(39d) Using Metadynamics to Resolve and Characterize Complex Reactions at the Molecular Scale

While molecular dynamics simulations can be a powerful tool for characterizing the thermodynamics and kinetics of reaction mechanisms, they often come at a significant computational cost. Specifically, analyzing reaction networks with many pathways and states dramatically increases the computational expense of the simulations due to the vast landscape of the system. Enhanced sampling methods, such as the metadynamics (MetaD) family of methods,¹ are often employed to help mitigate this issue, but typically require a high level of insight about the chemistry involved in a system, making it difficult to use a tool for studying poorly understood systems. MetaD, specifically, relies on biasing a few degrees of freedom, or collective variables (CVs), that dictate the transitions between stable states. For complex reacting systems the number of relevant CVs can be very high, constraining the effectiveness of the bias, or difficult to identify due to lack of knowledge about the system.

In this study we discuss the use of generic CVs, i.e., those CVs that do not rely on a priori knowledge of a chemical transformation, to help ease the challenge of discovering both complex chemical reaction networks and the associated kinetics of pathways in the networks. We present how two different generic CVs, namely Social Permutation Invariant (SPRINT) coordinates² and collective variable-driven hyperdynamics (CVHD),³ require a relatively low level of system knowledge to construct, but act as suitable CVs for estimating transition rates from biased simulations.⁴ We biased these generic CVs, as well as typical ones derived from chemical intuition, following the infrequent MetaD method⁵ to calculate the transition rates of two reaction systems: an SN2 reaction and a Diels Alder reaction. For both systems, we show that regardless of the biased CVs, consistent transition rates and energy barriers are recovered an ensemble of biased simulations, while reducing the simulation time. In addition, we demonstrate an approach for exploring large, complex reaction networks with high dimensionality by biasing the SPRINT coordinates of the atoms in a given system following the Parallel Bias MetaD method.⁶ Using only knowledge of the initial state, we explore the reaction pathways of the decomposition of g-ketohydroperoxide described by the PM6 Hamiltonian. From analyzing an ensemble of biased simulations at various temperatures, we are able to construct a network of species that encompasses pathways consistent with the Korcek reaction mechanism,⁷ as well as typical hydrocarbon chemistries. This presentation will close with notes on how these methods can be broadly applied to resolve and characterize the relevant pathways involved in poorly understood, complex reacting systems.

References:

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(4) Fu, C. D.; Oliveira, L. F. L.; Pfaendtner, J. Assessing Generic Collective Variables for Determining Reaction Rates in Metadynamics Simulations. J. Chem. Theory Comput. 2017, acs.jctc.7b00038.

(5) Tiwary, P.; Parrinello, M. From Metadynamics to Dynamics. Phys. Rev. Lett. 2013, 111 (23), 230602.

(6) Pfaendtner, J.; Bonomi, M. Efficient Sampling of High-Dimensional Free-Energy Landscapes with Parallel Bias Metadynamics. J. Chem. Theory Comput. 2015, 11 (11), 5062–5067.

(7) Jalan, A.; Alecu, I. M.; Aguilera-Iparraguirre, J.; Merchant, S. S.; Yang, K. R.; Merhcant, S. S.; Truhlar, D. G.; Green, W. H. New Pathways for Formation of Acids and Carbonyl Products in Low Temperature Oxidation. J. Am. Chem. Soc. 2013, 135, 11100–11114.