Collisional line shapes for low frequency vibrations of adsorbates on a metal surface

Alkali metal adsorption on metal surfaces: new insights from new tools

The adsorption of sodium on Ru(0001) is studied using ³He spin-echo spectroscopy (HeSE), molecular dynamics simulations (MD) and density functional theory (DFT). In the multi-layer regime, an analysis of helium reflectivity, gives an electron-phonon coupling constant of λ = 0.64 ± 0.06. At sub-monolayer coverage, DFT calculations show that the preferred adsorption site changes from hollow site to top site as the supercell increases and the effective coverage, θ, is reduced from 0.25 to 0.0625 adsorbates per substrate atom. Energy barriers and adsorption geometries taken from DFT are used in molecular dynamics calculations to generate simulated data sets for comparison with measurements. We introduce a new Bayesian method of analysis that compares measurement and model directly, without assuming analytic lineshapes. The value of adsorbate-substrate energy exchange rate (friction) in the MD simulation is the sole variable parameter. Experimental data at a coverage θ = 0.028 compares well with the low-coverage DFT result, giving an effective activation barrier E_eff = 46 ± 4 meV with a friction γ = 0.3 ps^-1. Better fits to the data can be achieved by including additional variable parameters, but in all cases, the mechanism of diffusion is predominantly on a Bravais lattice, suggesting a single adsorption site in the unit cell, despite the close packed geometry.

Amplitude of jump motion signatures in classical vibration-jump dynamics

The classical Langevin dynamics of a particle in a periodic potential energy landscape are studied via the intermediate scattering function (ISF). By construction, the particle performs coupled vibrational and activated jump motion with a wide separation of the vibrational period and the mean residence time between jumps. The long time limit of the ISF is a decaying tail proportional to the function that describes ideal jump motion in the absence of vibrations. The amplitude of the tail is unity in idealized jump dynamics models but is reduced from unity by the intra-well motion. Analytical estimates of the amplitude of the jump motion signature are provided by assuming a factorization of the conditional probability density of the particle position at long times, motivated by the separation of time scales associated with inter-cell and intra-cell motion. The assumption leads to a factorization of the ISF at long correlation times, where one factor is an ideal jump motion signature and the other component is the amplitude of the signature. The amplitude takes the form of a single-particle anharmonic Debye-Waller factor. The factorization approximation is exact at the diffraction conditions associated with the periodic potential. Numerical simulations of the Langevin equation in one and two spatial dimensions confirm that for a strongly corrugated potential the analytical approximation provides a good qualitative description of the trend in the jump signature amplitude, between the points where the factorization is exact.

Interpretation of surface diffusion data with Langevin simulations: a quantitative assessment

Diffusion studies of adsorbates moving on a surface are often analyzed using 2D Langevin simulations. These simulations are computationally cheap and offer valuable insight into the dynamics, however, they simplify the complex interactions between the substrate and adsorbate atoms, neglecting correlations in the motion of the two species. The effect of this simplification on the accuracy of observables extracted using Langevin simulations was previously unquantified. Here we report a numerical study aimed at assessing the validity of this approach. We compared experimentally accessible observables which were calculated using a Langevin simulation with those obtained from explicit molecular dynamics simulations. Our results show that within the range of parameters we explored Langevin simulations provide a good alternative for calculating the diffusion procress, i.e. the effect of correlations is too small to be observed within the numerical accuracy of this study and most likely would not have a significant effect on the interpretation of experimental data. Our comparison of the two numerical approaches also demonstrates the effect temperature dependent friction has on the calculated observables, illustrating the importance of accounting for such a temperature dependence when interpreting experimental data.

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

The van Hove formula for the dynamical structure factor (DSF) related to particle scattering at mobile adsorbates is extended to include the relaxation of the adsorbates' vibrational states. The total rate obtained from the DSF is assumed to be the sum of a diffusion and a relaxation rate. A simple kinetic model to support this assumption is presented. To illustrate its potential applicability, the formula is evaluated using wave functions, energies, and lifetimes of vibrational states obtained for H/Pd(111) from first-principle calculations. Results show that quantum effects can be expected to be important even at room temperature.

