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separation distances, but does not accurately describe molecular vibration when the separation distance becomes large. For an harmonic oscillator characterized by the parabolic potential (5.17) the restoring force increases with increasing separation, thus excluding the possibility of molecular dissociation. Since an actual diatomic molecule dissociates when the separation distance between the atoms becomes sufficiently large, the molecular potential should become asymptotic for sufficiently large values of r. The dissociation can be included by representing the molecule as an anharmonic oscillator for which the general. potential is

               V(r) = f(r - re )2 - g(r - re )3     (5.20)


The energy eigenvalues corresponding to the potential (5.20) are (51):


Ev hc e(v + 1) - xe(v + 1)     + Ye(v + 2


                                                    (5.21)

The proper form of the molecular potential can be conveniently represented by the Morse potential (50)


               V(r) = De [1 - e $(r-re)]            (5.22)


where De is the dissociation energy from the equilibrium