The carbon orbitals expanded in GTOs

Let us now expand the ground-state carbon orbitals in a minimal basis of GTOs with exponents chosen so as to match the expectation values of r given in Section 6.5.7. This prescription gives us the following basis functions 

As expected, the exponents are more spread out than in the corresponding STOs (6.5.34)-(6.5.36). The normalized least-squares approximations 

We have finally arrived at a set of basis functions suitable for nmlecular calculations the spherical-harmonic GTOs in the form (6.6.15) with variable exponents for the radial part of the 

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