Modularize radial rules about integratorxx HOT 5 CLOSED

I think we're working with a different set of vernacular here - what exactly do you mean by "primitive quadrature"?

For example, for the MHL quadrature, I would view the trapezoidal rule to be the "primitive quadrature" (i.e. the "base" quadrature), but it's not immediately obvious if that's what you mean.

Do you just mean Jacobian inclusion?

Can you perhaps provide a concrete example that exemplifies this issue?

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Yes, that is exactly what I mean. The radial quadratures are composed of two things:

1. the primitive quadrature rule, e.g. trapezoidal quadrature, Gauss-Legendre quadrature, Gauss-Chebyshev quadrature, and
2. the radial transform, which is the key difference between the various rules.

Our recent study J. Chem. Phys. 157, 174114 (2022) examined some combinations of various radial transforms and primitive quadratures. The Ahlrichs M4 grid with Chebyshev quadrature afforded the best convergence.

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Psi4 has a pretty nice implementation, see
https://github.com/psi4/psi4/blob/afd50aa42403e7980b5e2f1fdf5d8be0f239275a/psi4/src/psi4/libfock/cubature.cc#L2396

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from integratorxx.

No, we can definitely restrict to compile time only. A std::function interface would be awesome, though! What I have in my mind is a RadialTransform class that defines r and the Jacobian dr, since these are all what you need to compute the nodes and weights.

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