  Optical emission is detected from filaments around the central galaxies of
clusters of galaxies. These filaments have lengths of tens of kiloparsecs. The
emission is possibly due to heating caused by the dissipation of mechanical
energy and by cosmic ray induced ionisation. CO millimeter and submillimeter
line emissions as well as H$_{2}$ infrared emission originating in such
filaments surrounding NGC~1275, the central galaxy of the Perseus cluster, have
been detected. Our aim is to identify those molecular species, other than CO,
that may emit detectable millimeter and submillimeter line features arising in
these filaments, and to determine which of those species will produce emissions
that might serve as diagnostics of the dissipation and cosmic ray induced
ionisation. The time-dependent UCL photon-dominated region modelling code was
used in the construction of steady-state models of molecular filamentary
emission regions at appropriate pressures, for a range of dissipation and
cosmic ray induced ionisation rates and incident radiation fields.HCO$^+$ and
C$_2$H emissions will potentially provide information about the cosmic ray
induced ionisation rates in the filaments. HCN and, in particular, CN are
species with millimeter and submillimeter lines that remain abundant in the
warmest regions containing molecules. Detections of the galaxy cluster
filaments in HCO$^{+}$, C$_{2}$H, and CN emissions and further detections of
them in HCN emissions would provide significant constraints on the dissipation
and cosmic ray induced ionisation rates.
