This section supplements the discussion in Section 19.4 on the Morse potential energy function. You can change the value of the variable Molecule to see the Morse function and its parameters for any of the following six diatomics: H2, D2, Li2, F2, HF, and LiF. The equilibrium bond lengths Re and the two vibrational constants we and wexe for these molecules (taken from Table 19.2) are built into this page, and the Morse function quantities De (the potential well depth), b, and vD (the vibrational quantum number of the lasthighest energyvibrational level) are calculated from them. The vibrational levels for v = 0, 5, and 10 are also shown.
The Morse potential function itself is the red line, and the dotted orange line is the harmonic potential approximation to the Morse function. As you go from molecule to molecule, pay attention to the following changes:
The QuickTime movie below shows the vibrational wavefunctions of the Morse potential for H2. Note how the higher vibrational levels have wavefunctions that are largest in the region of the outer classical turning point and lack the symmetry of harmonic oscillator wavefunctions.
The QuickTime movie below follows the ground vibrational state (v = 0) wavefunction of H2 as the rotational quantum number J is increased. Note how the total energy increases with rotational energy (increasing J). Note as well the change in appearance of the potential energy function. As J increases, the effect of the centrifugal potential becomes more and more important. Follow the location of the peak of the wavefunction as J increases. You will see that the peak moves to larger R as J increases, demonstrating centrifugal distortion, the general phenomenon of increasing bond length with increasing rotational motion. Finally, note that the energy of the highest J level, J = 33, is above the dissociation limit at V(R) =0. The molecule in this state is unstable and will spontaneously dissociate; it has a rotational energy greater than its bond energy.