On the breakdown of the Ehrenfest method for molecular dynamics on surfaces

Abstract

Due to a continuum of electronic states present in periodic systems, the description of molecular dynamics on surfaces poses a serious computational challenge. One of the most used families of approaches in these settings are friction theories, which are based on the Ehrenfest (EH) approach. Yet, a mean-field treatment of electronic degrees of freedom in the EH method makes this approach inaccurate in some cases. Our aim is to clarify when EH breaks down for molecular dynamics on surfaces. Answering this question provides limits of applicability for more approximate friction theories derived from EH. We assess the EH method on one-dimensional, numerically exactly solvable models with a large but finite number of electronic states. Using the Landau-Zener formula and the Massey parameter, an expression that determines when EH breaks down is deduced. arXiv:1809.03829v1 [physics.chem-ph]

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

“…Often, it is difficult to know if the simulations are correctly describing reality as accurate reference results are rare. Progress has been made in this area from two directions, namely, verifying methods against quantum dynamics for simple analytical model Hamiltonians ,,, and comparing the outcomes of high-dimensional simulations, often based on first-principles electronic structure theory, to experimental observations. ,,− Both approaches have limitations. The former approach may unduly simplify the electronic structure and the influence of many coupled, anharmonic degrees of freedom.…”

Direct matter disassembly via electron beam control: electron-beam-mediated catalytic etching of graphene by nanoparticles

“…40 Affordable mean-field mixed quantum-classical simulation methods all fail categorically for metals decorated with small chemisorbed molecules. 41 For the present case, an explicit treatment of the correlated electronic and vibrational dynamics is required. Mixed quantum-classical methods that capture these correlations have been combined with simplified treatments of the excited-state electronic structure of a metal to simulate the electronic excitations induced by scattering of incident gasphase molecules from a metal surface, 42 but methods capable of simultaneously treating the dynamic electronic and vibrational correlations and the "strong" (static) electronic correlation that emerges as covalent bonds are broken, have yet to be put forth.…”

“…Since these reactions do not proceed adiabatically in a single electronic state, potential energy barriers calculated for the elementary reaction steps and molecular dynamics simulations couched in the Born-Oppenheimer approximation are insufficient to capture the reaction kinetics. Affordable mean-field mixed quantum-classical simulation methods also fail categorically to capture the evolution of metal surfaces decorated with small chemisorbed molecules [42]. Instead, an explicit treatment of the correlated electronic and vibrational dynamics is required.…”

High-order geometric integrators for representation-free Ehrenfest dynamics

“…Since S −1 = S and, by definition, any flow is symmetric (i.e., Φ −t = Φ −1 t ), 52,53 the satisfaction of Eq. ( 32) implies the satisfaction of the time reversibility condition (31).…”

“…Mixed quantum-classical methods, such as the surface hopping, [1][2][3][4][5] mean-field Ehrenfest dynamics, [6][7][8][9][10][11][12][13][14][15] and methods based on the mixed quantum-classical Liouville equation [16][17][18] or the Meyer-Miller-Stock-Thoss mapping Hamiltonian, [19][20][21][22][23][24][25][26] remedy one of the shortcomings of classical molecular dynamics: its inability to describe electronically nonadiabatic processes involving significantly coupled [27][28][29] states. Although a severe approximation to the exact quantum solution, 8,30,31 Ehrenfest dynamics can provide a useful first picture of nonadiabatic dynamics in some, especially strongly coupled systems. Indeed, Ehrenfest dynamics was successfully used to describe electron transfer, [32][33][34][35][36] nonadiabatic processes at metal surfaces, [37][38][39][40] and photochemical processes.…”