Anti-symmetrized integrals, coulomb and exchange integrals

Emieeel commented 3 years ago

Added functionality to extract anti-symmetrized integrals, coulomb and exchange integrals.

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Emieeel commented 3 years ago

@googlebot I signed it!

Emieeel commented 3 years ago

Ah, so, maybe there is some confusion here. Chemists often mean with the coulomb/exchange matrix: $J_{\mu,\nu} = \sum_{\lambda, \sigma} (\mu \nu|\lambda \sigma) D_{\lambda,\sigma}\\ K_{\mu,\nu} = \sum_{\lambda, \sigma} (\mu \lambda|\nu \sigma) D_{\lambda,\sigma}$ in the AO basis, where $D_{\lambda,\sigma}$ is the 1-RDM. I implemented instead $J_{p,q} = (pp|qq)\\ K_{p,q} = (pq|qp)$ in the MO basis.

Do you want to return the first or the second option? In standard quantum chemistry codes as psi4 and pyscf, usually the first case is returned when calling a function as get_jk().

ncrubin commented 3 years ago

I think as a first pass we'll want spin-orbital antisymmeterized 2-electron integrals. 1) we can formulate the Hamiltonian this way (with the 1/4 coeff out front) 2) we can use it to calculate overlaps of the 2-body operator and computational basis states that differ by 2 or fewer occupations. this also let's us calculate the fock operator (when it is not supplied by a computation) as einsum('ijjk', antisymm_spin_orb_tei[:, :occ, :occ, :]). So I think having spin-orbital antisymm 2 electron integrals will be nice to have.

Emieeel commented 3 years ago

The newest commit contains the following changes:

The anti-symmetrized integrals in the spin-orbital basis (and so documented)
A separate function to convert spatial orbitals to spin-orbitals, that is also employed in get_molecular_hamiltonian
Tests to calculate the HF ground state energy with these anti-symmetrized integrals in spin-orbital basis and with coulomb/exchange integrals in the spatial orbital basis

ncrubin commented 3 years ago

@Emieeel Thanks for adding the tests. It looks like formatting and linting are failing. You can use the ./check/pylint script and ./check/format-incremental scripts to help pass this check. ./check/format-incremental --apply will reformat your code according to our style guide.

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ncrubin commented 3 years ago

@googlebot I consent.

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ncrubin commented 3 years ago

Hi @Emieeel you have to run the ./check/format-incremental --apply for the script to automatically reformat the code. As for the coverage I checked the lines not covered and it seems that one was a residual if/else in the test and the others were code paths (MissingCalculations) that were not touched. I added coverage for those lines and resubmitted to your branch. It looks like everything is passing now.

Thank you for the commits. Feel free to open a PR editing the readme with your name and affiliations. You are now officially an OpenFermion developer! Welcome!

quantumlib / OpenFermion