# Blind search for complex chemical pathways using Harmonic Linear Discriminant Analysis

## TL;DR

This paper introduces a novel computational method combining Harmonic Linear Discriminant Analysis with metadynamics to systematically discover complex reaction pathways and intermediates in chemical reactions, reducing reliance on intuition and initial guesses.

## Contribution

The work presents a new approach that constructs collective variables systematically for reaction pathway exploration, enabling discovery of unexpected mechanisms at multiple theory levels.

## Key findings

- Successfully identified reaction intermediates and transition states
- Demonstrated the method on two chemical reactions with complex pathways
- Showed applicability to larger systems like catalysis and solutions

## Abstract

Disentangling the mechanistic details of a chemical reaction pathway is a hard problem that often requires a considerable amount of chemical intuition and a component of luck. Experiments struggle in observing short-life metastable intermediates, while computer simulations often rely upon a good initial guess. In this work, we propose a method that, from the simulations of a reactant and a product state, searches for reaction mechanisms connecting the two by exploring the configuration space through metadynamics, a well known enhanced molecular dynamics method. The key quantity underlying this search is based on the use of an approach called Harmonic Linear Discriminant Analysis which allows a systematic construction of collective variables. Given the reactant and product states, we choose a set of descriptors capable of discriminating between the two states. In order not to prejudge the results, generic descriptors are introduced. The fluctuations of the descriptors in the two states are used to construct collective variables. We use metadynamics in an exploratory mode to discover the intermediates and the transition states that lead from reactant to product. The search is at first conducted at a low theory level. The calculation is then refined and the energy of the intermediates and transition states discovered during metadynamics is computed again using a higher level of theory. The method's aim is to offer a simple reaction mechanism search procedure that helps in saving time and is able to find unexpected mechanisms that defy well established chemical paradigms. We apply it to two reactions, showing that a high level of complexity can be hidden even in seemingly trivial and small systems. The method can be applied to larger systems, such as reactions in solution or catalysis.