A proper representation of chemical kinetics is vital to understanding, modeling, and optimizing many important chemical processes. In liquid and surface phases, where diffusion is slow, the rate at which the reactants diffuse together limits the overall rate of many elementary reactions. Commonly, the textbook Smoluchowski theory is utilized to estimate effective rate coefficients in the liquid phase. On surfaces, modelers commonly resort to much more complex and expensive Kinetic Monte Carlo (KMC) simulations. Here, we extend the Smoluchowski model to allow the diffusing species to undergo chemical reactions and derive analytical formulas for the diffusion-limited rate coefficients for 3D, 2D, and 2D/3D interface cases. With these equations, we are able to demonstrate that when species react faster than they diffuse they can react orders of magnitude faster than predicted by Smoluchowski theory, through what we term “the reactive transport effect”. We validate the derived steady-state equations against particle Monte Carlo (PMC) simulations, KMC simulations, and non-steady-state solutions. Furthermore, using PMC and KMC simulations, we propose corrections that agree with all limits and the computed data for the 2D and 2D/3D interface steady-state equations, accounting for unique limitations in the associated derived equations. Additionally, we derive equations to handle couplings between diffusion-limited rate coefficients in reaction networks. We believe these equations should make it possible to run much more accurate mean-field simulations of liquids, surfaces, and liquid–surface interfaces accounting for diffusion limitations and the reactive transport effect.

Johnson, M. S., Mueller, J. N., Daniels, C., Najm, H. N., Zádor, J.: Diffusion limited kinetics in reactive systems. J. Phys. Chem. A, 2024, 128, 18, 3685–3702 https://doi.org/10.1021/acs.jpca.4c00727 

The Pynta workflow code accelerates reaction discovery for heterogeneous catalysis. Pynta automates many of the usual, but tedious and error prone steps of this work. More crucially, it also features a new saddle point estimating algorithm, termed as harmonically forced saddle point (HFSP) search, which allows the fast generation of many site-specific saddle point guesses. There are filtered with a harmonic filter that aims to keep the lower energy ones only, to be submitted for a full DFT calculation. 

Johnson, M. S., Gierada, M., Hermes, E. D., Bross, D. H., Sargsyan, K., Najm, H. N., Zádor, J.: Pynta - An automated workflow for calculation of surface and gas-surface kinetics. Journal of Chemical Information and Modeling, 2023. https://doi.org/10.1021/acs.jcim.3c00948 

https://github.com/zadorlab/pynta 

Scientific Achievement

Optimization of molecular geometries is best done in internal coordinates: bonds lengths, bond angles, and dihedral angles. However, these coordinates are coupled, creating complicated constraints and consequently loss of efficiency for widely used optimization algorithms. Our new optimization strategy interprets the space of all possible molecular geometries as a manifold, and molecular geometry displacements are taken along the geodesics on these manifold, inherently satisfying the necessary constraints. Compared to the traditional approach, this substantially reduces the number of steps required to reach convergence on a molecular geometry optimization benchmark 

Significance and Impact

Geometry optimization is a key aspect in any computational study of molecules. This step may be ratelimiting in automatic potential energy surface exploration frameworks suitable for use on exascale computational resources. Our geodesic optimization method dramatically speeds up optimization of molecules, thereby increasing the throughput in such applications.

Research Details

• Our method has been implemented in our open-source geometry optimization code, Sella.

• The method is a drop-in replacement for existing optimization codes using redundant internal coordinates.

• It can also be used in saddle point optimization for reaction network exploration.

Eric D. Hermes, Khachik Sargsyan, Habib N. Najm, and Judit Zádor, The Journal of Chemical Physics, 2021, 155, 094105. https://doi.org/10.1063/5.0060146

https://github.com/zadorlab/sella 

Scientific Achievement

A new method has been developed for locating saddle points on potential energy surfaces in atomistic simulations using iterative Hessian diagonalization. Our method scales better with respect to system size and converges more reliably than traditional approaches. The method is implemented in a new open-source software package, Sella, which provides a convenient way to use our method in combination with more than 40 electronic structure packages for molecules, solids and other atomic systems. 

Significance and Impact

Automated workflows to explore reactive potential energy landscapes combined with current peta- and upcoming exascale computing resources promise an unprecedented acceleration of the rate at which we can understand complex chemical phenomena at the atomic scale. Robust and efficient optimizers are the linchpins of these frameworks. Especially difficult in this context is to have reliable search methods for first order saddle points, these lowest energy passage points between the intermediates of a reaction networks, which ultimately determine the importance and rate of the various chemical processes.

Research Details

We use iterative diagonalization to update an approximate Hessian. Efficiency is gained by using it both to progress towards the saddle point and as a preconditioner for subsequent Hessians. Balancing the cost of diagonalization and the desired accuracy to make the right geometry steps results in a substantial reduction in the total cost of optimization compared to other low-scaling algorithms. Sella is being incorporated into automated potential energy landscape exploration codes, including KinBot (for gas-phase molecules) and the newly-developed pynta (for heterogeneous catalysis).

Eric D. Hermes, Khachik Sargsyan, Habib N. Najm, and Judit Zádor, Journal of Chemical Theory and Computation, 2019, 15, 6536-6549.

https://github.com/zadorlab/sella 

Scientific Achievement

The computational singular perturbation (CSP) method has been applied in gas phase chemical kinetic modeling, as well as biochemical modeling, but not hitherto in heterogeneous catalysis. It has been used for diagnosis of dynamical system response, time integration of stiff ordinary differential equations (ODEs), and for providing means for chemical model reduction. In this work, we extend its formulation to handle differential-algebraic equation (DAE) systems that are typically used in heterogeneous catalysis models. Using this new formulation, we demonstrated dynamical analysis of a catalytic system, highlighting important fast/slow processes, and identifying cause-and-effect relationships. We also used the DAE analysis results to examine the quality of different quasi steady state approximations, identifying choices resulting in minimal errors relative to the ODE formulation. 

Significance and Impact

CSP analysis is useful for dynamical systems that exhibit stiffness resulting from a wide range of time scales, as is the case e.g. in heterogeneous catalysis. Its main strategy is to decouple fast and slow dynamics through an alternative representation of the original system of equations, thereby providing a framework for dynamical analysis and reduction. Its application in catalytic DAE systems enables improved precision in the analysis of system dynamics, which facilitates diagnostic studies of chemical kinetic model behavior, assessment of the quality of DAE approximations, extraction of understanding of system response, and chemical model reduction in catalytic systems.

Research Details

• CSP analysis for DAE/ODE of catalysis systems has been implemented in open-source code, CSPlib: https://github.com/sandialabs/CSPlib

• CSP computations can be executed on modern computing platforms, i.e, GPUs and many-core CPUs

Oscar Díaz-Ibarra, Kyungjoo Kim, Cosmin Safta, Judit Zádor & Habib N. Najm (2021) Using computational singular perturbation as a diagnostic tool in ODE and DAE systems: A case study in heterogeneous catalysis, Combustion Theory and Modelling, https://doi.org/10.1080/13647830.2021.2002417