  We consider the influence of variation in the fine structure constant alpha
on a promising experiment proposed by DeMille et al. to search for variation in
the electron-to-proton mass ratio mu using diatomic molecules [DeMille et al.,
Phys. Rev. Lett. 100, 043202 (2008)]. The proposed experiment involves
spectroscopically probing the splitting between two nearly-degenerate
vibrational levels supported by different electronic potentials. Here we
demonstrate that this splitting may be equally or more sensitive to variation
in alpha as to variation in mu. For the anticipated experimental precision,
this implies that the alpha variation may not be negligible, as previously
assumed, and further suggests that the method could serve as a competitive
means to search for alpha variation as well.
