The Morse function

, where

is the internuclear distance, provides a useful approximation for the potential energy of a diatomic molecule. It is superior to the harmonic oscillator model in that it can account for anharmonicity and bond dissociation. The relevant experimental parameters are the dissociation energy

and the fundamental vibrational frequency

, both conventionally expressed in wavenumbers (

), the equilibrium internuclear distance

in Angstrom units (Å), and the reduced mass

in atomic mass units (amu). The exponential parameter is given by

in appropriate units. The Schrödinger equation for the Morse oscillator is exactly solvable, giving the vibrational eigenvalues

, for

. Unlike the harmonic oscillator, the Morse potential has a finite number of bound vibrational levels with

.