Molecular-orbital calculations of the lifetimes of the vibrational modes of CO on Cu(100)

Vibrationally Mode-Specific Molecular Energy Transfer to Surface Electrons in Metastable Formaldehyde Scattering from Cesium-Covered Au(111)

Nonadiabatic interaction of adsorbate nuclear motion with the continuum of electronic states is known to affect the dynamics of chemical reactions at metal surfaces. A large body of work has probed the fundamental mechanisms of such interactions for atomic and diatomic molecules at surfaces. In polyatomic molecules, the possibility of mode-specific damping of vibrational motion due to the effects of electronic friction raises the question of whether such interactions could profoundly affect the outcome of chemistry at surfaces by selectively removing energy from a particular intramolecular adsorbate mode. However, to date, there have not been any fundamental experiments demonstrating nonadiabatic electron-vibration coupling in a polyatomic molecule at a surface. In this work, we scatter excited metastable formaldehyde and formaldehyde-d2 from a low work function surface and detect ejected exoelectrons that accompany molecular relaxation. The exoelectron ejection efficiency exhibits a strong dependence on the vibrational mode that is excited: out-of-plane bending excitation (ν4) leads to significantly more exoelectrons than does CO stretching excitation (ν2). The results provide clear evidence for mode-specific energy transfer from vibration to surface electrons.

Plasmonic enhancement of molecular hydrogen dissociation on metallic magnesium nanoclusters

Light-driven plasmonic enhancement of chemical reactions on metal catalysts is a promising strategy to achieve highly selective and efficient chemical transformations. The study of plasmonic catalyst materials has traditionally focused on late transition metals such as Au, Ag, and Cu. In recent years, there has been increasing interest in the plasmonic properties of a set of earth-abundant elements such as Mg, which exhibit interesting hydrogenation chemistry with potential applications in hydrogen storage. This work explores the optical, electronic, and catalytic properties of a set of metallic Mg nanoclusters with up to 2057 atoms using time-dependent density functional tight-binding and density functional theory calculations. Our results show that Mg nanoclusters are able to produce highly energetic hot electrons with energies of up to 4 eV. By electronic structure analysis, we find that these hot electrons energetically align with electronic states of physisorbed molecular hydrogen, occupation of which by hot electrons can promote the hydrogen dissociation reaction. We also find that the reverse reaction, hydrogen evolution on metallic Mg, can potentially be promoted by hot electrons, but following a different mechanism. Thus, from a theoretical perspective, Mg nanoclusters display very promising behaviour for their use in light promoted storage and release of hydrogen.

Local decomposition of hybridization functions: Chemical insight into correlated molecular adsorbates

Hybridization functions are an established tool for investigating the coupling between a correlated subsystem (often a single transition metal atom) and its uncorrelated environment (the substrate and any ligands present). The hybridization function can provide valuable insight into why and how strong correlation features such as the Kondo effect can be chemically controlled in certain molecular adsorbates. To deepen this insight, we introduce a local decomposition of the hybridization function, based on a truncated cluster approach, enabling us to study individual effects on this function coming from specific parts of the systems (e.g., the surface, ligands, or parts of larger ligands). It is shown that a truncated-cluster approach can reproduce the Co 3d and Mn 3d hybridization functions from periodic boundary conditions in Co(CO)₄/Cu(001) and MnPc/Ag(001) qualitatively well. By locally decomposing the hybridization functions, it is demonstrated at which energies the transition metal atoms are mainly hybridized with the substrate or with the ligand. For the Kondo-active 3d_x²-y² orbital in Co(CO)₄/Cu(001), the hybridization function at the Fermi energy is substrate-dominated, so we can assign its enhancement compared with ligand-free Co to an indirect effect of ligand-substrate interactions. In MnPc/Ag(001), the same is true for the Kondo-active orbital, but for two other orbitals, there are both direct and indirect effects of the ligand, together resulting in such strong screening that their potential Kondo activity is suppressed. A local decomposition of hybridization functions could also be useful in other areas, such as analyzing the electrode self-energies in molecular junctions.

