Generalized Langevin Oscillator Model Research Articles

Three-dimensional Langevin dynamics of N atom scattering from N-covered Ag(1 1 1)

We analyzed the dynamics of N atom scattering from N -covered Ag(1 1 1), using the generalized Langevin oscillator (GLO) method and a three-dimensional neural network potential energy surface. Two values for the mass of the surface oscillator were considered in the GLO model to account for the energy exchange with the surface, i.e., that of Ag and that of N. For these mass values different trends were found for the dependence of the ratio of the average final divided by the average initial translational energy on the scattering angle. Using the nitrogen mass gives a trend closer to the experimental results for the dependence of the energy of the in-plane scattered atoms on the scattering angle, but worse agreement with experiment for the angular distribution of the in-plane scattered atoms. Two different algorithms are applied to integrate the stochastic equations of motion in the presence of energy dissipation. Our calculations show that a trivially extended Bulirsch-Stoer algorithm is more efficient than an algorithm based on a Langevin Liouville operator splitting technique, in that it yields the same results with a much larger time step.

Dynamics Studies of O2 Collision on Pt(111) Using a Global Potential Energy Surface

The dynamics of O2 collision on Pt(111) has been studied by molecular dynamics simulations using a global potential energy surface (PES), which was developed by fitting ∼4800 plane-wave density functional theory points using the permutation invariant polynomial-neural network method. The simulations were performed for the normal and off-normal incidences at a wide range of incident energies and surface temperatures. A generalized Langevin oscillator model was used to incorporate the molecule–surface coupling that plays an important role in this collision process. The trapping probability, final energy distribution, scattering angle distributions of scattered molecules, and the energy transfer to surface distribution were determined and analyzed. The PES shows an activated path to the chemisorption states, as the trapping probability directly increases with incident energy (larger than 0.1 eV) to reach a maximum and then decreases at high incident energy. The trapping probability obviously reduces by raising surface temperature at low incident energy because the initial kinetic energy of molecule is more likely to be dissipated into surface motions than molecular internal ro-vibrational modes. Additional parallel momentum of off-normal incidence leads to a strong suppression of the trapping probability, caused by the energetic corrugation of the lateral barrier heights. The scattering angular distributions are found to be quasispecular and the final translational energy slightly increases with scattering angle deviating significantly from the hard-cube model, indicating the nonconservation of parallel momentum during the collision on the corrugate PES.

Vibrational response and motion of carbon monoxide on Cu(100) driven by femtosecond laser pulses: Molecular dynamics with electronic friction

Carbon monoxide on copper surfaces continues to be a fascinating, rich microlab for many questions evolving in surface science. Recently, hot-electron mediated, femtosecond-laser pulse induced dynamics of CO molecules on Cu(100) were the focus of experiments [Inoue et al., Phys. Rev. Lett. 117, 186101 (2016)] and theory [Novko et al., Phys. Rev. Lett. 122, 016806 (2019)], unraveling details of the vibrational nonequilibrium dynamics on ultrashort (subpicoseconds) timescales. In the present work, full-dimensional time-resolved hot-electron driven dynamics are studied by molecular dynamics with electronic friction (MDEF). Dissipation is included by a friction term in a Langevin equation which describes the coupling of molecular degrees of freedom to electron-hole pairs in the copper surface, calculated from gradient-corrected density functional theory (DFT) via a local density friction approximation (LDFA). Relaxation due to surface phonons is included by a generalized Langevin oscillator model. The hot-electron induced excitation is described via a time-dependent electronic temperature, the latter derived from an improved two-temperature model. Our parameter-free simulations on a precomputed potential energy surface allow for excellent statistics, and the observed trends are confirmed by on-the-fly ab initio molecular dynamics with electronic friction (AIMDEF) calculations. By computing time-resolved frequency maps for selected molecular vibrations, instantaneous frequencies, probability distributions, and correlation functions, we gain microscopic insight into hot-electron driven dynamics and we can relate the time evolution of vibrational internal CO stretch-mode frequencies to measured data, notably an observed redshift. Quantitatively, the latter is found to be larger in MDEF than in experiment and possible reasons are discussed for this observation. In our model, in addition we observe the excitation and time evolution of large-amplitude low-frequency modes, lateral CO surface diffusion, and molecular desorption. Effects of surface atom motion and of the laser fluence are also discussed.

A modified generalized Langevin oscillator model for activated gas-surface reactions.

Surface motion has proven to influence the gas-surface reactions in various ways. An adequate model to describe the complex lattice effects in a relatively simple way is therefore highly desirable. In this work, we have modified the widely used Generalized Langevin Oscillator (GLO) model to incorporate the molecule-surface coupling that plays an important role in activated dissociation of polyatomic molecules on metal surfaces. To this end, taking the well-studied CHD3+Ni(111) system as an example, we add a coupling potential linearly dependent on the surface oscillating coordinate, which becomes essential in predicting the dissociative sticking coefficients for reactive scattering. We further scale the mass of the surface oscillator on the basis of a mechanic coupling parameter, which has significantly improved the description of the molecule-surface energy transfer for nonreactive scattering. This so-called modified GLO (MGLO) model retains the simplicity and advantages of the original GLO, while yields much more accurate dynamics results that are in remarkably good agreement with the benchmark data calculated using ab initio molecular dynamics. We argue that the MGLO model is applicable to these highly activated gas-surface reactions with strong molecule-surface couplings.

