Horacio González Duhart hgd20@bath.ac.uk

What is TST?

E. Weinan and E. Vanden-Eijnden. Metastability, conformation dynamics, and transition ways in complex systems. 2004

“Transition State Theory is the oldest attempt to describe metastability in ergodic systems.”

“Transition State Theory is the oldest attempt to describe metastability in ergodic systems.”

Acceleration

Mass

Position

Momentum

Potential energy

“Transition State Theory is the oldest attempt to describe metastability in ergodic systems.”

C

TST simplification:

Example of metastable sets in the context of TST:

Example of metastable sets in the context of TST:

Example of metastable sets in the context of TST:

Ergodic theorem

“Transition State Theory is the oldest attempt to describe metastability in ergodic systems.”

IF

Then

Just think of Jack… he is not always wearing shoes, nor he is not always without them… he continuously keeps changing from one state to the other.

q

“Rate of reaction is the rate of change in the concentration of one of the reactants or products”

“Transition State Theory is the oldest attempt to describe metastability in ergodic systems.”

N. E. Henriksen and F. Y. Hansen. Theories of Molecular Reaction Dynamics. 2008

Ergodicity

Ergodicity

Metastable

Ergodicity

Metastable

Assuming Gibbs distribution

Ergodicity

Metastable

Assuming Gibbs distribution

Original papers from 1935, 1938. Several issues have been addressed, and current research involves techniques on: 1. Dividing surfaces

2. Transition path sampling, reactive trajectories

3. Finite String and MCMC methods

“Transition State Theory is the oldest attempt to describe metastability in ergodic systems.”

C

q

No Jack was hurt during the making of this presentation.

Horacio González Duhart hgd20@bath.ac.uk