  We study the formation and destruction of the first molecules at the epochs
of the Dark Ages and Cosmic Dawn to evaluate the luminosity of the protogalaxy
clumps (halos) in the molecular lines. The cosmological recombination is
described using the model of an effective three-level atom, while the chemistry
of the molecules is examined using the relevant basic kinetic equations. We
then studied the effect of collisional and radiative excitation of molecules on
the intensity of molecular emission in both warm and hot halos. Using the
Planck data on the reionization of the intergalactic medium at z~6-8, we
evaluated the upper limits of the light energy density for four models of
thermal light from the first sources that appeared in the Cosmic Dawn epoch.
Assuming that in the halos, the light energy density may essentially be even
higher, we estimated the impact of the light from the first sources on the
formation and destruction of the first molecules. We show that the molecules H2
and HD are destroyed by photodissociation processes shortly before the full
reionization in the inter-halo medium, in the medium of both types of halos and
for all models of the first light. At the same time, the number density of
helium hydride ions, HeH+, shows essentially more complicated dependences on
the kinetic temperature of halos and the models of the first light.
Furthermore, we estimated the differential brightness temperature of the
individual halo in the rotational lines of H2, HD and HeH+ molecules at
redshifts corresponding to the Dark Ages and Cosmic Dawn epochs. It does not
exceed the microkelvin, but its detection may be an important source of
information about the physical processes taking place at the beginning of the
formation of the first stars and galaxies at the epochs of the Dark Ages and
Cosmic Dawn.
