He pointed out that we could use functions that consisted only of the the spherical harmonics and the exponential term. Slater-type orbitals represent the real situation for the electron density in the valence region and beyond, but are not so good nearer to the nucleus. However, it soon became clear that there was a practical problem. It is very difficult to evaluate the necessary integrals over these STOs when the orbitals in the integral are centred on three or four different atoms. An immense amount of effort has been put into this problem of integral evaluation over STOs, but it still remains a problem.
Accurate results are just about possible, but they are very time-consuming.
In the 1950s, Frank Boys from Cambridge in the UK, suggested an alternative which has been widely taken up. Some early calculations used a large number of individual GTOs. It was then suggested that the GTOs be contracted into separate functions. Each basis function in this approach consists of several GTOs combined together in a linear fashion with fixed coefficients. They are not varied in the variational calculation.