  We discuss in detail very little known results obtained by Majorana as early
as 1931, regarding the quantum theory of the chemical bond in homopolar
molecules, based on the key concept of exchange interaction. After a brief
historical overview of the quantum homopolar valence theory, we address the
intriguing issues of the formation of the helium molecular ion, He2+, and of
the accurate description of the hydrogen molecule, H2. For the first case, the
group theory-inspired approach used by Majorana is contrasted with that more
known followed by Pauling (and published few months after that of Majorana),
while for the second case we focus on his proposal concerning the possible
existence of ionic structures in homopolar compounds, just as in the hydrogen
molecule. The novelty and relevance of Majorana's results in the modern
research on molecular and chemical physics is emphasized as well.
