(*comparing the Morse and harmonic potentials that lead to the same force constant*)
a=0.25
Dys=3.
Morse1=Dys*Exp[-a*R]*(Exp[-a*R]-2)
Show[
Plot[Morse1,{R,-5.,25.},PlotRange->{-3.5,3.5},Axes->False,PlotPoints->101,PlotStyle->{Black,Thickness[0.009]}],
Plot[-Morse1,{R,-4.,25.},Axes->False,PlotPoints->101,PlotStyle->{LightGray,Thickness[0.009]}],
Plot[-Dys+0.25*R^2,{R,-10.,25.},Axes->False,PlotPoints->101,PlotStyle->{Green,Thickness[0.004]}]
]
Plot[Morse1,{R,-4.,25.},PlotRange->{-3.5,3.5},Axes->False,PlotPoints->101,PlotStyle->{Black,Thickness[0.009]}]

0.5`