  Hylleraas in 1929 carried out a variational computation on the Schrodinger
equation for the helium atom which gave, for the first time, a ground-state
energy in essential agreement with experimental results. Coolidge and James in
1933, likewise did the first accurate computation for the hydrogen molecule.
These are considered epoch-making contributions in the development of ab initio
quantum chemistry, since they provided definitive evidence for the validity of
the multiple-particle Schrodinger equation for atoms and molecules. Before
then, exact solutions had been obtained only for one-electron hydrogenlike
atoms. The helium and hydrogen work was done long before the advent of
electronic computers and required many months of drudgery, using hand-cranked
calculating machines. Nowadays, students of chemistry and physics can carry out
these same computations in a matter of hours, or even minutes, using relatively
straightforward Mathematica routines. Moreover, the results can be easily
improved far beyond the capabilities of the original workers.
