  The interaction between excited states of a molecule and excited states of
metal nanostructure (e.g. plasmons) leads to hybrid states with modified
optical properties. When plasmon resonance is swept through molecular
transition frequency an avoided crossing may be observed, which is often
regarded as a signature of strong coupling between plasmons and molecules. Such
strong coupling is expected to be realized when $2|U|/{\hbar\Gamma}>1$, where
$U$ and ${\Gamma}$ are the molecule-plasmon coupling and the spectral width of
the optical transition respectively. Because both $U$ and ${\Gamma}$ strongly
increase with decreasing distance between a molecule and a plasmonic structure
it is not obvious that this condition can be satisfied for any molecule-metal
surface distance. In this work we investigate the behavior of $U$ and
${\Gamma}$ for several geometries. Surprisingly, we find that if the only
contributions to ${\Gamma}$ are lifetime broadenings associated with the
radiative and nonradiative relaxation of a single molecular vibronic
transition, including effects on molecular radiative and nonradiative lifetimes
induced by the metal, the criterion $2|U|/{\hbar\Gamma}>1$ is easily satisfied
by many configurations irrespective of the metal-molecule distance. This
implies that the Rabi splitting can be observed in such structures if other
sources of broadening are suppressed. Additionally, when the molecule-metal
surface distance is varied keeping all other molecular and metal parameters
constant, this behavior is mitigated due to the spectral shift associated with
the same molecule-plasmon interaction, making the observation of Rabi splitting
more challenging.
