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GQCG / GQCP

The Ghent Quantum Chemistry Package for electronic structure calculations
https://gqcg.github.io/GQCP/
GNU Lesser General Public License v3.0
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Implement spin expectation values for all HF models #584

Open lelemmen opened 4 years ago

lelemmen commented 4 years ago

Describe the feature you'd like It would be nice if the spin expectation values (for S_x, S_y, S_z) could be calculated from the HF QCModels.

Describe what the current code offers in relation to what it lacks It's already possible to calculate these spin expectation values generally, using a contraction of the quantized ElectronicSpin operator and the density matrix, so we can check this specialized implementation with the general implementation

Additional context

xdvriend commented 4 years ago

I will tackle this issue in a separate PR, in order to prevent the current one from becoming too large.

The GHF expectation values are already implemented, so there's just RHF and UHF left to do.

xdvriend commented 4 years ago

@lelemmen I'm a bit confused here. For UHF, I can implement the S_z expectation value using the traces of the alpha-alpha and beta-beta overlap matrices. Should the function just return 0 for S_x and S_y? As for RHF, I can do the same for S_z, but this essentially comes down to trace - trace which seems redundant to me. For S_x and S_y the same problem occurs s with UHF, since the mixed components vanish.

lelemmen commented 4 years ago

Yep, for RHF and UHF you can hard-code the values wherever applicable.

xdvriend commented 4 years ago

@lelemmen Is it possible that RSpinorBasis can't quantize an ElectronicSpinOperator, like the GSpinorBasis can?

lelemmen commented 4 years ago

@lelemmen Is it possible that RSpinorBasis can't quantize an ElectronicSpinOperator, like the GSpinorBasis can?

In principle, any spinor basis may quantize the electronic spin operator. However, in this code, we're making a difference between RSpinorBasis and USpinorBasis, versus GSpinorBasis. The first two are spin-orbital bases, representing the situation where the off-diagonal coefficient blocks in GSpinorBasis are zero. This means that one-electron integrals in the first two spin-orbital basis can be represented by K x K-matrices, while we use 2K x 2K-matrices to represent the one-electron integrals in a GSpinorBasis.

As for your remark, I think that RSpinorBasis can quantize ElectronicSpinOperator, but the resulting SQOneElectronOperator should encapsulate 2K x 2K-matrices, just like the the result of GSpinorBasis.

Your question seems related to #559, since the spin operators aren't singlet operators like the non-relativistic spin-free molecular Hamiltonian.