GQCG
Integrals over spherical GTO shells
Right now, we can only calculate integrals over all-Cartesian ShellSets with Libcint. The problem with the initial development of this interface was that Libcint makes a distinction (_cart vs _sph) for the functions that calculate integrals over these types of shells.
Since we haven't made any distinction between Cartesian GTO shells and spherical GTO shells, we have no possibility to check at compile time which Libcint function should be used.
One solution to this problem is to internally convert any spherical GTO shells into Cartesian GTO shells (using the applicable transformation formulas) and keep only using Cartesian GTO shells with Libcint.
Following this approach, we keep the benefits of using spherical GTO shells: using less basis functions for higher angular momenta.
We need Shell to accommodate both Cartesian and spherical shells, but we only have to convert a spherical shell to Cartesian GTOs.
HORTON has the transformation formulas for spherical GTOs to Cartesian GTOs, so we could test against it.