A Collective Coordinate to Obtain Free Energy Profiles for Complex Reactions in Condensed Phases

Abstract

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Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration

“…This approach, modified to use internal coordinates, was used recently by Zinovjev et al to study the aqueous phase reaction of pyruvate to salycilate, and in the CO bond-breaking/proton transfer in PchB [183]. A generalization to multidimensional paths (i.e., sheets) can be obtained by assigning a generic vector v i to each of the precomputed snapshots and computing its average [184]:…”

Exploring chemical reactivity of complex systems with path‐based coordinates: Role of the distance metric

“…In “PMF along the path‐based coordinate and activation free energy” section, we show that the activation free energy derived from the PMF traced using such a function as RC is equivalent to the value that would be obtained using the committor function directly as RC. Our proposal uses a functional form of the path CV similar to the one published by Branduardi et al because of our previous experience with this RC; but other path‐based CVs could be reformulated in a similar way.…”

“…In the last decade, path‐based reaction coordinates (RCs) have become an important tool for free‐energy calculations in complex molecular systems . The idea of sampling the system along some relevant path in a multidimensional space of predefined descriptors (like Cartesian coordinates of essential atoms or, in general, any collective variables [CVs]) helps to overcome the so‐called “curse of dimensionality”: the exponential scaling of the computational cost versus the number of descriptors used.…”

“…For this approach to be meaningful, the reference path should represent the actual mechanism of the process under study. Such a path can be guessed from the knowledge of the potential energy surface, using for example the intrinsic reaction coordinate (IRC), or generated from a steered molecular dynamics simulation . However, in most cases the free energy surface (FES), or its projection in a subspace of reduced dimensionality, must be explored to find a suitable reference path.…”

“…. However, in most cases this metric tensor is assumed to be constant or it is simply ignored . As shown in this article, while taking a constant metric can be a reasonable approximation if one is not interested in maximizing the transmission coefficient, ignoring the metric tensor can be a severe approximation.…”