This lab models the hydrogen molecule with a Morse potential. As you change the H–H distance, the simulator updates the shared electron density, the potential energy and the restoring force, and an optional animation makes the bond vibrate about its minimum.
• Two hydrogen nuclei, a shared bonding density cloud and a potential well with a cursor that follows the separation. • Sliders for H–H separation (0.55 to 2.5 Å) and vibration amplitude (0.01 to 0.15 Å), with toggles for vibration and explanatory particles. • Readouts: instantaneous separation, Morse potential energy in eV, restoring force in nN and the equilibrium separation. • Experiments: at equilibrium (0.74 Å) the energy is −4.52 eV and the force is zero; a stretched bond at 1.3 Å is pulled back toward the minimum.
U(r) = D[1 − exp(−a(r − r₀))]² − D with D = 4.52 eV, a = 1.94 Å⁻¹ and r₀ = 0.74 Å. The force is F = −dU/dr, converted using 1 eV/Å = 1.60218 nN. The well depth is the bond energy, and the force is zero at the minimum.
This is an illustrative H₂ Morse potential, not an ab initio calculation or a quantum vibrational spectrum. Animation frequency is slowed and arbitrary, and the amplitude is prescribed rather than energy-integrated.
At short distances nuclear repulsion dominates, and at long distances the attraction fades. The balance gives a minimum energy at about 0.74 Å in this model.
It is the negative slope of the energy curve. It points toward equilibrium when the bond is stretched or compressed and is zero at the minimum.
Only qualitatively. The frequency is slowed and the amplitude is prescribed. A real treatment needs quantized vibrational levels.
The well depth, D = 4.52 eV, is the energy at equilibrium relative to separated atoms, shown as −4.52 eV in the readout.