Cartesian Gaussian representation

The reason for the first computer implementations preferring the Cartesian Gaussian representation of the one-particle basis set rather than the real spherical harmonic Gaussian is not quite clear to the author. However, because the Cartesian Gaussians have more elements for a given angular momentum beyond the p shell, and efficient methods to compute ERIs for... 

An alternative (and in fact dominating) representation uses the possibility to represent the Gaussian function of the squared distance in a form of a product of three Cartesian Gaussian orbitals. Indeed as one can easily see... 

In practice the evaluation of the ERIs in the real spherical harmonic representation runs over the Cartesian representation and a transformation occurs between the Cartesian and the real spherical harmonic representation (see Table 2). This is not due to the lack of explicit formulae for ERI generation in the real spherical harmonic Gaussian representation but rather a matter of implementation. The transformation is expressed as... 

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