Personal computer realizations for two classics of quantum chemistry

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.