---
title: "Reaction Dynamics: Trajectories Across a Potential Energy Surface"
description: "Rate theory treats a reaction as a population crossing a barrier. Dynamics follows individual trajectories instead, and some of them do not behave: they recross the barrier, or they skip the expected "
canonical: https://lightmysky.com/learn/science/reaction-dynamics-trajectories-across-a-potential-energy-surface-mt_6ctTUYqYtS
source: https://lightmysky.com/learn/science/reaction-dynamics-trajectories-across-a-potential-energy-surface-mt_6ctTUYqYtS.md
retrieved: 2026-09-12
---

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# Reaction Dynamics: Trajectories Across a Potential Energy Surface

Rate theory treats a reaction as a population crossing a barrier. Dynamics follows individual trajectories instead, and some of them do not behave: they recross the barrier, or they skip the expected intermediate and land somewhere else.

Subject: Science · Area: Chemistry · Ages 23 to 24
Page: https://lightmysky.com/learn/science/reaction-dynamics-trajectories-across-a-potential-energy-surface-mt_6ctTUYqYtS

## Ready when they can

- Reads a two-dimensional surface and traces the path a trajectory would take across it
- Explains what recrossing does to a rate constant predicted from a barrier height
- Describes an outcome that a statistical theory predicts wrongly and says why
- Names an experiment whose product ratio is evidence for dynamic rather than statistical control

## Lesson: When molecules ignore the expected path

Before molecules react they must meet, but most collisions are gentle bumps that change nothing. A working collision needs enough energy at once plus the right orientation, with the wrong ends touching dooming even a fast hit. Picture the reaction as a mountain pass: reactants in one valley, products in another, and the barrier between them setting the climb.

The top of the pass is the transition state, where old bonds are half broken and new ones half formed. Heating speeds the reaction because more molecules move fast enough to clear the barrier. The Arrhenius equation turns this into math, linking the rate constant to barrier height and temperature: higher barrier, slower reaction.

**Example.** Rate theory assumes every crosser of the barrier lands as product. Dynamics follows single trajectories instead, and some misbehave: they reach the top and fall back, which is called recrossing. Recrossing makes the true rate smaller than the barrier height alone predicts.

**Tip.** Watch for product ratios that refuse to match the computed barriers. Some trajectories skip the expected intermediate valley entirely and land elsewhere, steered by the surface shape after the transition state. A ratio set by that downhill shape, not by barrier heights, is evidence for dynamic rather than statistical control.

**Recap.** Barriers set the expected rate, but recrossing and downhill steering can rewrite the ending.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Molecular Dynamics and Free Energy from Sampling](https://lightmysky.com/learn/science/molecular-dynamics-and-free-energy-from-sampling-mt_ajdYrZOzEd)
- [Transition State Theory and the Eyring Equation](https://lightmysky.com/learn/science/transition-state-theory-and-the-eyring-equation-mt_JVjDMcXds1)
- [Computed Geometries, Frequencies and Reaction Barriers](https://lightmysky.com/learn/science/computed-geometries-frequencies-and-reaction-barriers-mt_pdiFjK2wPe)

## Opens up

- [Ultrafast Spectroscopy and Watching a Reaction Happen](https://lightmysky.com/learn/science/ultrafast-spectroscopy-and-watching-a-reaction-happen-mt_wxQgetzzW5)