Density functional study of relaxation of adsorbate vibration modes: Dominance of anharmonic interaction

Formulation and density functional workflow for calculating the lifetime of vibrational modes of molecular adsorbates on solid surfaces due to vibration-phonon coupling are presented. The anharmonic coupling is invoked to give the correct description of the origin of temperature dependence. Using pyrrolidine (C₄H₉N) absorbed on the Cu(001) surface as a concrete example, we show that the anharmonic coupling can be one to two orders more significant than the harmonic interaction for the broadening of vibrational spectra, especially as temperature increases. These results challenge the common assumption that the anharmonic interaction is weak and call for attention of considering its effect in quantum relaxation and related problems.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

A practical ansatz for evaluating the electronic friction tensor accurately, efficiently, and in a nearly black-box format

It is well-known that under conditions of fast electronic equilibration and weak nonadiabaticity, nonadiabatic effects induced by electron-hole pair excitations can be partly incorporated through a frictional force. However, ab initio computation of the electronic friction tensor suffers from numerical instability and usually demands a convergence check. In this study, we present an efficient and accurate interpolation method for computing the electronic friction tensor in a nearly black-box manner as appropriate for molecular dynamics. In almost all cases, our method agrees quite well with the exact friction tensor which is available for several quadratic Hamiltonians. As such, we outperform more conventional approaches that are based on the introduction of a broadening parameter. Future work will implement this interpolation approach within ab initio software packages.

Adlayer structure dependent ultrafast desorption dynamics in carbon monoxide adsorbed on Pd (111)

We report our ultrafast photoinduced desorption investigation of the coverage dependence of substrate-adsorbate energy transfer in carbon monoxide adlayers on the (111) surface of palladium. As the CO coverage is increased, the adsorption site population shifts from all threefold hollows (up to 0.33 ML), to bridge and near bridge (>0.5 to 0.6 ML) and finally to mixed threefold hollow plus top site (at saturation at 0.75 ML). We show that between 0.24 and 0.75 ML this progression of binding site motifs is accompanied by two remarkable features in the ultrafast photoinduced desorption of the adsorbates: (i) the desorption probability increases roughly two orders magnitude, and (ii) the adsorbate-substrate energy transfer rate observed in two-pulse correlation experiments varies nonmonotonically, having a minimum at intermediate coverages. Simulations using a phenomenological model to describe the adsorbate-substrate energy transfer in terms of frictional coupling indicate that these features are consistent with an adsorption-site dependent electron-mediated energy coupling strength, ηel, that decreases with binding site in the order: three-fold hollow > bridge and near bridge > top site. This weakening of ηel largely counterbalances the decrease in the desorption activation energy that accompanies this progression of adsorption site motifs, moderating what would otherwise be a rise of several orders of magnitude in the desorption probability. Within this framework, the observed energy transfer rate enhancement at saturation coverage is due to interadsorbate energy transfer from the copopulation of molecules bound in three-fold hollows to their top-site neighbors.

Mixed Quantum-Classical Dynamics Using Collective Electronic Variables: A Better Alternative to Electronic Friction Theories

An accurate description of nonadiabatic dynamics of molecular species on metallic surfaces poses a serious computational challenge associated with a multitude of closely spaced electronic states. We propose a mixed quantum-classical scheme that addresses this challenge by introducing collective electronic variables. These variables are defined through analytic block-diagonalization applied to the time-dependent Hamiltonian matrix governing the electronic dynamics. We compare our scheme with a simplified Ehrenfest approach and with a full-memory electronic friction model on a 1D "adatom + atomic chain" model. Our simulations demonstrate that collective-mode dynamics with only a few (two to three) electronic variables is robust and can describe a variety of situations: from a chemisorbed atom on an insulator to an atom on a metallic surface. Our molecular model also reveals that the friction approach is prone to unpredictable and catastrophic failures.

Role of Tensorial Electronic Friction in Energy Transfer at Metal Surfaces

An accurate description of nonadiabatic energy relaxation is crucial for modeling atomistic dynamics at metal surfaces. Interfacial energy transfer due to electron-hole pair excitations coupled to motion of molecular adsorbates is often simulated by Langevin molecular dynamics with electronic friction. Here, we present calculations of the full electronic friction tensor by using first order time-dependent perturbation theory at the density functional theory level. We show that the friction tensor is generally anisotropic and nondiagonal, as found for hydrogen atom on Pd(100) and CO on Cu(100) surfaces. This implies that electron-hole pair induced nonadiabatic coupling at metal surfaces leads to friction-induced mode coupling, therefore, opening an additional channel for energy redistribution. We demonstrate the robustness and accuracy of our results by direct comparison to established methods and experimental data.

