Instanton theory
In a chemical reaction, molecules evolve from a reactant state to a product state and we wish to describe this process while considering the quantum-mechanical nature of the atoms; as opposed to a classical description that does not include quantum effects.
One way to understand these molecular processes is to use Feynman's path-integral picture, where we have to take into account every possible way of starting from reactants and evolving into products (i.e. integrate over all paths). This includes paths that venture into the classically forbidden region below the energy barrier, even when the molecule does not have enough energy to do so, in a phenomenon called quantum tunnelling.
Quantum tunnelling is a common, yet complicated feature of
molecular processes and needs to be properly understood to obtain accurate
predictions in areas like atmospheric chemistry, astrochemistry or catalysis.
Unfortunately, it is computationally incredibly expensive to run fully quantum-mechanical
simulations of molecular evolution and consequently to generate predictions. For this reason, we are developing an approximate semiclassical instanton theory in our group.With instanton theory, we only have to consider the most important path in Feynman's path integral (called the instanton). The theory is rigorous and becomes exact in the limit that ℏ tends to 0, and is systematically improvable by considering higher-order effects. In this way, we can achieve high accuracy at a reasonable computational cost.
Applications
Instanton Theory in the adiabatic regime has been successful in describing the tunnelling behaviour of Hydrogen in water clusters, calculate accurate tunnelling splittings of molecules such as Malonaldehyde, Tropolone etc.