Effects of surface motion and electron-hole pair excitations in CO2 dissociation and scattering on Ni(100).

The energy transfer between different channels is an important aspect in chemical reactions at surfaces. We investigate here in detail the energy transfer dynamics in a prototypical system, i.e., reactive and nonreactive scattering of CO2 on Ni(100), which is related to heterogeneous catalytic processes with Ni-based catalysts for CO2 reduction. On the basis of our earlier nine-dimensional potential energy surface for CO2/Ni(100), dynamical calculations have been done using the generalized Langevin oscillator (GLO) model combined with local density friction approximation (LDFA), in which the former accounts for the surface motion and the latter accounts for the low-energy electron-hole pair (EHP) excitation. In spite of its simplicity, it is found that the GLO model yields quite satisfactory results, including the significant energy loss and product energy disposal, trapping, and steering dynamics, all of which agree well with the ab initio molecular dynamics ones where many surface atoms are explicitly involved with high computational cost. However, the GLO model fails to describe the reactivity enhancement due to the lattice motion because it intrinsically does not incorporate the variance of barrier height on the surface atom displacement. On the other hand, in LDFA, the energy transferred to EHPs is found to play a minor role and barely alter the dynamics, except for slightly reducing the dissociation probabilities. In addition, vibrational state-selected dissociative sticking probabilities are calculated and previously observed strong mode specificity is confirmed. Our work suggests that further improvement of the GLO model is needed to consider the lattice-induced barrier lowering.

Stereodynamics of Diatom Formation through Eley–Rideal Abstraction

Using adiabatic and nonadiabatic quasiclassical molecular dynamics simulations within the single adsorbate limit, we study the dependence on the incidence angle of the Eley–Rideal (ER) recombination of H2 and N2 on the (100) and (110) tungsten surfaces. In the nonadiabatic simulations, effects due to electron–hole pair excitations and the energy exchange between the recombination partners and the surface lattice are included in the dynamics by combining the local density friction approximation and the generalized Langevin oscillator model. Our adiabatic and nonadiabatic results, which are qualitatively similar, show that the incidence angle affects much more N2 recombination than H2 recombination due mainly to the higher corrugation of the potential energy surface for the former case. In particular, for N abstraction from W(110), we find a very efficient ER recombination pathway at grazing incidence angles. This new mechanism significantly influences the energy partition among the different degrees of fre...

Femtosecond-laser induced dynamics of CO on Ru(0001): Deep insights from a hot-electron friction model including surface motion

A Langevin model accounting for all six molecular degrees of freedom is applied to femtosecond-laser induced, hot-electron driven dynamics of Ru(0001)($2\ifmmode\times\else\texttimes\fi{}2$):CO. In our molecular dynamics with electronic friction approach, a recently developed potential energy surface based on gradient-corrected density functional theory accounting for van der Waals interactions is adopted. Electronic friction due to the coupling of molecular degrees of freedom to electron-hole pairs in the metal are included via a local density friction approximation, and surface phonons by a generalized Langevin oscillator model. The action of ultrashort laser pulses enters through a substrate-mediated, hot-electron mechanism via a time-dependent electronic temperature (derived from a two-temperature model), causing random forces acting on the molecule. The model is applied to laser induced lateral diffusion of CO on the surface, ``hot adsorbate'' formation, and laser induced desorption. Reaction probabilities are strongly enhanced compared to purely thermal processes, both for diffusion and desorption. Reaction yields depend in a characteristic (nonlinear) fashion on the applied laser fluence, as well as branching ratios for various reaction channels. Computed two-pulse correlation traces for desorption and other indicators suggest that aside from electron-hole pairs, phonons play a non-negligible role for laser induced dynamics in this system, acting on a surprisingly short time scale. Our simulations on precomputed potentials allow for good statistics and the treatment of long-time dynamics (300 ps), giving insight into this system which hitherto has not been reached. We find generally good agreement with experimental data where available and make predictions in addition. A recently proposed laser induced population of physisorbed precursor states could not be observed with the present low-coverage model.

Modeling surface motion effects in N2 dissociation on W(110): Ab initio molecular dynamics calculations and generalized Langevin oscillator model.

Accurately modeling surface temperature and surface motion effects is necessary to study molecule-surface reactions in which the energy dissipation to surface phonons can largely affect the observables of interest. We present here a critical comparison of two methods that allow to model such effects, namely, the ab initio molecular dynamics (AIMD) method and the generalized Langevin oscillator (GLO) model, using the dissociation of N2 on W(110) as a benchmark. AIMD is highly accurate as the surface atoms are explicitly part of the dynamics, but this advantage comes with a large computational cost. The GLO model is much more computationally convenient, but accounts for lattice motion effects in a very approximate way. Results show that, despite its simplicity, the GLO model is able to capture the physics of the system to a large extent, returning dissociation probabilities which are in better agreement with AIMD than static-surface results. Furthermore, the GLO model and the AIMD method predict very similar energy transfer to the lattice degrees of freedom in the non-reactive events, and similar dissociation dynamics.

