⚗️ Potential Energy Surface
Müller-Brown PES
Particle

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Statistics
Current energy
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Activation Ea
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PES: The Müller-Brown potential has 3 minima (R, P, I) and 2 saddle points (TS1, TS2). A particle rolls with friction γ and thermal noise kT. Activation energy Ea = V(TS) − V(R). Contour lines = constant potential.

About this simulation

This simulation visualises a 2D chemical potential energy surface built from the classic Müller-Brown potential, a sum of four Gaussian-like terms that produces three energy minima (reactant, intermediate, product) connected by two saddle points. A particle representing the reacting system moves under the local force −∇V with friction and thermal noise, so you can watch it hop between wells the way a real molecule crosses a reaction barrier.

🔬 What it shows

The Müller-Brown surface V(x,y), a sum of four exponential terms with fixed centres and curvatures, drawn as a filled contour map from about −300 to +200 (energy colour scale) with 20 contour lines. Three labelled minima — Reactant R, Intermediate I, Product P — sit in the wells, joined by two transition states TS1 and TS2 at the saddle points the particle must cross to react. Live readouts show the particle's current energy V, its (x,y) position, the activation energy Ea = V(TS1) − V(R), and which named region it's currently nearest to.

🎮 How to use

Click anywhere on the surface to drop the particle there and watch it roll downhill toward the nearest minimum. Increase Friction to make the motion more overdamped and deterministic, or increase Temperature to add thermal kicks that can push the particle back over a barrier it just crossed — the essence of a reversible reaction. The Barrier scale slider multiplies every term in the potential together, raising or lowering all three wells and both transition states in lock-step so you can see how a uniformly higher barrier slows the reaction.

💡 Did you know?

The Müller-Brown potential was originally published in 1979 specifically as a benchmark surface for testing algorithms that find minimum-energy reaction paths and transition states, and it is still used today to validate new computational chemistry methods before they're applied to real molecules. Its two saddle points and three wells were deliberately chosen to mimic a realistic multi-step reaction — reactant to intermediate to product — rather than a simple one-barrier crossing.

Frequently asked questions

What is the Müller-Brown potential?

It is a widely used two-dimensional analytic potential energy surface built from a sum of four Gaussian-like exponential terms, each with its own amplitude, position and curvature. It was designed to have exactly three local minima and two first-order saddle points arranged so that a path from one minimum to another must pass through both saddles, making it a standard test case for algorithms that search for reaction paths and transition states.

How does the particle move on the surface?

The particle follows Langevin-like dynamics: at each time step its velocity is updated using the negative gradient of the potential (the force pulling it downhill), a friction term proportional to its current velocity, and a random thermal kick scaled by the temperature slider. The gradient is computed with a central finite-difference approximation, and the particle bounces back with reduced velocity if it reaches the edge of the plotted domain.

What do Friction and Temperature actually control?

Friction damps the particle's velocity every step, so higher friction makes the motion slower and more overdamped, settling into a minimum without much oscillation. Temperature adds a random force scaled to its value at every step, giving the particle enough kinetic energy to occasionally climb back over a barrier it has already crossed — exactly analogous to how thermal energy in a real molecule allows it to cross an activation barrier even though the reaction is uphill in potential energy.

What is activation energy and how is it shown here?

Activation energy Ea is the energy difference between a transition state and the reactant well it starts from — in this simulation, Ea = V(TS1) − V(R), read live from the readout panel. A higher activation energy means the barrier between reactant and product is taller, so at a fixed temperature the particle needs a larger, rarer thermal fluctuation to cross it, exactly mirroring why real reactions with high activation energies proceed more slowly at a given temperature.

Why do real chemical reactions have multiple minima and transition states like this?

Many real chemical reactions do not go directly from reactants to products in a single step; instead they pass through one or more intermediates — stable but higher-energy species — each separated from its neighbours by its own transition state. Enzyme-catalysed reactions, SN1 nucleophilic substitutions, and multi-step organic mechanisms are classic examples. Mapping out the full potential energy surface, as this simulation does in a simplified two-dimensional form, is exactly how computational chemists identify these intermediates and the rate-limiting transition state that controls the overall reaction speed.