Character theory and Quantum Chemistry Who (presumably a chemist) realized first the efficiency of character theory in calculations of orbitals of atoms? In which year?
 A: Introducing groups into quantum theory, by Erhard Scholz (2006):

In quantum chemistry, representations of permutation groups made their
  first appearance about the same time as they did in spectroscopy. The
  topic was opened up by a joint publication [1] of two young physicists, 
  Walter  Heitler  and  Fritz  London,  who  had  come  to  Zürich  on 
  Rockefeller  grants  in  1926, respectively 1927, to work with E.
  Schrödinger. Group theoretic methods were
  first applied in two papers by W. Heitler [2,3].
[1] Heitler, W., London,  F.  Wechselwirkung 
  neutraler  Atome  und  homöpolare  Bindung  nach  der 
  Quanten-mechanik. Zeitschrift für Physik 44, 455–472 (1927).
  [2] Heitler, W., Zur Gruppentheorie der homöopolaren chemischen
  Bindung. Zeitschrift für Physik 47, 835–858 (1928).
  [3] Heitler, W., Zur
  Gruppentheorie der Wechselwirkung von Atomen. Zeitschrift für Physik
  51, 805–816 (1928).    

A: I think this realization is an immediate consequence of that of the efficiency of group theory in the quantum theory of angular momentum.
The early culprits for the Gruppenpest are Weyl in his 1931 book "Gruppentheorie und quantenmechanik"
and B. van der Waerden in his 1932 book "Die gruppentheoretische Methode in der Quantenmechanik". You can probably also find a discussion of this in the more recent book by Biedenharn and Louck.
