Morse potential

https://dx.doi.org/10.1351/goldbook.MT07073
The empirical function relating the potential energy of a molecule to the inter-atomic distance r accounting for the anharmonicity (See: harmonic approximation) of bond stretching:
E r = D e ( 1 − e − a ( r − r e ) ) 2
where D e is the bond-dissociation energy, r e is the equilibrium bond length, and a is a parameter characteristic of a given molecule.
Source:
PAC, 1999, 71, 1919 (Glossary of terms used in theoretical organic chemistry) on page 1953