  In this work we demonstrate vibrational spectroscopy of polyatomic ions that
are trapped and sympathetically cooled by laser-cooled atomic ions. We use the
protonated dipeptide tryptophane-alanine (HTyrAla+) as a model system, cooled
by Barium ions to less than 800mK secular temperature. The spectroscopy is
performed on the fundamental vibrational transition of a local vibrational mode
at 2.74 {\mu}m using a continuous-wave optical parametric oscillator (OPO).
Resonant multi-photon IR dissociation spectroscopy (without the use of a UV
laser) generates charged molecular fragments, which are sympathetically cooled
and trapped, and subsequently released from the trap and counted. We measured
the cross section for R-IRMPD under conditions of low intensity, and found it
to be approximately two orders smaller than the vibrational excitation cross
section. The observed rotational bandwidth of the vibrational transition is
larger than the one expected from the combined effects of 300 K black-body
temperature, conformer-dependent line shifts, and intermolecular vibrational
relaxation broadening (J. Stearns et al., J. Chem. Phys., 127, 154322-7
(2007)). This indicates that as the internal energy of the molecule grows, an
increase of the rotational temperature of the molecular ions well above room
temperature (up to on the order of 1000K), and/or an appreciable shift of the
vibrational transition frequency (approx. 6-8 cm$^{-1}$) occurs.
