When Classical Trajectories Get to Quantum Accuracy: The Scattering of H₂on Pd(111)

Abstract

When elementary reactive processes occur at so low energies that only few states of reactants and/or products are available, quantum effects strongly manifest and the standard description of the dynamics within the classical framework fails. We show here, for H 2 scattering on Pd(111), that by pseudo-quantizing in Bohr's spirit the relevant final actions of the system, along with adequately treating the diffractionmediated-trapping of the incoming wave, classical simulations get to an unprecedented and spectacular agreement with state-of-the-art quantum dynamics calculations.

When classical trajectories get to quantum accuracy: II. The scattering of rotationally excited H2 on Pd(111)

“…We briefly summarize here the approach described in detail in Part I. 37 For nonreactive trajectories, the four final actions of the system are the vibrational action x f , the rotational action J f and the diffractional actions (a n f , a m f ). These are given by:…”

“…For simplicity's sake, we assume that the redistribution is democratic, so one may ignore adiabatic paths and renormalize to unity the probability carried by the remaining trajectories. [35][36][37] Moreover, Eq. ( 19) suggests that type-PA paths should be assigned thin Gaussian weights G(J f − j f ) = exp[−(J f − j f ) 2 /ε 2 ]/( √ πε) in order to mimic the delta function (see Eq.…”

“…Now, if all the dimensions of the process are taken into account, the weights for type-PA paths will depend on the final diffractional actions a n f and a m f in addition to J f whereas the weights for type-NA paths will depend on all the final actions, as in our previous calculations (see Part I). 37 For type-PA trajectories, we chose the product…”

“…This correction is supported by the semiclassical initial value representation (SCIVR) of molecular collisions. 35,36 In a recent work, 37 called Part I in the following, the 1GB-AC-QCT approach was applied to the gas-surface reaction H 2 + Pd(111), with H 2 in its rovibrational ground state, and nearly quantitative agreement was found with exact time-dependent quantum scattering calculations. The goal of the present work, called Part II further on, is to check whether this agreement is maintained when H 2 is rotationally excited.…”

“…For more than 2 or 3 quantized degrees-offreedom (DOFs) of the final fragments, however, GB lacks precision when applied as such to a quantum state having an energy close to the total energy available. 37 In such a case, a more accurate variant of GB consists in Gaussian weighting the energy deposited on the final quantized DOFs, rather than the actions. 33 Since only one Gaussian weight is involved in this procedure, it is usually called 1GB.…”