Parallel replica dynamics with a heterogeneous distribution of barriers: Application to n-hexadecane pyrolysis

Abstract

Parallel replica dynamics simulation methods appropriate for the simulation of chemical reactions in molecular systems with many conformational degrees of freedom have been developed and applied to study the microsecond-scale pyrolysis of n-hexadecane in the temperature range of 2100-2500 K. The algorithm uses a transition detection scheme that is based on molecular topology, rather than energetic basins. This algorithm allows efficient parallelization of small systems even when using more processors than particles (in contrast to more traditional parallelization algorithms), and even when there are frequent conformational transitions (in contrast to previous implementations of the parallel replica algorithm). The parallel efficiency for pyrolysis initiation reactions was over 90% on 61 processors for this 50-atom system. The parallel replica dynamics technique results in reaction probabilities that are statistically indistinguishable from those obtained from direct molecular dynamics, under conditions where both are feasible, but allows simulations at temperatures as much as 1000 K lower than direct molecular dynamics simulations. The rate of initiation displayed Arrhenius behavior over the entire temperature range, with an activation energy and frequency factor of E(a) = 79.7 kcal/mol and log A/s(-1) = 14.8, respectively, in reasonable agreement with experiment and empirical kinetic models. Several interesting unimolecular reaction mechanisms were observed in simulations of the chain propagation reactions above 2000 K, which are not included in most coarse-grained kinetic models. More studies are needed in order to determine whether these mechanisms are experimentally relevant, or specific to the potential energy surface used.

A mathematical formalization of the parallel replica dynamics

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Motivation and contextThe purpose of this article is to lay the mathematical foundations of a well known numerical approach in computational statistical physics, namely the parallel replica dynamics, introduced by A.F. Voter in [18] and improved and popularized in the context of Molecular Dynamics simulations in [19,10,17,16], for example. The aim of the approach is to efficiently generate a coarse-grained evolution (in terms of state-to-state dynamics) of a given stochastic process.

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The parallel replica dynamics method – Coming of age

“…As discussed above, ParRep is an extremely flexible simulation methodology. Since its inception in 1998, it has been used to simulate a wide range of material systems, including the diffusion of H 2 in crystalline C 60 [59], the pyrolysis of hexadecane [60], the transformation of voids into stacking fault tetrahedra in FCC metals [23], the stretching of carbon nanotubes [58], grain boundary sliding in Cu [61], friction-force microscopy [62,63], the diffusion of Li through a polymer matrix [64], the fracture process in metals [65] and the folding dynamics of small proteins [66]. The goal here is not to provide an extensive review of all of these applications but to illustrate some of the key points addressed above and provide context and inspiration to the reader wishing to use ParRep to study novel classes of materials, especially with respect to the definition of states.…”

“…While the examples above show the power of associating each energy basin with a single state, it has long been recognized that ParRep can sometimes benefit from a more general state before the formalization in terms of QSDs, this procedure was understood as being valid as long as states could be defined such that escape statistics were approximately Markovian. The generic strategy is to identify good degrees of freedom that can be used to flag the occurrence of The first example of such a generalized state definition was reported in [71], where ParRep was used to study the pyrolysis of n-hexadecane at high temperatures. Given the very low barriers associated with conformational changes in the molecules compared to the barriers for bond breaking, the traditional definition of states would have led to extremely poor performance.…”

Jump Markov models and transition state theory: the quasi-stationary distribution approach

“…In other applications, for example in biology, there may be too many local minima, not all of them being significant in terms of macroscopic states. In that case, one could think of using a few degrees of freedom (reaction coordinates) to define the states, see for example 53 . Actually, in the original work by Kramers 14 , the states are also defined using reaction coordinates, see the discussion in 16 .…”