  We present a theoretical calculation of the influence of ultraviolet
radiative pumping on the excitation of the rotational levels of the ground
vibrational state for HD molecules under conditions of the cold diffuse
interstellar medium (ISM). Two main excitation mechanisms have been taken into
account in our analysis: (i) collisions with atoms and molecules and (ii)
radiative pumping by the interstellar ultraviolet (UV) radiation field. The
calculation of the radiative pumping rate coefficients $\Gamma_{\rm ij}$
corresponding to Drane's model of the field of interstellar UV radiation,
taking into account the self-shielding of HD molecules, is performed. We found
that the population of the first HD rotational level ($J = 1$) is determined
mainly by radiative pumping rather than by collisions if the thermal gas
pressure $p_{\rm
th}\le10^4\left(\frac{I_{\rm{UV}}}{1}\right)\,\mbox{K\,cm}^{-3}$ and the column
density of HD is lower than $\log N({\rm{HD}})<15$. Under this constraint the
populations of rotational levels of HD turns out to be as well a more sensitive
indicator of the UV radiation intensity than the fine-structure levels of
atomic carbon. We suggest that taking into account radiative pumping of HD
rotational levels may be important for the problem of the cooling of primordial
gas at high redshift: ultraviolet radiation from first stars can increase the
rate of HD cooling of the primordial gas in the early Universe.
