  In our recent papers (Kereslidze et all 2019a, 2021) a non-standard
quasi-molecular mechanism was suggested and applied to treat the cosmological
recombination. It was assumed that in the pre-recombination stage of evolution
of the Universe an electron combined with two neighbouring protons and created
the hydrogen molecular ion, $H_2^+$ in highly excited states, which then
descended into the lower-lying states or dissociated. In this work, we
elaborate the scheme of calculation for free-bound radiative transitions into
attractive states of $H_2^+$ as functions of redshift $z$. Together with the
earlier developed treatment of bound-bound radiative transitions in $H_2^+$,
the elaborated scheme of calculation can be used for the design of a fast and
complete cosmological recombination code.
