  A critical early stage for the origin of life on Earth may have involved the
production of hydrogen cyanide (HCN) in a reducing, predominantly H$_2$
atmosphere. HCN is crucial for the origin of life as it is a possible precursor
to several biomolecules that make up RNA and proteins including nucleobases,
nucleotides, amino acids, and ribose. In this work, we perform an in depth
experimental and theoretical investigation of HCN production in reducing
atmospheric conditions (89-95% H$_2$) possibly representing the earliest stages
of the Hadean eon, ~4.5-4.3 billion years ago. We make use of cold plasma
discharges - a laboratory analog to shortwave UV radiation - to simulate HCN
production in the upper layers of the atmosphere for CH$_4$ abundances ranging
from 0.1-6.5%. We then combine experimental mass spectrum measurements with our
theoretical plasma models to estimate the HCN concentrations produced in our
experiments. We find that upper atmospheric HCN production scales linearly with
CH$_4$ abundance with the relation [HCN] = 0.13 $\pm$ 0.01[CH$_4$].
Concentrations of HCN near the surface of the Hadean Earth are expected to be
about 2-3 orders of magnitude lower. The addition of 1% water to our
experiments results in a ~50% reduction in HCN production. We find that four
reactions are primarily responsible for HCN production in our experiments: (i)
$^4$N + CH$_3$ -> H$_2$CN + H -> HCN + H$_2$, (ii) $^4$N + CH -> CN + H
followed by CN + CH$_4$ -> HCN + CH$_3$, (iii) C$_2$H$_4$ + $^4$N -> HCN +
CH$_3$, and (iv) $^4$N + $^3$CH$_2$ -> HCN + H. The most prebiotically
favorable Hadean atmosphere would have been very rich in CH$_4$ (> 5%), and as
a result of greenhouse effects the surface would be likely very hot. In such a
prebiotic scenario, it may have been important to incorporate HCN into organic
hazes that could later release biomolecules and precursors into the first
ponds.
