Potential energy curves are a compact model for how two atoms interact as their distance changes.

This diagram shows a typical potential energy curve for a covalent bond plotted against internuclear distance. The minimum marks the equilibrium bond length $r_e$, while the vertical gap from the minimum to the separated-atoms reference level represents the bond dissociation energy. Labeled regions indicate where attractive forces dominate versus where short-range repulsion rises sharply. Source

Reading these graphs lets you identify stable bond lengths and the energy required to break a bond.

Interpreting potential energy curves

What a potential energy curve represents

On these graphs, the horizontal axis is internuclear distance (how far apart the nuclei are), and the vertical axis is potential energy of the two-atom system (relative energy due to electrostatic attractions and repulsions). The zero of energy is a chosen reference level; many curves set $E=0$ at infinite separation (atoms not interacting).

Why the curve has a minimum

As two atoms move from far apart toward each other:

• At large $r$, the atoms interact weakly, so potential energy is near the reference level.

• At intermediate $r$, attractive interactions dominate (each nucleus attracts the other atom’s electrons), lowering potential energy.

• At very small $r$, repulsive interactions dominate (nucleus–nucleus repulsion and electron cloud overlap), raising potential energy sharply.

This graph emphasizes the asymmetry of a realistic diatomic potential: a steep repulsive wall at short distances and a more gradual rise on the stretching side. The equilibrium bond length $r_e$ is identified at the minimum, visually reinforcing that stable bonding occurs at the energy minimum. The flattening toward large internuclear distance corresponds to approaching the separated-atoms limit where interactions become negligible. Source

The competition between attraction and repulsion produces a well-shaped curve with a lowest point. That lowest point corresponds to the most stable separation.

At $r=r_e$, small displacements in either direction increase potential energy, so the system naturally tends to return toward $r_e$.

This figure plots energy versus internuclear distance for two hydrogen atoms and shows a distinct minimum at the H–H bond length. The curve illustrates why an optimum separation exists: moving either closer (repulsion) or farther apart (reduced attraction) increases the system’s potential energy. Reading the bond length directly from the x-axis at the minimum helps avoid confusing bond length with bond energy. Source

This is why bonds have characteristic lengths that can be measured.

Bond energy from the curve

The depth of the “well” indicates how much energy is needed to fully separate the atoms.

Bond energy is an energy difference read vertically from the minimum of the curve up to the reference level for separated atoms. In many AP-style diagrams, that reference is $E=0$ at $r\to\infty$, so bond energy corresponds to the magnitude of the minimum energy.

Because $E(r_e)$ is lower than $E(r\to\infty)$, $D$ is positive. If a diagram shows the minimum at a negative value, that does not mean the bond energy is negative; it means the bonded state is lower in potential energy than the separated state.

What you can infer from curve shape

Strength and stability comparisons

When comparing two potential energy curves (two different bonds):

• Deeper well $\Rightarrow$ larger bond energy $\Rightarrow$ bond is harder to break.

• Minimum at smaller $r_e$ $\Rightarrow$ shorter bond length for that bond.

• A curve that rises more steeply on either side of $r_e$ indicates the energy increases rapidly when the bond is stretched or compressed, reflecting a “stiffer” interaction.

Only conclusions supported by the graph should be stated. For example, you can compare which bond has greater bond energy by comparing well depths, without needing to explain the cause.

Interpreting “bond breaking” on the curve

Bond breaking corresponds to moving from the minimum up and out toward large $r$:

• Energy must be added to go from the minimum to separated atoms.

• Once sufficiently far apart, additional separation changes potential energy very little (atoms effectively stop interacting).

Common AP pitfalls in reading these graphs

• Bond length vs. bond energy: bond length is the x-value at the minimum; bond energy is the vertical difference between the minimum and the separated-atom level.

• Reference levels: if the curve’s “zero” is not explicitly labeled, rely on the diagram’s indicated separated-atom level rather than assuming a particular numeric value.

• Minimum is not “zero energy”: the minimum is the most stable point, not necessarily zero on the y-axis.