Assessing Mixed Quantum-Classical Molecular Dynamics Methods for Nonadiabatic Dynamics of Molecules on Metal Surfaces

Abstract

Mixed quantum-classical (MQC) methods for simulating the dynamics of molecules at metal surfaces have the potential to accurately and efficiently provide mechanistic insight into reactive processes. Here, we introduce simple two-dimensional models for the scattering of diatomic molecules at metal surfaces based on recently published electronic structure data. We apply several MQC methods to investigate their ability to capture how nonadiabatic effects influence molecule−metal energy transfer during the scattering process. Specifically, we compare molecular dynamics with electronic friction, Ehrenfest dynamics, independent electron surface hopping, and the broadened classical master equation approach. In the case of independent electron surface hopping, we implement a simple decoherence correction approach and assess its impact on vibrationally inelastic scattering. Our results show that simple, low-dimensional models can be used to qualitatively capture experimentally observed vibrational energy transfer and provide insight into the relative performance of different MQC schemes. We observe that all approaches predict similar kinetic energy dependence but return different vibrational energy distributions. Finally, by varying the molecule−metal coupling, we can assess the coupling regime in which some MQC methods become unsuitable.

A Linearized Semiclassical Dynamics Study of the Multiquantum Vibrational Relaxation of NO Scattering from a Au(111) Surface

“…Nonadiabatic energy transfer from molecules to metal surfaces has been a topic of much interest in the past couple of decades, with potential applications in heterogeneous catalysis. − The breakdown of the Born–Oppenheimer approximation allows nuclear degrees of freedom, especially molecular vibrations, to couple to the continuum of electronic states of the metal. Metal–molecule scattering experiments have significantly improved our understanding of these processes while also raising several interesting questions regarding the mechanism. − In particular, experiments quantifying the vibrational relaxation of NO molecules scattering from Au(111), − and more recently Ag(111), − have provided fertile ground for theoretical study. Vibrationally hot NO molecules have been shown to lose multiple quanta of vibrational energy upon inelastic scattering from a Au(111) surface. ,,− When the gold surface is doped to decrease its work function, the loss of vibrational energy from the NO molecules can even promote the ejection of an electron from the metal surface. , These experiments demonstrate the strong coupling between NO vibrations and electron–hole pair (EHP) excitations in the metal; however, to date theoretical efforts to capture these effects have had limited success.…”

“…Novel MDEF methods with improved friction tensors and a new approach, valid for both weak and strong metal–molecule coupling limits, the broadened classical master equation (BCME), have also been developed. , In spite of these advances, simulations have not been able to predict all aspects of the experimental results. All of these methods underestimate multiquantum relaxation from NO molecules initially in a low-energy vibrational state (ν i = 3) to a final vibrational state (ν f = 1). , In addition, MDEF and IESH underestimate multiquantum relaxation for higher incident vibrational states, ν i = 11 and 16, as well. , The BCME approach has had some success in reproducing experiments for the high incident vibrational state ν i = 16 …”

“…Following the recently introduced Gardner–Habershon–Maurer (GHM) model, we work with just two nuclear coordinates to capture essential features of the problem: the NO bond length, R , and the distance between the NO center of mass and the surface, Z , assuming the molecule approaches the surface in an N-first configuration allowing no rotation. The diabatic potentials, U 0 ( X ) and U 1 ( X ), and the coupling elements, V k ( X ), are assumed to have functional form, U 0 ( R , Z ) = V normalM ( R − R 0 ; D 0 , a 0 ) + exp [ − b 0 false( Z − Z 0 false) ] + c 0 U 1 false( R , Z false) = V M false( R − R 1 ; D 1 , a 1 false) + V M false( Z − Z 1 ; D 2 , a 2 false) + c 1 …”

“…In eq , V̅ k = Γ 2 π w k , where Γ is the coupling strength, w k = normalΔ E / N , and Δ E is the bandwidth of the metal. , In the GHM model, coupling strength Γ is obtained by fitting the ground state adiabatic energy of the NAH Hamiltonian to the ground state energy obtained from reference DFT calculations, while using a wide band (Δ E = 100 eV). In this work, we refit the model, following the same procedure as in ref , to obtain the ground state energy of the NAH Hamiltonian, but with a more realistic bandwidth for gold (Δ E = 7 eV). , Upon refitting, we obtain a coupling strength Γ = 3.5 eV. More details about the refitting procedure can be found in the Supporting Information, and numerical values for all parameters in eqs – can be found in Table 1 of ref .…”

“…In this work, we refit the model, following the same procedure as in ref , to obtain the ground state energy of the NAH Hamiltonian, but with a more realistic bandwidth for gold (Δ E = 7 eV). , Upon refitting, we obtain a coupling strength Γ = 3.5 eV. More details about the refitting procedure can be found in the Supporting Information, and numerical values for all parameters in eqs – can be found in Table 1 of ref . We note that the GHM Hamiltonian employed omits several factors that are likely to affect its ability to fully describe experimental observations.…”