  We measure the band strengths in the far-infrared region of interstellar ice
analogs of astrophysically relevant species, such as H$_2$O, CO$_2$, CH$_3$OH,
and NH$_3$, deposited at low temperature (8-10 $\mathrm{K}$), followed by
warm-up, to induce amorphous-crystalline phase transitions when relevant. The
spectra of pure H$_2$O, NH$_3$, and CH$_3$OH ices have been measured in the
near-, mid- and far-infrared spectroscopic regions using the Interstellar
Astrochemistry Chamber (ISAC) ultra-high-vacuum setup. In addition,
far-infrared spectra of NH$_3$ and CO$_2$ were measured using a different
set-up equipped with a bolometer detector. Band strengths in the far-infrared
region were estimated using the corresponding near- and mid-infrared values as
a reference. We also performed theoretical calculations of the amorphous and
crystalline structures of these molecules using solid state computational
programs at density functional theory (DFT) level. Vibrational assignment and
mode intensities for these ices were predicted. Infrared band strengths in the
25-500 ${\mu}$m range have been determined for the considered ice samples by
direct comparison in the near- and mid-infrared regions. Our values were
compared to those we calculated from the literature complex index of
refraction. We found differences of a factor of two between the two sets of
values. The calculated far-infrared band strengths provide a benchmark for
interpreting the observational data from future space telescope missions,
allowing the estimation of the ice column densities.
