What is the biggest known difference between $r_e$ and $r_0$? Where $r_0$ is the average bond length of the lowest vibrational state, and $r_e$ is the location where the potential is lowest.

For a perfect harmonic oscillator, these are the same (notice that the peak probability is exactly at the minimum of the potential):

[![peak probability of lowest vibrational state and harmonic oscillator][1]][1]

What is the largest known difference between $r_e$ and $r_0$ in a real molecule? 

This is important because the CRC Handbook on Chemistry and Physics almost always gives $r_0$ because that's what can be determined more easily from experiment, but *ab initio* geometry optimization almost always gives $r_e$, yet many publications do not even say which type of bond length they are reporting.


  [1]: https://i.sstatic.net/ubqmtm.png