  We review the essentials of the formalism of quantum mechanics based on a
deformed Heisenbeg algebra, leading to the existence of a minimal length scale.
We compute in this context, the energy spectra of the pseudoharmonic oscillator
and Kratzer potentials by using a perturbative approach. We derive the
molecular constants, which characterize the vibration--rotation energy levels
of diatomic molecules, and investigate the effect of the minimal length on each
of these parameters for both potentials. We confront our result to experimental
data for the hydrogen molecule to estimate an order of magnitude of this
fundamental scale in molecular physics.