Perspectives on external electric fields in molecular simulation: progress, prospects and challenges

In this review, the application of a wide variety of external electric fields in molecular simulation shall be discussed, including time-varying and electromagnetic, as well as the utility and potential impact and prospects for exploitation of such simulations for real-world and industrial end use. In particular, non-equilibrium molecular dynamics will be discussed, as well as challenges in addressing adequate thermostatting and scaling field amplitudes to more experimentally relevant levels. Attention shall be devoted to recent progress and advances in external fields in ab initio molecular simulation and dynamics, as well as elusive challenges thereof (and, to some extent, for molecular dynamics from empirical potentials), such as timescales required to observe low-frequency and intensity field effects. The challenge of deterministic molecular dynamics in external fields in sampling phase space shall be discussed, along with prospects for application of fields in enhanced-sampling simulations. Finally, the application of external electric fields to a wide variety of aqueous, nanoscale and biological systems will be discussed, often motivated by the possibility of exploitation in real-world applications, which serve to underpin our molecular-level understanding of field effects in terms of microscopic mechanisms, and possibly with a view to control thereof.

Electronically non-adiabatic influences in surface chemistry and dynamics

Electronically nonadiabatic interactions between molecules and metal surfaces are now well known. But evidence that such interactions influence reaction rates is still scarce. This paper reviews research related to this topic and proposes pathways forward.

Applications of time-domain spectroscopy to electron-phonon coupling dynamics at surfaces

Photochemistry is one of the most important branches in chemistry to promote and control chemical reactions. In particular, there has been growing interest in photoinduced processes at solid surfaces and interfaces with liquids such as water for developing efficient solar energy conversion. For example, photoinduced charge transfer between adsorbates and semiconductor substrates at the surfaces of metal oxides induced by photogenerated holes and electrons is a core process in photovoltaics and photocatalysis. In these photoinduced processes, electron-phonon coupling plays a central role. This paper describes how time-domain spectroscopy is applied to elucidate electron-phonon coupling dynamics at metal and semiconductor surfaces. Because nuclear dynamics induced by electronic excitation through electron-phonon coupling take place in the femtosecond time domain, the pump-and-probe method with ultrashort pulses used in time-domain spectroscopy is a natural choice for elucidating the electron-phonon coupling at metal and semiconductor surfaces. Starting with a phenomenological theory of coherent phonons generated by impulsive electronic excitation, this paper describes a couple of illustrative examples of the applications of linear and nonlinear time-domain spectroscopy to a simple adsorption system, alkali metal on Cu(111), and more complex photocatalyst systems.

Selective ultrafast probing of transient hot chemisorbed and precursor states of CO on Ru(0001)

We have studied the femtosecond dynamics following optical laser excitation of CO adsorbed on a Ru surface by monitoring changes in the occupied and unoccupied electronic structure using ultrafast soft x-ray absorption and emission. We recently reported [M. Dell'Angela et al. Science 339, 1302 (2013)] a phonon-mediated transition into a weakly adsorbed precursor state occurring on a time scale of >2 ps prior to desorption. Here we focus on processes within the first picosecond after laser excitation and show that the metal-adsorbate coordination is initially increased due to hot-electron-driven vibrational excitations. This process is faster than, but occurs in parallel with, the transition into the precursor state. With resonant x-ray emission spectroscopy, we probe each of these states selectively and determine the respective transient populations depending on optical laser fluence. Ab initio molecular dynamics simulations of CO adsorbed on Ru(0001) were performed at 1500 and 3000 K providing insight into the desorption process.

Quantum corrected Langevin dynamics for adsorbates on metal surfaces interacting with hot electrons

We investigate the importance of including quantized initial conditions in Langevin dynamics for adsorbates interacting with a thermal reservoir of electrons. For quadratic potentials the time evolution is exactly described by a classical Langevin equation and it is shown how to rigorously obtain quantum mechanical probabilities from the classical phase space distributions resulting from the dynamics. At short time scales, classical and quasiclassical initial conditions lead to wrong results and only correctly quantized initial conditions give a close agreement with an inherently quantum mechanical master equation approach. With CO on Cu(100) as an example, we demonstrate the effect for a system with ab initio frictional tensor and potential energy surfaces and show that quantizing the initial conditions can have a large impact on both the desorption probability and the distribution of molecular vibrational states.

