  Some new physics models of quantum gravity or dark matter predict drifts or
oscillations of the fundamental constants. A relatively simple model relates
molecular vibrations to the proton-to-electron mass ratio $\mu$. Many
vibrational transitions are at optical frequencies with prospects for use as
highly accurate optical clocks. We give a brief summary of new physics models
that lead to changes in $\mu$ and the current limits on drifts and oscillation
amplitudes. After an overview of laboratory procedures, we give examples of
molecules with experiments currently in development or underway. These
experiments' projected systematic and statistical uncertainties make them
leading candidates in next-generation searches for time-variation of $\mu$.
