Reactive Molecular Dynamics of the Thermal Decomposition of CF3OCF3
Bangwu Jiang, David J. Keffer, and Brian J. Edwards
Department of Chemical Engineering
University of Tennessee
Knoxville , TN 37996-2200 Abstract
In this work, we examine the feasibility of using conventional, well-tested, non-reactive interaction potentials for molecular dynamics of reactive systems undergoing chemical reaction. Our test system is the thermal decomposition of CF3OCF3, which is relevant as a simple molecule containing the necessary architectural elements to study chemical stability of perfluoropolyether lubricants. The reactivity of the Reactive Molecular Dynamics (RMD) procedure is implemented through the simulation algorithm, rather than through the potential. The molecular-level simulation algorithm must incorporate elements from both the quantum scale and the macroscopic scale.
Macroscopic Model: At the macroscopic scale, a chemical reaction that occurs via an elementary mechanism is completely defined by four specifications. The first specification is the stoichiometry of the chemical reaction. For the thermal decomposition of CF3OCF3, the stoichiometry is
(1)
Since this is an elementary reaction, we can write an expression for the macroscopic rate of reaction as
(2)
where k is a rate constant, and the square bracket represents concentrations. The rate constant can be expressed as
(3)
where ko is a prefactor that represents the frequency at which the reaction is attempted, Ea is the activation energy of the prefactor, kB is Boltzmann's constant, and T is absolute temperature. The reaction rate prefactor and the activation energy are the second and third specifications that must be made to uniquely describe the reaction at the macroscopic level. The fourth and final specification required is the heat of reaction, , which indicates the amount of heat generated or consumed by the reaction.
Quantum Mechanical Input: Quantum mechanical calculations provide information on the same four specifications, as required by the macroscopic model: stoichiometry, ko, Ea, and . The thermal decomposition of CF3OCF3 was investigated by Pancansky et. al1. through quantum mechanics, in which they reported the three static properties: stoichiometry, Ea. and
. We have repeated these calculations and additionally have calculated the rate constant, ko, via transition state theory, using a combination of quantum mechanics and statistical mechanics.
Molecular Simulation Reaction Algorithm: We perform classical equilibrium molecular dynamics simulations in the canonical ensemble with a non-reactive potential. For the sake of this demonstration, we use the Universal Force Field2. The reactive algorithm has three steps. The first step is the reaction trigger, in which we check each CF3OCF3 molecule to determine if it is sufficiently near the transition state (both geometrically and energetically) to trigger a reaction. The determination of this state is based upon a mapping of the quantum mechanical transition state to a set of reaction geometric and energetic triggers. The geometric triggers ensure that the CF3OCF3 molecule is near the proper configuration, as determined through quantum mechanical calculations. There is an additional energetic trigger to determine if the relevant atoms have sufficient kinetic energy to overcome the known activation barrier. Each of these triggers has a numerical limit associated with it. The geometrical triggers are based upon quantum mechanical configurations. The energetic limit is tied to the known activation energy (from either quantum or experimental sources).
The second step of the reactive algorithm is the instantaneous reaction. Here we coarse-grain out the quantum mechanical details of the intermediate state of the molecule during chemical reaction. We replace the reactants (CF3OCF3) with the two product molecules (CF4 and CF2O), attempting to disturb the local structure as little as possible. The third and final step of this procedure is local equilibration, which is performed to satisfy exactly the target , which in turn ensures that, regardless of the reaction path taken, the final destination is correct. Once all three steps of the reactive algorithm are complete, we continue the classical simulation using the non-reactive potential.
Algorithm Validation: Using this procedure, we can match all four elements that uniquely define a macroscopic description of the reaction: the stoichiometry, ko, Ea, and . The matching of the stoichiometry is mandated through the reaction trigger. The matching of the heat of reaction is mandated through the local equilibration following reaction. The matching of ko and Ea are accomplished as follows. During an MD simulation, we monitor the rate of reaction. If we perform a suite of reactions varying only temperature, then we can generate an Arrhenius plot, which yields the ko and Ea. We adjust the numerical values of the limits on the geometrical triggers to control ko. We then adjust the numerical values of the limit on the energetic trigger to control Ea. The fitting of these parameters can be tuned to either quantum mechanical calculations or experimental measurements of ko and Ea.
Algorithm Advantages: The RMD algorithm used here has several advantageous features. It is generalizable and has been used to model both the structural diffusion of protons and the thermal decomposition of perfluorinated ethers. The RMD algorithm has easy implementation because it fits in existing MD codes and is a computationally efficient multiscale scheme. The RMD algorithm can be quickly developed because it uses existing non-reactive interaction potentials and because most triggers are already known from TS without fitting. The RMD algorithm is rigorous, satisfying quantum mechanical transition state criteria and satisfying macroscopic models of reaction, with equal emphasis. The RMD algorithm is intrinsic adaptable; it can be applied to dilute or dense systems at high or low temperatures without reparameterization, because the triggers automatically capture the local environmental (in this case, density and temperature) dependence.
Acknowledgements:
This work has been supported by Air Force Office of Scientific Research through contract # FA 9550-05-1-0342. The authors wish to acknowledge resources of the Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the DOE under Contract DE-AC05-00OR22725.
References:
(1) Pacansky, J.; Waltman, R. J. Journal of Fluorine Chem. 1997, 82, 79.
(2) Rappe, A. K.; Casevit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024.
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