Two-dimensional infrared surface spectroscopy for CO on Cu(100): Detection of intermolecular coupling of adsorbates

Surface-specific infrared signals obtained by subjecting the system to two infrared laser pulses are calculated for an admixture of CO and isotopic CO on Cu(100) by using molecular dynamics simulation based on a stability matrix formalism. The two-dimensional profiles of the signals in the frequency domain show both diagonal and cross peaks. The former peaks mainly arise from the overtones of the CO and isotopic CO, while the latter represent the couplings between those. As temperature is increased, the phases of cross peaks in a second-order infrared response function change significantly, while those of diagonal peaks are unchanged. The authors show that the phase shifts are originated from the potential anharmonicities due to the electronic interaction between adsorbates. Using a model with two dipole moments, they find that the frustrated rotational mode activated with temperature has effects on the anharmonicity. These results indicate that two-dimensional infrared surface spectroscopy reveals the anharmonic couplings between adsorbates and surface atoms or between adsorbates which cannot be observed in first-order spectroscopy.

Vibrational lifetimes of molecular adsorbates on metal surfaces

We report density functional theory calculations of electron-hole pair induced vibrational lifetimes of diatomic molecules adsorbed on metal surfaces. For CO on Cu(100), Ni(100), Ni(111), Pt(100), and Pt(111), we find that the C-O internal stretch and the bending modes have lifetimes in the 1-6 ps range, and that the CO-surface stretch and the frustrated translational modes relax more slowly, with lifetimes >10 ps for all cases except CO on Ni(111). This strong mode selectivity confirms earlier calculations for CO on Cu(100) and demonstrates that the trends carry over to other metal substrates. In contrast, for NO adsorbed on Pt(111), whereas we still find that the bending mode has the shortest lifetime, about 1.3 ps, we predict the other three modes to have almost equal lifetimes of 8-10 ps. Similarly, for CN adsorbed on Pt(111), we calculate that the internal stretching and molecule-surface stretching modes have approximately equal lifetimes of about 15 ps. Our results are in reasonable agreement with experiment, where available. We discuss some of the underlying factors that may contribute to the observed mode selectivity with adsorbed CO and the altered selectivity with NO and CN.

Quantum equations for vibrational dynamics on metal surfaces

A first principles treatment of the vibrational dynamics of molecular chemisorbates on metal surfaces is presented. It is shown that the mean field quantum evolution of the vibrational position operator is determined by a quantum Langevin equation with an electronic friction. In the mean field limit, the quantum noise and friction are related by the quantum fluctuation-dissipation theorem. The classical limit of this model is shown to agree with previously proposed models. A criterion is presented to describe the validity of the weak-coupling approximation and equations of motion for the dynamics in the presence of strong nonadiabatic coupling to electron-hole pairs are presented.

Femtosecond laser induced associative desorption of H2 from Ru(0001): Comparison of “first principles” theory with experiment

A three dimensional model based on molecular dynamics with electronic frictions is developed to describe the femtosecond laser induced associative desorption of H2 from Ru(0001)(1 x 1)H. Two molecular coordinates (internuclear separation d and center of mass distance to surface z) and a single phonon coordinate are included in the dynamics. Both the potential energy surface and the electronic friction tensor are calculated by density functional theory so that there are no adjustable parameters in the comparison of this model with the wide range of experiments available for this system. This "first principles" dynamic model gives results in semiquantitative agreement with all experimental results; nonlinear fluence dependence of the yield, isotope effect, two pulse correlation, and energy partitioning. The good agreement of theory with experiment supports a description of this surface femtochemistry in terms of thermalized hot electron induced chemistry with coupling to nuclear coordinates through electronic frictions. By comparing the dynamics with the analytical one dimensional frictional model used previously to fit the experiments for this system, we show that the success of the one dimensional model is based on the rapid intermixing of the z and d coordinates as the H-H climbs out of the adsorption well. However, projecting the three dimensional dynamics onto one dimension introduces a fluence (adsorbate temperature) dependent "entropic" barrier in addition to the potential barrier for the chemistry. This implies that some caution must be used in interpreting activation energies obtained in fitting experiments to the one dimensional model.

Optimal control in a dissipative system: Vibrational excitation of CO∕Cu(100) by IR pulses

The question as to whether state-selective population of molecular vibrational levels by shaped infrared laser pulses is possible in a condensed phase environment is of central importance for such diverse fields as time-resolved spectroscopy, quantum computing, or "vibrationally mediated chemistry." This question is addressed here for a model system, representing carbon monoxide adsorbed on a Cu(100) surface. Three of the six vibrational modes are considered explicitly, namely, the CO stretch vibration, the CO-surface vibration, and a frustrated translation. Optimized infrared pulses for state-selective excitation of "bright" and "dark" vibrational levels are designed by optimal control theory in the framework of a Markovian open-system density matrix approach, with energy flow to substrate electrons and phonons, phase relaxation, and finite temperature accounted for. The pulses are analyzed by their Husimi "quasiprobability" distribution in time-energy space.

