Chemical Reactions

Chemical reactions are ubiquitous in nature. From transfer of electrons in light-harvesting solar cells to fermentation of milk into yougurt,  a colorful variety of physical processes are governed by conversion of one set of chemical species to another. A typical reaction involves transformation of reactants into products.  One of the simplest reactions found in nature is the following,

H+H_2 \rightarrow H_2+H

This reaction is characterized by the existence of a single electronic state, and falls under the category of the so-called adiabatic reaction. It involves dissociation of H_2 into two separate H atoms. This is followed by a subsequent formation of a covalent bond between a dissociated H atom and another H atom. These are scattering-type reactions, which occur as a result of thermal fluctuations among others. Another typical example of reactive scattering is a one-dimensional barrier transmission of a Gaussian wavepacket shown below,

Classically, a particle is going to cross the barrier if it has energy larger than the energy at the barrier-top. However, quantum mechanically, the particle can tunnel through the barrier, and this is illustrated by the movie above. Not only does the quantum particle transmit the barrier, it is also capable of reflecting off of it. This is intrinsically a quantum phenomena, and is exhibited especially by light particles. However, to characterize tunneling, one requires knowledge of the wavefunction \psi(x) of the particle at all points in space. This is useful in the computation of reflection and transmission probabilities, which are central quantities of interest in scattering theory. Unfortunately, wavefunctions are not easily obtainable for realistic systems, as it requires one to solve the Schrodinger equation, which is computational expensive. One therefore resorts to approximate approaches such as those inspired by the semiclassical formulation of quantum mechanics.

Instanton theory is one powerful semiclassical approach, and is seen to be remarkably accurate to treat tunneling in a variety of chemical reactions.  An instanton is a dominant tunneling path, and accurately depicts the reaction mechanism. For a two-dimensional model potential energy surface, a cartoon illustration of this path is shown below in green and blue- colored beads,

Representation of a quantum particle delocalizing in space. This cartoon illustration indicates tunneling through a two-dimensional potential barrier. 

Note: Accurately quantifying tunneling in a chemical reaction is the central part of my Ph.D. thesis at ETH Zurich.