Simple spin-free calculations for small molecules

A simple treatment of spin-free quantum theory is applied to 3-electron systems,
constructing the matrix representations and the corresponding projection
operators. The theory is used to treat two example molecules HeH
using a model where an helium atom interacts first with a proton and then
an electron; and linear H3 where a basis of three 1s functions is used to calculate
a set of allowed states. For both systems the energies compare well to
earlier, more extensive, calculations.