Probing the non-pairwise interactions between CO molecules moving on a Cu(111) surface

The coverage dependent dynamics of CO on a Cu(111) surface are studied on an atomic scale using helium spin-echo spectroscopy. CO molecules occupy top sites preferentially, but also visit intermediate bridge sites in their motion along the reaction coordinate. We observe an increase in hopping rate as the CO coverage grows; however, the motion remains uncorrelated up to at least 0.10 monolayers (ML). From the temperature dependence of the diffusion rate, we find an effective barrier of 98 ± 5 meV for diffusion. Thermal motion is modelled with Langevin molecular dynamics, using a potential energy surface having adsorption sites at top and bridge positions and the experimental data are well represented by an adiabatic barrier for hopping of 123 meV. The sites are not degenerate and the rate changes observed with coverage are modelled successfully by changing the shape of the adiabatic potential energy surface in the region of the transition state without modifying the energy barrier. The results demonstrate that sufficient detail exists in the experimental data to provide information on the principal adsorption sites as well as the energy landscape in the region of the transition state.

Coherence, decoherence, and memory effects in the problems of quantum surface diffusion

We consider surface diffusion of a single particle, which performs site-to-site under-barrier hopping, fulfils intrasite motion between the ground and the first excited states within a quantum well, and interacts with surface phonons. On the basis of quantum kinetic equations for one-particle distribution functions, we study the coherent and incoherent motion of the adparticle. In the latter case, we derive the generalized diffusion coefficients and study various dynamic regimes of the adparticle. The critical values of the coupling constant G(cr)(T,Ω), which separate domains with possible recrossing from those with the monotonic motion of the adparticle, are calculated as functions of temperature T and vibrational frequency Ω. These domains are found to coincide with the regions where the experimentally observed diffusion coefficients change their behavior from weakly dependent on T to quite a sensitive function of the temperature. We also evaluate the off-diagonal distribution functions both in the Markovian limit and when the memory effects become important. The obtained results are discussed in the context of the "long tails" problem of the generalized diffusion coefficients, the recrossing/multiple crossing phenomena, and an eventual interrelation between the adparticle dynamics at short times and the temperature dependence of the diffusion coefficients measured experimentally.

Density Matrix Treatment of the Nonmarkovian Dissipative Dynamics of Adsorbates on Metal Surfaces

A density matrix treatment is presented for the vibrational relaxation of the frustrated translational mode of a molecule adsorbed on a metal surface. The system is modeled as a vibrating adsorbate oscillator coupled to a bath of harmonic oscillators representing either phonons or electronic density fluctuations. The integrodifferential equations for time evolution of the density matrix including a (nonmarkovian) delayed dissipation are solved using a generalized Runge-Kutta scheme. The equations are also solved in the instantaneous dissipation and the Markov limits, to ascertain their validity. Numerical results are presented for Na/Cu, CO/Cu, and CO/Pt systems. The population of an initially excited state is given over time for varying temperatures and shows that memory effects are needed in a proper description valid even at short times. Calculations of populations for different coupling strengths between the adsorbate species and the substrate metal surface indicate that a weaker coupling leads to increased oscillation amplitudes and longer relaxation times. The time evolution of quantum coherence is also described.

Excitation of frustrated translation and nonadiabatic adatom hopping induced by inelastic tunneling

The dynamics of lateral manipulation for cobalt/Cu(111) has been investigated combining the model of vibrational heating and first-principles density functional calculations. The frustrated translational mode responsible for lateral excitation is identified as a vibrational resonance involving a concerted motion between the adatom and surface phonons. The calculated frequency shows good agreement with the onset energy for adatom hopping induced by inelastic tunneling. Simulation of the power law, compared with experiment, suggests that the atom hopping overcomes a nonadiabatic barrier due to the nonequilibrium local heating of the translational mode.