Nonadiabatic Vibrational Damping of Molecular Adsorbates: Insights into Electronic Friction and the Role of Electronic Coherence

Abstract

We present a perturbation approach rooted in time-dependent density-functional theory to calculate electron-hole (e-h) pair excitation spectra during the nonadiabatic vibrational damping of adsorbates on metal surfaces. Our analysis for the benchmark systems CO on Cu(100) and Pt(111) elucidates the surprisingly strong influence of rather short electronic coherence times. We demonstrate how in the limit of short electronic coherence times, as implicitly assumed in prevalent quantum nuclear theories for the vibrational lifetimes as well as electronic friction, band structure effects are washed out. Our results suggest that more accurate lifetime or chemicurrentlike experimental measurements could characterize the electronic coherence. DOI: 10.1103/PhysRevLett.119.176808 The tortuous ways in which kinetic and chemical energy is transferred between adsorbates and substrate atoms fundamentally govern the dynamics of surface chemical reactions, for instance, in the context of heterogeneous catalysis or advanced deposition techniques. For metal substrates, the two main energy dissipation mechanisms in this regard are the adsorbate interaction with lattice vibrations, i.e., substrate phonons, and the excitation of electronhole (e-h) pairs. The latter are attributable to the nonadiabatic coupling of nuclear motion to the substrate electronic degrees of freedom (d.o.f.) and seem to be substantial in order to rationalize an increasing number of experimental findings [1,2]. Important steps towards an accurate, yet efficient firstprinciples-based modeling of the energy uptake into phononic d.o.f. have recently been taken [3][4][5][6][7][8][9][10]. In contrast, the explicit description of e-h pair excitations and corresponding nonadiabatic couplings directly from first principles still poses a formidable challenge.In this regard, electronic friction theory (EFT) [11,12] has become a popular workhorse to effectively capture the effects of such nonadiabatic energy loss on the adsorbate dynamics in a computationally convenient way [13][14][15][16][17][18][19]. Inspired by vibrational lifetimes obtained via response theory [20] or Fermi's golden rule in the nuclear system [21], a Langevin equation for the nuclei emerges from a semiclassical picture implying complete electronic decoherence in terms of the Markov approximation [12]. This approach thus avoids an explicit propagation of the electron dynamics and concomitant ultrafast time scales by coarse-graining the effects into electronic friction forces linear in nuclear velocities. This enables an efficient combination even with density-functional theory (DFT) based ab initio molecular dynamics (AIMD) simulations on high-dimensional potential energy surfaces as required for surface dynamical studies [15,22,23].Independent of the particular recipe employed to obtain the electronic friction coefficients [12,14,17,20,24,25], however, the downside of the coarse-graining of the electron dynamics is that it precludes a more fundamental understanding of the underlying e-h pair excit...

Adiabatic and nonadiabatic energy dissipation during scattering of vibrationally excited CO from Au(111)

“…[4-7] Such a short lifetime for a high frequency mode (ω=2129 cm -1 ) can only be explained by its nonadiabatic coupling with surface EHPs, because its direct coupling with the low-frequency phonons is unlikely. This nonadiabatic energy dissipation mechanism has been characterized by various theoretical models, [8][9][10][11][12][13][14][15][16][17][18] cumulating with the latest first-principles calculations that quantitatively reproduced the observed lifetime. [19,20] It was thus a surprise when Shirhatti et al reported a long lifetime (~10 2 ps) for trapped CO(ν=1) in the scattering of vibrationally excited CO(ν=2) from Au (111).[21] It was postulated that physisorption might be involved, given the relatively low desorption temperature of CO from Au (111).[22] Indeed, a recent density functional theory (DFT) study by Lončarić et al did find such a physisorption well for CO on Au(111),[23] using the Bayesian Error Estimation Functional method with van der Waals corrections (BEEF-vdW).[24] The lifetime of physisorbed CO(ν=1) was calculated within first-principles many-body perturbation theory and found to be consistent with the experimental value.[21] The long vibrational lifetime was attributed to the weaker couplings with EHPs because of the large distance between the adsorbate and surface.…”

Electron-Mediated Phonon-Phonon Coupling Drives the Vibrational Relaxation of CO on Cu(100)

“…The ensuing theoretical efforts aimed to comprehend these experimental observations are remarkable. In particular, the nonadiabatic relaxation of vibrationally excited adsorbates is most commonly studied either by * dino.novko@gmail.com relaxation-rate calculations based on first-order perturbation theory [15][16][17][18][19] or by performing molecular dynamics with the corresponding electronic friction [20,21]. In the former case, the intermode coupling is usually tackled by including an additional damping rate due to direct anharmonic coupling [22,23].…”

Nonadiabatic scattering of NO off Au3 clusters: A simple and robust diabatic state manifold generation method for multiconfigurational wavefunctions

“…A number of computational tools for studying nonadiabatic processes of adsorbates on metal surfaces exist in the literature. Time dependent density functional theory algorithms for evaluating electron–hole pair excitations have been successfully applied to a number of systems . Similarly, molecular dynamics with electronic friction algorithms have been applied to obtain vibrational lifetimes of adsorbates on surfaces .…”

“…Time dependent density functional theory algorithms for evaluating electron-hole pair excitations have been successfully applied to a number of systems. [18][19][20] Similarly, molecular dynamics with electronic friction algorithms [21,22] have been applied to obtain vibrational lifetimes of adsorbates on surfaces. [21][22][23] Despite the success and simplicity of the electronic friction approach, its applicability to describe the experimental results for NO scattering from noble metal surfaces obtained by Wodtke and Co. [3,24] has been questioned.…”