Transition state theory

Small bits of stuff change into new things.

They must pass through a special spot first. This spot is like a tiny hill to climb. This spot is called a transition state.

The bits stay in this spot for a short time. This helps us know how fast they change. We can use this to learn about the change. It is a way to see how things work.

How do tiny bits of matter change into new things? Scientists use a set of steps called transition state theory to explain this. This theory helps us understand how fast a reaction happens.

When things react, they must pass through a special spot. This spot is called the transition state. Think of it like a tiny hill. The bits of matter must climb the hill to get to the other side.

At the top of this hill, the bits form what we call activated complexes. These are special, short-lived groups of molecules. The theory says these complexes are in a state called quasi-equilibrium with the reactants. This means the complexes and the starting bits stay in a steady balance.

In 1935, Henry Eyring, Meredith Gwynne Evans, and Michael Polanyi worked on this idea. They helped create the Eyring equation. This math helps scientists study how these parts move. It also helps them find the energy needed to cross the hill. By looking at these tiny changes, we can learn how the whole world works.

Transition state theory, or TST, helps scientists explain how fast chemical reactions happen. It is also known by names like activated-complex theory or absolute-rate theory. This theory is a way to understand the steps of a reaction. It focuses on how starting materials turn into new products. Scientists use it to look at the way reactions take place.

To understand how it works, imagine a tiny hill. The starting bits of matter must climb this hill to change. The top of this hill is called the transition state. At this peak, the bits form special groups called activated complexes. These complexes are in a state called quasi-equilibrium with the reactants. This means they stay in a steady balance with the starting parts.

The complexes then move forward to become the final products.

Many smart people helped build this idea over many years. Before TST, people used the Arrhenius rate law from 1889. That older law did not explain the inner workings of reactions. In 1935, Henry Eyring worked at Princeton University on this theory. At the same time, Meredith Gwynne Evans and Michael Polanyi worked at the University of Manchester. Together, they developed the Eyring equation. This math helped solve problems that the older Arrhenius law could not.

There are many important facts and numbers in this history. In 1884, Jacobus van 't Hoff wrote about how temperature affects reactions. Later, in 1910, René Marcelin introduced the Gibbs energy of activation. Dutch chemists like Philip Abraham Kohnstamm also added to our knowledge. In 1919, the physicist Karl Ferdinand Herzfeld found a very important factor. This factor is written as kBT/h in math equations. It appeared in a rate equation for the first time during his work.

This theory links to how we see energy in the world. It uses the idea of a potential-energy surface to show the path. This surface is like a 3D map of energy levels. In 1931, Eyring and Polanyi built one for a specific reaction. They used quantum-mechanical principles to make this map. This helps us see how molecules move through a "saddle point." A saddle point is a specific spot on the energy map.

Transition state theory, or TST, is a framework used to explain the rates of elementary chemical reactions. It helps scientists understand how quickly starting materials, called reactants, turn into new substances called products. The theory is also known by several other names. These include activated-complex theory, absolute-rate theory, and the theory of absolute reaction rates. While it is difficult to use TST to calculate exact absolute reaction rates, it is very useful for other tasks. It helps researchers calculate the standard enthalpy, entropy, and Gibbs energy of activation. These values describe the energy and disorder changes that occur during a reaction.

The mechanism of TST relies on the idea of a special balance called quasi-equilibrium. In a chemical reaction, reactant molecules do not turn into products instantly. Instead, they must first form special, high-energy groups called activated complexes. TST assumes these complexes exist in a quasi-equilibrium with the reactants. This means that even as the reaction progresses, the concentration of these complexes stays in a steady relationship with the starting materials. These complexes are located at a specific point on a potential-energy surface. This point is called the saddle point, or the transition state. Once the complex reaches this peak, it can convert into the final products.

To visualize this process, scientists use the concept of a potential-energy surface. This is a three-dimensional map that shows how energy changes as atoms move. The progress of a reaction can be seen as a point moving across this surface. A critical part of this map is the saddle point. This is a specific location that represents the highest energy barrier the molecules must overcome. In 1931, Henry Eyring and Michael Polanyi constructed a potential-energy surface for a specific reaction. They used quantum-mechanical principles and experimental data to build this map. Later, Hans Pelzer and Eugene Wigner studied how reactions move through this saddle point. They concluded that the rate of a reaction depends on how the system moves through this specific point.

Before TST was developed, scientists relied on the Arrhenius rate law. Svante Arrhenius proposed this law in 1889 based on observations. However, the Arrhenius equation was empirical, meaning it was based on patterns rather than deep mechanical reasons. It used two main parts: the pre-exponential factor, or frequency factor, and the activation energy. While useful, the Arrhenius law did not explain the actual molecular dynamics of a reaction. It did not account for whether reactive intermediates were involved. It took 46 years of scientific progress to move from the Arrhenius law to the more detailed Eyring equation. This gap allowed many researchers to contribute to the new understanding of chemical kinetics.

The history of TST involves many important scientists and mathematical discoveries. In 1884, Jacobus van 't Hoff proposed how temperature affects equilibrium. In 1910, René Marcelin introduced the concept of standard Gibbs energy of activation. Around that same time, Dutch chemists Philip Abraham Kohnstamm, Frans Eppo Cornelis Scheffer, and Wiedold Frans Brandsma introduced the terms for entropy and enthalpy of activation. In 1912, Alfred Berthoud used the Maxwell–Boltzmann distribution law to find a rate constant expression. A major breakthrough came in 1919 from physicist Karl Ferdinand Herzfeld. He was the first to include the factor $k_BT/h$ in a rate equation. This factor is a critical component of modern transition state theory.

Another important figure was the American chemist Richard Chace Tolman. In 1920, he further developed ideas regarding the "critical increment" of a reaction. He concluded that the activation energy is the difference between the average energy of all molecules undergoing a reaction and the average energy of all reactant molecules. This helped bridge the gap between statistical mechanics and chemical observation. Additionally, Hendrik Kramers used Langevin motion to model reactions. He showed how the shape of the potential-energy surface relates to transition rates. His work looked at how systems move through energy wells, such as the well for state A and the well for state B.

Transition state theory connects several complex fields of science together. It brings together thermodynamics, which studies energy and heat, and statistical mechanics, which studies molecular motion. It also uses kinetic theory to calculate how fast complexes convert into products. By combining these areas, TST provides a way to see the "why" behind the speed of a reaction. It moves chemistry from simple observations of patterns to a deep understanding of molecular behavior. This allows scientists to predict how changes in temperature or concentration will affect the way matter transforms in the world.