Femtosecond-laser-driven molecular dynamics on surfaces: Photodesorption of molecular oxygen from Ag(110)

We simulate the femtosecond laser induced desorption dynamics of a diatomic molecule from a metal surface by including the effect of the electron and phonon excitations created by the laser pulse. Following previous models, the laser induced surface excitation is treated through the two temperature model, while the multidimensional dynamics of the molecule is described by a classical Langevin equation, in which the friction and random forces account for the action of the heated electrons. In this work, we propose the additional use of the generalized Langevin oscillator model to also include the effect of the energy exchange between the molecule and the heated surface lattice in the desorption dynamics. The model is applied to study the laser induced desorption of O$_2$ from the Ag(110) surface, making use of a six-dimensional potential energy surface calculated within density functional theory. Our results reveal the importance of the phonon mediated process and show that, depending on the value of the electronic density in the surroundings of the molecule adsorption site, its inclusion can significantly enhance or reduce the desorption probabilities.

Fingerprints of energy dissipation for exothermic surface chemical reactions: O2 on Pd(100).

We present first-principles calculations of the sticking coefficient of O2 at Pd(100) to assess the effect of phononic energy dissipation on this kinetic parameter. For this, we augment dynamical simulations on six-dimensional potential energy surfaces (PESs) representing the molecular degrees of freedom with various effective accounts of surface mobility. In comparison to the prevalent frozen-surface approach, energy dissipation is found to qualitatively affect the calculated sticking curves. At the level of a generalized Langevin oscillator model, we achieve good agreement with experimental data. The agreement is similarly reached for PESs based on two different semi-local density-functional theory functionals. This robustness of the simulated sticking curve does not extend to the underlying adsorption mechanism, which is predominantly directly dissociative for one functional or molecularly trapped for the other. Completely different adsorption mechanisms therewith lead to rather similar sticking curves that agree equally well with the experimental data. This highlights the danger of the prevalent practice to extract corresponding mechanistic details from simple fingerprints of measured sticking data for such exothermic surface reactions.

Dynamical reaction pathways in Eley-Rideal recombination of nitrogen from W(100)

The scattering of atomic nitrogen over a N-pre-adsorbed W(100) surface is theoretically described in the case of normal incidence off a single adsorbate. Dynamical reaction mechanisms, in particular Eley-Rideal (ER) abstraction, are scrutinized in the 0.1-3.0 eV collision energy range and the influence of temperature on reactivity is considered between 300 and 1500 K. Dynamics simulations suggest that, though non-activated reaction pathways exist, the abstraction process exhibits a significant collision energy threshold (0.5 eV). Such a feature, which has not been reported so far in the literature, is the consequence of a repulsive interaction between the impinging and the pre-adsorbed nitrogens along with a strong attraction towards the tungsten atoms. Above threshold, the cross section for ER reaction is found one order of magnitude lower than the one for hot-atoms formation. The abstraction process involves the collision of the impinging atom with the surface prior to reaction but temperature effects, when modeled via a generalized Langevin oscillator model, do not affect significantly reactivity.

Energy dissipation channels in the adsorption of N on Ag(1 1 1)

We theoretically study the competition between different energy dissipation channels in the adsorption of N atoms on Ag(111) surfaces. The three-dimensional potential energy surface that describes the interaction between the N atoms and the metal surface is built from density functional theory calculations. Classical dynamics simulations are subsequently performed to evaluate the adsorption probabilities. The contribution of electron–hole pairs excited in the surface during the adsorption process is included in the simulation by an electronic friction coefficient. Phonon excitations are also considered through the Generalized Langevin Oscillator model. We show that the role of the two channels during the adsorption dynamics is very different: phonons are responsible for determining the adsorption probability but electronic excitations are relevant at a later stage to fix the N atoms to the adsorption positions. We conclude that a theoretical model that intrinsically combines both energy dissipation channels is necessary to properly describe the full dynamics of the process.

Trapping, Molecular Adsorption, and Precursors for Nonactivated Chemisorption

Many fundamental questions are still unanswered regarding the very existence of precursor states and the microscopic mechanism of its population in the case of dissociative adsorption of light molecules on metal surfaces. We report results of classical trajectory calculations for H(2)/Pd(110) based on a six-dimensional potential energy surface obtained from ab initio calculations and a generalized Langevin oscillator model to account for energy exchange with the surface and dissipation. A quantitative characterization of the dynamic process is obtained which elucidates the respective roles played by direct dissociation, dynamic trapping, and precursor mediated adsorption. We predict the existence of H2 molecular chemisorption and provide the precise adsorption conditions for its experimental observation.