(Mis)using Fermi.jl with unusual Hamiltonians

[jarvist]

Hello,

I've been developing a little PPP package, and thought it would make sense to re-use the excited state methods from Fermi:
https://github.com/Frost-group/PPP.jl/blob/bb7ea75ff64361e94e684b49528b90d83b9fd45c/src/Fermi.jl#L55-L85

This took me a while, as I ended up hijacking the Molecule builder to create something with a similar sort of number of basis functions. An earlier version was then incorrectly using the STO integrals built into Fermi, but I think this version now correctly packs the PPP / Huckel basis into a form that is used by Fermi.

My question is whether Fermi.jl can do any excited state methods. I believe that the full CI method should have excited states, but currently is solving only for the ground state (first eigenvalue). Is there any fundamental reason why I can't edit that code to look for more states?

Is there any intent to add CIS/CISD/etc. methods to Fermi? Or for EOM CCSD? Or any interest if we were to implement these in Fermi?

[gustavojra]

Hey @jarvist, I would welcome any new methods into Fermi if you feel like it! I think CIS is pretty straightforward to implement and would be a good first step toward excited states.

For the FCI method, you are correct, we are solving it for the first eigenvalue. I am using KrylovKit.jl as the solver as you can see in this line on the RFCI.jl file

tree = build_tree(Is, Nelec - Nfrozen, Nvir - Ninac)
    
    linmap(x) = begin 
        a = get_σ1(Is, hp, eri, x, tree, Nelec)
        a += get_σ3(Is, tree, eri, x, Nelec)
    end
    output("\nStarting eigsolve routine\n")
    klv = eigsolve(linmap, C0, 1, :LM; issymmetric=true, tol=1e-8)

    output("\nKrylov Solver Summary:\n {}", string(klv[3]))

So maybe changing 1 to 2 would be the most straightforward way to get an excited state.

You can even add a new option to the option library something like "fci_num_states" and pass that nember to the krylov solver.

I would love to work on this on the future, but I am changing jobs right now so it may take some time until I can commit to this project. But feel free to play with it and contact me with any questions/comments!

Gustavo

[gustavojra]

Hi @jarvist ! Thank you for the interest in Fermi. This is a follow up to my answer above -- apologies for my delayed response. I am in the middle of a job change (taking up a faculty position and boy it's a lot of work!!)

We certainly would be happy to have excited states methods in Fermi! I think CIS would be the perfect starting point.

Currently, the only way to get excited states in Fermi is hacking the FCI method.

[jarvist]

Thank you Gustavo!

Yes, I think editing Fermi to add fci_num_states is probably the most sensible next step. I will Fork & do this when I get a spare mo.

We have a working CIS within our PPP code; I always get a bit confused about Singlet and Triplet character within here, but I suppose the PPP CIS code is fairly generic , it's essentially just this:
https://github.com/Frost-group/PPP.jl/blob/24523378c412d5cd8146cdca90ec81bd6036bb94/src/CI.jl#L67-L102

Once I get some excitations from FCI, and confirm that the PPP -> Fermi.jl transformation works correctly, that would be a good starting point for then adding CIS to Fermi...