He-atom scattering is a well established and valuable tool for investigating surface structure. The correct interpretation of the experimental data requires an accurate description of the He-surface interaction potential. A quantum-mechanical treatment of the interaction potential is presented using the current dominant methodologies for computing ground state energies (Hartree-Fock, local and hybrid-exchange density functional theory) and also a novel post-Hartree-Fock ab initio technique for periodic systems (a local implementation of Møller-Plesset perturbation theory at second order). The predicted adsorption well depth and long range behavior of the interaction are compared with that deduced from experimental data in order to assess the accuracy of the interaction potential.

The experimental line shape broadening observed in adsorbate diffusion on metal surfaces with increasing coverage is usually related to the nature of the adsorbate-adsorbate interaction. Here we show that this broadening can also be understood in terms of a fully stochastic model just considering two noise sources: (i) a Gaussian white noise accounting for the surface friction, and (ii) a shot noise replacing the physical adsorbate-adsorbate interaction potential. Furthermore, contrary to what could be expected, for relatively weak adsorbate-substrate interactions the opposite effect is predicted: line shapes get narrower with increasing coverage.

Abstract. The study of diffusion and low frequency vibrational motions of particles on metal surfaces is of paramount importance; it provides valuable information on the nature of the adsorbate-substrate and the substrate-substrate interactions. In particular, the experimental broadening observed in the diffusive peak with increasing coverage is usually interpreted in terms of a dipole-dipole like interaction among adsorbates via extensive molecular dynamics calculations within the Langevin framework. Here we present an alternative way to interpret this broadening by means of a purely stochastic description, namely the interacting single adsorbate approximation, where two noise sources are considered: (1) a Gaussian white noise accounting for the surface friction and temperature, and (2) a white shot noise replacing the interaction potential between adsorbates. Standard Langevin numerical simulations for flat and corrugated surfaces (with a separable potential) illustrate the dynamics of Na atoms on a Cu(100) surface which fit fairly well to the analytical expressions issued from simple models (free particle and anharmonic oscillator) when the Gaussian approximation is assumed. A similar broadening is also expected for the frustrated translational mode peaks.

Here, an approach in terms of shot noise is proposed to study and characterize surface diffusion and low vibrational motion when having interacting adsorbates on surfaces. In what we call statistical limit, that is, at long times and high number of collisions, one expects that diffusing particles display an essential Markovian behavior. Accordingly, the action of the pairwise potentials accounting for particle-particle collisions is equivalent to considering a shot noise acting on a single particle. We call this approach the interacting single adsorbate approximation, which gathers three important advantages: (i) the dynamics underlying surface diffusion and low vibrational motion can be easily understood in terms of relatively simple stochastic processes; (ii) from our model, appropriate (and well justified) working formulas are easily obtained, which explain the results arising from more complicated (but commonly used) molecular dynamics simulations within the Langevin formulation; and (iii), at the same time, it is less demanding computationally than the latter type of calculations. In order to illustrate the application of this model, numerical results are presented. Specially, our model reproduces the experimental observation regarding the broadening of the quasielastic peak ruling surface diffusion.

A quantum Markovian activated atom-surface diffusion model with interacting adsorbates is proposed for the intermediate scattering function, which is shown to be complex-valued and factorizable into a classical-like and a quantum-mechanical factor. Applications to the diffusion of Na atoms on flat (weakly corrugated) and corrugated-Cu(001) surfaces at different coverages and surface temperatures are analyzed. Quantum effects are relevant to diffusion at low surface temperatures and coverages even for relatively heavy particles, such as Na atoms, where transport by tunneling is absent.PACS numbers: 68.35. Fx,05.10.Gg,68.43.Jk In 1954, van Hove 1 introduced the space-time correlation function G (a generalization of the well-known pair-distribution function from the theory of liquids) as a tool to study the scattering of probe particles off quantum systems consisting of ensembles of interacting particles. Within the Born approximation in scattering theory, the nature of the scattered particles as well as the details of the interaction potential are largely irrelevant. Hence, following Lovesey, 2 the scattering processes with interacting particles essentially reduce to a typical problem of statistical mechanics. The linear response function of the interacting particles, also known as dynamic structure factor or scattering law, is then related to the spontaneous-fluctuation spectrum of such particles (measured from G) by the fluctuation-dissipation theorem and can be expressed in terms of particle density-density correlation functions. 2 In general, G is a complex-valued function, what can be considered as a signature of the quantum nature of the problem. The imaginary part of G is important at small values of time (of the order of β, with β = 1/k B T ), extending its range of influence by decreasing the temperature. This dynamical regime takes place when the thermal de Broglie wavelength λ B = / √ 2mk B T (m is the adsorbate mass) is of the order of or greater than the typical interparticle distances. The quantum system is then assumed to obey the fundamental condition of stationarity and the scattering problem satisfies the detailed balance principle, displaying the recoil effect. Here, we study the quantum observable effects of Na-atom diffusion on flat (weakly corrugated) and corrugated-Cu(001) surfaces probed by He atoms at different values of the Na coverage (θ) and the surface temperature. For simplicity, in our model only coupling to substrate phonons (phonon friction) and not to low-lying electron-hole pair excitations (electronic friction) is considered. Nevertheless, as an extension of this stochastic model, the electronic friction could be accounted for by simply adding it to the total friction coefficient. Moreover, diffusion by tunneling will not be considered in this work.The observable magnitude in this type of scattering experiments is the so-called differential reflection coefficient, which gives the probability that the He atoms reach a certain solid angle Ω with an energy exchange ω = E f −E i ...

