  HCN is a key ingredient for synthesizing biomolecules such as nucleobases and
amino acids. We calculate 42 reaction rate coefficients directly involved with
or in competition with the production of HCN in the early Earth or Titan
atmospheres. These reactions are driven by methane and nitrogen radicals
produced via UV photodissociation or lightning. For every reaction in this
network, we calculate rate coefficients at 298 K using canonical variational
transition state theory (CVT) paired with computational quantum chemistry
simulations at the BHandHLYP/augcc-pVDZ level of theory. We also calculate the
temperature dependence of the rate coefficients for the reactions that have
barriers from 50 to 400 K. We present 15 new reaction rate coefficients with no
previously known value; 93% of our calculated coefficients are within an order
of magnitude of the nearest experimental or recommended values. Above 320 K,
the rate coefficient for the new reaction H2CN -> HCN + H dominates. Contrary
to experiments, we find the HCN reaction pathway, N + CH3 -> HCN + H2, to be
inefficient and suggest that the experimental rate coefficient actually
corresponds to an indirect pathway, through the H2CN intermediate. We present
CVT using energies computed with density functional theory as a feasible and
accurate method for calculating a large network of rate coefficients of
small-molecule reactions.
