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Disentangling the mechanistic details of a chemical reaction pathway is ahard problem that often requires a considerable amount of chemical intuitionand a component of luck. Experiments struggle in observing short-lifemetastable intermediates, while computer simulations often rely upon a goodinitial guess. In this work, we propose a method that, from the simulations ofa reactant and a product state, searches for reaction mechanisms connecting thetwo by exploring the configuration space through metadynamics, a well knownenhanced molecular dynamics method. The key quantity underlying this search isbased on the use of an approach called Harmonic Linear Discriminant Analysiswhich allows a systematic construction of collective variables.  Given the reactant and product states, we choose a set of descriptors capableof discriminating between the two states. In order not to prejudge the results,generic descriptors are introduced. The fluctuations of the descriptors in thetwo states are used to construct collective variables. We use metadynamics inan exploratory mode to discover the intermediates and the transition statesthat lead from reactant to product. The search is at first conducted at a lowtheory level. The calculation is then refined and the energy of theintermediates and transition states discovered during metadynamics is computedagain using a higher level of theory.  The method's aim is to offer a simple reaction mechanism search procedurethat helps in saving time and is able to find unexpected mechanisms that defywell established chemical paradigms. We apply it to two reactions, showing thata high level of complexity can be hidden even in seemingly trivial and smallsystems. The method can be applied to larger systems, such as reactions insolution or catalysis.

Blind search for complex chemical pathways using Harmonic Linear Discriminant Analysis