Thanks for your answer. However, I'm looking for a 1D array, not a 2D array. I ran the code in the section you referenced and all of those outputs were also 2D arrays. — Steve Cox Jan 20 at 16:22

@SteveCox I believe if you have a 2D numpy array, you can flatten it into a 1D array as you need. — S R Maiti Jan 20 at 19:41

Yes, I could flatten it but that isn't what I'm looking for. The mo_coeff is 10x10 and I'm looking for a 10-vector so flattening it would just give me a 100-vector. Also, the shape is just an indication that it isn't what I want. I'm looking for a very specific vector. It might help if I knew better what exactly this mo_coeff matrix is. Does it just transform the basis functions into molecular orbitals? If it does, then summing over the columns of the matrix would give the AO coefficients. Can anyone verify that? — Steve Cox Jan 20 at 20:13

Ok I understand what's going on here. The STO-3G basis refers to the basis we use to represent the Kohn-Sham orbitals, not the density itself. We optimize the coefficients of the orbitals, not the density directly. In pyscf the density is represented on a real space grid which can be generated from the orbitals. Now how should I edit my answer? Either: A) I can explain in more detail ideas like AO coefficients and why we don't optimize the density directly or B) I can show you the code that can get you those grid point values. What is your actual goal? — KobeGote Jan 21 at 3:53

I guess that my goal was to learn how the wave function was represented in DFT calculations. The first Hohenberg-Kohns theorem says that the ground-state density determines the wavefunction so I assumed that DFT methods optimized the density itself but they usually optimize the KS orbitals instead (it looks like orbital-free DFT optimizes the density directly but isn't very accurate). I think option A answers my question best. — Steve Cox Jan 21 at 5:25

You are absolutely correct, and that's a good way to frame it. I've tried to update answer along those lines. This of course changes the answer quite a bit, so anyone who approved the old answer might want to double check... — KobeGote 2 days ago

The answer omits spin dependence; eq 2 is wrong by a factor of 2. The expansion coefficients in eq 3 are transposed from the usual notation (basis functions are in rows, molecular orbitals in columns). Also, the statement "so that it is not straightforward to compute the density in the original basis. Furthermore, just because the original basis can represent the KS orbitals well, there is no guarantee it can represent the density." is wrong; the density is just expanded in the product basis. — Susi Lehtola 6 hours ago

I can edit it to “just because the KS orbitals can be represented well as a linear combination of the original basis functions, there is no guarantee that the density can” if you think that the linear combination part needs to be made clear. The point is to address the comment which asks why we don’t have a vector of coefficients describing the density in the STO-3G basis they used — KobeGote 1 hour ago