Generalized Langevin theory for many-body problems in chemical dynamics: General formulation and the equivalent harmonic chain representation

Abstract

A comprehensive theoretical framework for classical trajectory simulations of many-body chemical processes is presented. This framework generalizes previous theoretical methods designed to treat the many-body problems arising in gas molecule collisions off perfect harmonic solids [S. A. Adelman and J. D. Doll, J. Chem. Phys. 64, 2374 (1976); S. A. Adelman and B. J. Garrison, J. Chem. Phys. 65, 3571 (1976)]. The present version of the theory is not restricted to the harmonic systems and thus provides a formal framework for treating liquid state as well as solid state chemical phenomena. Basic to the theory is the molecular time scale generalized Langevin equation (MTGLE), a formally exact representation of the dynamics of a chemical system coupled to an arbitrary heat bath in an arbitrary manner. The MTGLE is equivalent to but distinct from the conventional [Mori–Kubo] generalized Langevin representation. It, however, is more natural for chemical dynamics simulation work because in the MTGLE the apparent vibrational frequencies of the chemical system are those which govern the molecular time scale response of the system. In the conventional Langevin representation, the apparent vibrational frequencies are those which govern the static reponse of the chemical system. The MTGLE is next rigorously transformed into an effective equation of motion for a fictitious nearest neighbor collinear harmonic chain. The parameters characterizing the chain are calculable from the velocity autocorrelation function of the chemical system. The rigorous chain representation of many-body dynamics: (i) provides a simple quasiphysical picture of energy transfer between the heat bath and chemical system during a chemical process; (ii) provides an equivalent Hamiltonian for the chemical system; (iii) permits one to construct a sequence of heat bath models whose response converges to that of the true heat bath in a rapid and systematic manner. The heat bath models are sets of collinear nearest neighbor harmonic chains composed of N=1,2,3,... fictitious atoms. Atom N in the chain is subject to time-local functional damping and is driven by a white noise stochastic force. The remaining atoms 1,2,...N-1 are undamped. The heat bath models (i) produce effective equations of motion for the chemical process which do not involve time nonlocal kernels and which may, hence, be readily solved by standard classical trajectory methods; (ii) allow one to rigorously generalize the Fokker–Planck theory of stochastic dynamics to non-Markovian systems. Finally, the treatment of selected chemical processes via the theory is briefly outlined.

Reactions of Gas-Phase Atomic Hydrogen with Chemisorbed Hydrogen on a Graphite Surface

“…34 The friction coefficient is very close to ωD/6, where ωD is the Debye frequency 420 K for graphite. 35 All values of the frequencies and friction coefficients in Eqs.…”

Dynamics of H2 Eley-Rideal abstraction from W(110): Sensitivity to the representation of the molecule-surface potential

“…ER recombination is considered to take place whenever both hydrogen atoms reach the initial altitude of the projectile with a positive H 2 center-of-mass momentum along Z, an inter-atomic distance r ≤ 2.2 Å after only one rebound of the diatom center-of-mass along the trajectory. 83,84 In order to compare our results with experimental data, 10 we have also performed QCT calculations using a generalized Langevin oscillator (GLO) model [85][86][87][88][89] to account for surface temperature effects and energy exchange with phonons. 83,84 However, we have found that adding such ingredients in the dynamics simulations barely alter the results obtained within the rigid surface approximation (at least, as far as the total ER reaction cross sections and products energy distributions are concerned).…”

Influence of the van der Waals interaction in the dissociation dynamics of N2 on W(110) from first principles

“…More likely, the role of phonons can be another factor to consider, particularly, because it might affect the indirect dissociation mechanism. In order to obtain a qualitative understanding on how the experimental surface temperature of 800 K may affect our conclusions based on the frozen surface approximation, we have used the PW91-and RPBE-CRP PESs to perform MD calculations based on the generalized Langevin oscillator model (GLO), [75][76][77] which accounts for energy exchange between the molecule and the surface lattice. Using the same GLO parameters of Ref.…”