorption sites, respectively.

Figure 3

Comparison of the embedding density for a hydrogen atom on a palladium (111) surface. The dots represent the palladium atoms and the first metal layer defines the zero of the surface. In the left panel, fcc (f) and hcp (h) adsorption sites, as well as subsurface (s) and bulk (b) absorption sites are indicated. The contours range from 0 to $0.2a_0^{-3}$ and are separated by $0.006666a_0^{-3}$ increments. Left panel: Free metal density. Right panel: Perturbed metal density.

Figure 4

(Color online) Rate of the perpendicular mode overtones for H on Pd(111) in different sites obtained using the pure metal density for the embedding density. The red circles are the state-to-state lifetimes and the total lifetimes are represented by black squares. The quantum numbers were obtained by visual inspection of one-dimensional cuts of the wave functions integrated on the parallel mode coordinates.

Figure 5

Selected states involved in the enforced reaction path for the full-dimensional Hamiltonian. The transition dipole moments $\mu$ (in $e{a}_0$), the state-to-state lifetimes $\tau$ (in fs) and the transition energies $\omega$ (in ${\text{cm}}^{-1}$) as well as the state assignments are noted beside the transitions. The labels ${}^{\left(s\right)}$ and ${}^{\left(f\right)}$ refer to the subsurface and fcc adsorption sites, respectively. The state-to-state lifetime is given in parenthesis for the jellium model, the free metal model and the perturbed metal model, respectively.

Figure 6

(Color online) Comparison of the short-term dynamics for the selective subsurface absorption of hydrogen in the palladium (111) octahedral subsurface site. The average laser intensity is $I={10}^{13}\text{W}/{\text{cm}}^2$ for a single pulse of 500 fs duration tuned at a transition frequency of $\omega =940{\text{cm}}^{-1}$.

Figure 7

(Color online) Selective subsurface absorption of hydrogen in the palladium octahedral subsurface site using laser distillation affected by our different dissipation models. The solid curves represent the subsurface ground state population and the dotted curves the fcc ground state population. The red, blue, and black curves are obtained with the jellium model, the free metal model and the perturbed metal model, respectively.