  Precision measurements with ultracold molecules require development of robust
and sensitive techniques to produce and interrogate the molecules. With this
goal, we theoretically analyze factors that affect frequency measurements
between rovibrational levels of the Sr$_2$ molecule in the electronic ground
state. This measurement can be used to constrain the possible time variation of
the proton-electron mass ratio. Sr$_2$ is expected to be a strong candidate for
achieving high precision due to the spinless nature and ease of cooling and
perturbation-free trapping of Sr \cite{Zelevinsky2008}. The analysis includes
calculations of two-photon transition dipole moments between deeply and weakly
bound vibrational levels, lifetimes of intermediate excited states, and Stark
shifts of the vibrational levels by the optical lattice field, including
possibilities of Stark-cancellation trapping.
