Pressure-dependent reactions are ubiquitous in applications of gas-phase chemical kinetics to practical problems, such as combustion (<100 bar), atmospheric chemistry (≤1 bar), and chemical vapor deposition (<<1 bar). These reactions can take various forms involving chemical or thermal activation, single or multiple unimolecular potential wells, and single or multiple sets of bimolecular products. Such reactions are enormously complicated problems to treat theoretically, even for a single-channel, single-well dissociation, which is the case we focus on here. The accurate first-principles prediction of pressure-dependent rate coefficients would dramatically improve the utility of theoretical kinetics as a tool for global chemical modeling.

—Jasper et al.

Combustion scientists have worked for years to better understand the thousands of chemical reactions that take place during the combustion process, said Sandia’s Ahren Jasper, the study’s lead author. As scientists determine and understand the speeds and outcomes of more and more of these reactions, he said, they can use models to more fully characterize what’s occurring inside an engine, and thus better predict combustion efficiency and the emissions formed during combustion.

A more detailed, fundamental understanding of the chemistry of combustion, in turn, may lead to cleaner and more efficient strategies in automotive vehicle and fuel design.

Argonne chemist Stephen Klippenstein, a corresponding author of the study, said this method should aid development of global models for all gas phase chemical environments, including the Earth’s atmosphere. Better models will improve understanding of climate change and boost efforts to address it.

Many of the key steps underlying gas-phase combustion involve elementary chemical reactions that are strongly pressure-dependent, and researchers who develop combustion models require detailed descriptions of these reactions.

While significant progress has been made over the years in understanding combustion chemistry, the outcome and rates of pressure-dependent chemical reactions—those that depend on the pressure of the gas in the engine—have been very difficult to predict. These reactions depend on the pressure because the redistribution of energy and angular momentum that occurs when the reacting molecules collide with other gas molecules changes the speed and outcome of the reactions.

Previous qualitative research focused on how various molecular properties influence energy transfer rates, but no accurate method could make a priori predictions of the rate constants, that is, predictions based on theoretical deduction, not observation.

We’ve desperately needed the ability to compute and calculate precisely how chemical reactions depend on temperature and pressure, and now we have that.

—Ahren Jasper

The team focused on modeling the collisions of molecules in atomistic detail and characterizing the transfer of energy and angular momentum that takes place as a result of those collisions. Using more accurate models for describing the interaction of the colliding species and focusing on only those aspects of energy transfer that are most relevant in determining the reaction rate allowed the researchers to develop a detailed description of collision outcomes.

Energy lost means products gained. As a methyl radical CH3 and a proton H approach, the potential energy of interaction decreases as the C-H bond is formed. The newly formed, highly excited methane, CH4*, will dissociate back to the reactants unless some energy is lost in collisions with a third body, M. In modeling the overall reaction and calculating the pressure- and temperature-dependent rate constant for formation of CH4 from CH3 + H, Jasper et al. determined quantitatively how the energy and the angular momentum of CH4 are changed in collisions with M. Source: Pilling (2014). Click to enlarge.

Jasper and his colleagues then were able to obtain that collision outcome information using direct “classical trajectories” that explicitly describe the motion of the atoms in the molecules, and to use this information in calculating chemical reaction rates.

A key step, Jasper said, was the development of a model for the collisional energy and angular momentum transfer function that reproduced detailed features predicted by the trajectories and was simple enough to be used in practical reaction rate calculations.

Finding a way to accurately compute and represent the energy and angular momentum transfer from these vibrationally-excited molecules proved to be the final piece needed to solve the problem.

—Ahren Jasper

The overall theoretical model is rather complex, involving many separate unrelated calculations, and it is remarkable how accurately one can now treat all aspects of the problem in developing such completely a priori predictions.

—Stephen Klippenstein

The study was also co-authored by Klippenstein and Larry Harding, both distinguished fellows at Argonne, and the influential combustion modeler Jim Miller, a former Sandia staff member now at Argonne. The work continues the team’s longstanding development of master equation and elementary reaction rate theories.

The work was supported by the Department of Energy’s Office of Science.

Commenting on the work in his Perspective, Pilling observed that:

This [the accord between Jasper et al.’s findings and experimental data] is a substantial achievement, in that no fitting of the calculations to experiment was used—the calculations were entirely ab initio, and their work provides a means of accurately predicting rate parameters for pressure-dependent reactions.

There is still some way to go before predictions can be routinely made for all pressure-dependent reactions. Some such reactions involve multiple potential energy wells as the initial adduct isomerizes by intramolecular atom transfer. Dissociation from the isomers to several products is often possible, and the rate constants for the different product channels depend in different ways on the total energy and angular momentum. Such reactions are central components of, for example, models to increase the efficiency of automotive engines. The extension of the methodology described by Jasper et al. to such reactions places considerable demands on the quantitative description of the E- and J-dependent energy transfer processes and on the master equation modeling. Although extension to such reactions is challenging, their work shows that it is achievable.

—Pilling (2014)

Resources

• Ahren W. Jasper, Kenley M. Pelzer, James A. Miller, Eugene Kamarchik, Lawrence B. Harding, and Stephen J. Klippenstein (2014) “Predictive a priori pressure-dependent kinetics” Science 346 (6214), 1212-1215 doi: 10.1126/science.1260856

• Michael J Pilling (2014) “Calculating the pressure dependence of chemical reactions” Science 346 (6214), 1183-1184. doi: 10.1126/science.aaa1257