Thanks, @jmisiewicz for the response. Yes, I agree that for the purpose of specifying a basis set, this would be a bad idea. I guess it’s probably helpful if I spell out what I want to do.
What I have is a set of coefficients, ci, that define a molecular density in an auxiliary basis set:
density = sum(ci*Xi),
where Xi are the primitives of the auxiliary basis set. What I would like to do is compute the integral for the Hellmann-Feynman force on atom i from that density:
Fi = integral(Zi * density / r^3)
This question relates to the first equation. If there is a way, how do I get that function represented in psi4. If I can do that I think that @andysim has already answered the second part (second equation) in this post. Thanks!