Reaction Pathways and Transition States

Locating transition states and tracing reaction paths on the potential energy surface turns quantum-chemical calculations into mechanistic and kinetic understanding of how reactions occur.

Definition

The computational study of how chemical reactions proceed, centered on locating transition states and reaction paths and on estimating reaction rates from them.

Scope

Covers transition-state theory and its computational application, methods for finding first-order saddle points, the intrinsic reaction coordinate connecting reactants and products, chain-of-states methods such as the nudged elastic band, and the estimation of rate constants from computed barriers and partition functions.

Core questions

• How is a transition state located and verified computationally?
• How does the intrinsic reaction coordinate confirm which minima a saddle point connects?
• How are reaction rates estimated from computed barriers within transition-state theory?
• How do chain-of-states methods find minimum energy paths?

Key theories

Transition-state theory

Casts the reaction rate in terms of an activated complex at the saddle point, relating the computed barrier and partition functions to the rate constant.

Minimum energy path methods

Techniques such as the intrinsic reaction coordinate and nudged elastic band trace the lowest-energy route between reactants and products, characterizing the mechanism.

Mechanisms

A mechanism is mapped by optimizing reactant and product minima, locating the connecting transition state, verifying it with a single imaginary frequency, and following the intrinsic reaction coordinate downhill to confirm the species it links.

Clinical relevance

Computed mechanisms, barriers, and rates illuminate catalysis, selectivity, and reaction design, allowing chemists to rationalize observed products and to screen reaction conditions and catalysts in silico.

History

Eyring's 1935 activated-complex theory provided the conceptual core; reliable saddle-point optimization, intrinsic-reaction-coordinate following, and chain-of-states methods later made computational mechanism determination a standard practice.

Key figures

• Henry Eyring
• Donald Truhlar
• Hans Eyring
• Graeme Henkelman

Seminal works

• eyring1935
• cramer2004

Frequently asked questions

How is a computed transition state validated?

It should have exactly one imaginary vibrational frequency whose motion corresponds to the reaction coordinate, and following the intrinsic reaction coordinate from it should reach the expected reactant and product.

Can computed barriers predict reaction rates accurately?

Transition-state theory connects barriers to rates, but accuracy is sensitive to the computed barrier height, tunneling, and dynamical effects, so predicted rates carry meaningful uncertainty.