In this work we employ ab initio electronic structure theory at a very high level to resolve a long standing experimental controversy; the interaction between helium and the MgO (100) surface has been studied extensively by other groups, employing diverse experimental approaches. Nevertheless, the binding energy of the lowest bound state is still unclear: the existence of a state at around −5.5 meV is well established but a state at −10 meV has also been reported. The MgO (100)-He system captures the fundamental physics involved in many adsorption problems; the weak binding is governed by long-range electronic correlation for which a fully predictive theory applicable to the solid state has been elusive. The above-mentioned experimental controversy can now be resolved on the basis of the calculations presented in this work. We performed three-dimensional vibrational dynamics calculations on a highly accurate potential-energy surface. The latter was constructed using a method which systematically approaches the exact limit in its treatment of electronic correlation. The outcome is clear: our calculations do not support the existence of a bound state around −10 meV. The interaction between molecules and crystalline surfaces is of great fundamental and technological interest and is extensively studied both experimentally and theoretically [1][2][3]. One particular example is physisorption and scattering of helium atoms on oxide surfaces. In the last two decades the latter process, employing molecular-beam techniques, has been developed into a powerful tool for the analysis of surface structure and dynamics [4][5][6][7][8]. It is particularly useful for studying insulating surfaces, such as MgO [4,9]. At close proximity the helium-surface interaction potential is dominated by the exponentially growing corrugated repulsive wall, which is a consequence of the mutual exchange repulsion between the helium and surface electron densities. The repulsive potential is two-dimensional (2D) corrugated and leads to a complicated diffraction pattern for helium scattered from the surface. In the range of intermediate He-surface distances, there exists a very shallow attractive potential due to the weak van der Waals interactions, which drops off with distance from the surface as 1/z 3 [10]. Such a potential can support several bound states (in fact several 2D bands of bound states), which correspond to vibrational levels of helium atoms physisorbed on the surface.The delicacy of the balance between different components of the helium-surface interaction makes quantitatively accurate theoretical predictions of the behavior of helium atoms on the surface extremely difficult. Standard density functional theory (DFT), which is the common tool in solid-state simulations (i.e., local-density approximation, generalized gradient approximation, or hybrids), does not capture van der Waals dispersion. In principle it can be used for calculating * r.martinezcasado@imperial.ac.uk † denis.usvyat@chemie.uni-regensburg.de the repulsive wall at th...

Classical viscid media are quite common in our everyday life. However, we are not used to find such media in quantum mechanics, and much less to analyze their effects on the dynamics of quantum systems. In this regard, the Caldirola-Kanai time-dependent Hamiltonian constitutes an appealing model, accounting for friction without including environmental fluctuations (as it happens, for example, with quantum Brownian motion). Here, a Bohmian analysis of the associated friction dynamics is provided in order to understand how a hypothetical, purely quantum viscid medium would act on a wave packet from a (quantum) hydrodynamic viewpoint. To this purpose, a series of paradigmatic contexts have been chosen, such as the free particle, the motion under the action of a linear potential, the harmonic oscillator, or the superposition of two coherent wave packets. Apart from their analyticity, these examples illustrate interesting emerging behaviors, such as localization by "quantum freezing" or a particular type of quantum-classical correspondence. The reliability of the results analytically determined has been checked by means of numerical simulations, which has served to investigate other problems lacking of such analyticity (e.g., the coherent superpositions).

Quasi-elastic helium atom scattering measurements have provided clear evidence for a two-dimensional free gas of Xe atoms on Pt(111) at low coverages. Increasing the friction due to the surface, a gradual change of the shape of the quasi-elastic peak is predicted and analyzed for this system in terms of the so-called motional narrowing effect. The type of analysis presented here for the quasi-elastic peak should be prior to any deconvolution procedure carried out in order to better extract information from the process, e.g. diffusion coefficients and jump distributions. Moreover, this analysis also provides conditions for the free gas regime different than those reported earlier.