Morse Potential – Diatomic Molecule

Potential Parameters

Dissociation energy Dₑ2.0 Well width α1.0 Equilibrium rₑ1.5 Energy level E0.5

Energy Levels

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Bound levels

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ω₀ (harmonic)

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Anharmonicity

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Turn. points

Science

The Morse potential models molecular bonds more accurately than the harmonic approximation:

V(r) = Dₑ(1−e^{−α(r−rₑ)})²

Quantum energy levels (exact solution!):

Eₙ = ℏω₀(n+½) − [ℏω₀(n+½)]²/4Dₑ

Number of bound states: N_max = floor(2Dₑ/ℏω₀ − ½). As E→Dₑ, the oscillation period → ∞ (bond breaking). Anharmonicity causes unequal level spacing and thermal expansion.