How adiabatic is activated adsorption/associative desorption?

Using density-functional theory we calculate friction coefficients describing the damping of nuclear motion into electron-hole pair excitation for the two best-known examples of activated adsorption: H2 dissociation on a Cu(111) surface and N2 dissociation on a Ru(0001) surface. In both cases, the frictions increase dramatically along the reaction path towards the transition state and can be an order of magnitude larger there than typical in the molecularly adsorbed state. In addition, the frictions for N2/Ru(0001) are typically an order of magnitude larger than for H2/Cu(111). We rationalize these trends in terms of the electron structure as the systems proceed to dissociation along the reaction paths. Combining these friction coefficients with the potential-energy surface in quasiclassical dynamics allows first-principles studies of the importance of the breakdown in the Born-Oppenheimer approximation in describing the chemistry. We find that nonadiabatic effects are minimal for the H2/Cu(111) system, but are quite important for N2/Ru(0001).

Structures of HCN-Mgn (n=2–6) complexes from rotationally resolved vibrational spectroscopy andab initiotheory

High-resolution infrared laser spectroscopy has been used to determine the structures of HCN-Mgn complexes formed in helium nanodroplets. The magnesium atoms are first added to the droplets to ensure that the magnesium complexes are preformed before the HCN molecule is added. The vibrational frequencies, structures, and dipole moments of these complexes are found to vary dramatically with cluster size, illustrating the nonadditive nature of the HCN-magnesium interactions. All of the complexes discussed here have the nitrogen end of the HCN pointing towards the magnesium clusters. For Mg3, the HCN binds to the "threefold" site, yielding a symmetric top spectrum. Although the HCN-Mg4 complex also has C3v symmetry, the HCN sits "on-top" of a single magnesium atom. These structures are confirmed by both ab initio calculations and measurements of the dipole moments. Significant charge transfer is observed in the case of HCN-Mg4, indicative of charge donation from the lone pair on the nitrogen of HCN into the lowest unoccupied molecular orbital of the Mg4.

Real-Space Observation of Molecular Motion Induced by Femtosecond Laser Pulses

Femtosecond laser irradiation is used to excite adsorbed CO molecules on a Cu110 surface; the ensuing motion of individual molecules across the surface is characterized on a site-to-site basis by in situ scanning tunneling microscopy. Adsorbate motion both along and perpendicular to the rows of the Cu110 surface occurs readily, in marked contrast to the behavior seen for equilibrium diffusion processes. The experimental findings for the probability and direction of the molecular motion can be understood as a manifestation of strong coupling between the adsorbates' lateral degrees of freedom and the substrate electronic excitation produced by the femtosecond laser radiation.

Energy loss of atoms at metal surfaces due to electron-hole pair excitations: first-principles theory of "chemicurrents"

A method is presented for calculating electron-hole pair excitation due to an incident atom or molecule interacting with a metal surface. Energy loss is described using an ab initio approach that obtains a position-dependent friction coefficient for an adsorbate moving near a metal surface from a total energy pseudopotential calculation. A semiclassical forced oscillator model is constructed to describe excitation of the electron gas due to the incident molecule. This approach is applied to H and D atoms incident on a Cu(111) surface, and we obtain theoretical estimates of the "chemicurrents" measured by Nienhaus et al. [Phys. Rev. Lett. 82, 446 (1999)] for these atoms incident on the surface of a Schottky diode.

Chemical dynamics at metal surfaces

Theoretical aspects of dynamical processes at metal surfaces are reviewed. Experimental challenges to theory are presented and progress toward meeting these challenges is appraised. Topics include adsorbate vibrational energy flow, inelastic molecule-surface scattering, adsorption, transient mobility, dissociation, desorption, photochemistry, and electron-induced chemistry at metal surfaces. Experimental examples cited illustrate the richness of dynamical phenomena to be understood and the necessity of developing multidimensional, beyond Born-Oppenheimer, formulations of adsorbate dynamics. Classical mechanical and quantum mechanical treatments of dynamics are contrasted. The importance of including phonon and electron-hole pair dissipation in theories of adsorbate dynamics is emphasized, and strategies for doing this in classical and quantum treatments are presented.