Testing Electronic Friction Models: Vibrational De-excitation in Scattering of H₂ and D₂ from Cu(111)

Abstract

At present, molecular dynamics with electronic friction (MDEF) is the workhorse model to go beyond the Born–Oppenheimer approximation in modeling dynamics of molecules at metal surfaces. Concomitant friction coefficients can be calculated with either the local density friction approximation (LDFA) or orbital-dependent friction (ODF), which, unlike LDFA, accounts for anisotropy while relying on other approximations. Due to the computational cost of ODF, extensive high-dimensional MDEF trajectory calculations of experimentally measurable observables have hitherto only been performed based on LDFA. We overcome this limitation with a continuous neural-network-based representation. In our first application to the scattering of vibrationally excited H2 and D2 from Cu(111), we predict up to three times higher vibrational de-excitation probabilities with ODF than with LDFA. These results indicate that anisotropic electronic friction can be important for specific molecular observables. Future experiments can test for this “fingerprint” of different approximations underlying state-of-the-art MDEF.

Symmetry-Adapted High Dimensional Neural Network Representation of Electronic Friction Tensor of Adsorbates on Metals

“…Finally, we present some preliminary results to support that the symmetry-adapted 20 EANN representation also works for non-frozen surface. To this end, we allow one top Ag atom to move vertically, violating the presupposed surface symmetry of a rigid Ag(111) surface that would cause problems in the previous two different methods 52,54 .…”

“…18,[42][43] Despite these successes, LDFA has been continuously questioned in describing non-adiabatic interactions between molecules and metal surfaces, because the atomic friction coefficients intrinsically lack the directional dependence and molecular anisotropy that arises from the electron-nuclear coupling of a many-electron system described in a realistic potential. 35,[44][45][46][47][48] In principle, the full-rank EFT can be obtained by the first-order time-dependent perturbation theory (TDPT) based on KS orbitals of DFT that fully accounts for the electronic structure of molecule-surface system. 21 Very recently, Meyer et al [52][53] and we [54][55] have independently discussed the influence of mode specific electronic frictions on dissociative sticking and state-to-state scattering probabilities of N2 and H2 on metal surfaces, both using a neural network (NN) representation but with different approaches to describe the symmetry properties of EFT.…”

“…35,[44][45][46][47][48] In principle, the full-rank EFT can be obtained by the first-order time-dependent perturbation theory (TDPT) based on KS orbitals of DFT that fully accounts for the electronic structure of molecule-surface system. 21 Very recently, Meyer et al [52][53] and we [54][55] have independently discussed the influence of mode specific electronic frictions on dissociative sticking and state-to-state scattering probabilities of N2 and H2 on metal surfaces, both using a neural network (NN) representation but with different approaches to describe the symmetry properties of EFT. Meyer and coworkers started from a reduced-dimensional NN representation of EFT with a fixed reference molecular orientation, followed by the multiplication with an approximate rotation matrix to obtain the six-dimensional EFT.…”

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

“…[39] Finally, LDFA might not be sufficiently accurate, as suggested by the alternative first-principles friction coefficients. [14,40,41] A remaining puzzle is the CO(ν=1) product observed in the experiment, which has a fast and slow components. [21] As discussed above, our adiabatic simulations produce little vibrational relaxation and the only possible mechanism is due to EHPs.…”

An improved static corrugation model

“…For the dissociative chemisorption probabilities of H 2 and D 2 on Cu(111), it is known that the BOA performs well. 17,18 One way to determine the overall accuracy of the electronic structure is to calculate the probability of H 2 reacting on the Cu(111) surface at specific translational and rovibrational energies and compare the result with experiments. DFT can be used together with the specific reaction parameter (SRP) method to compute a chemically accurate PES for the H 2 on the Cu(111) system.…”