I would like to create a basis set with the following 5 functions and unique sets of parameters alpha, beta, gamma, and position a.

1. 1S type orbital GTO(alpha, [0,0,0])
2. 2S type orbital GTO(beta, [0,0,0])
   2P type delocalized orbitals
3. GTO(gamma, [a, 0, 0]) - GTO(gamma, [-a, 0, 0])
4. GTO(gamma, [0, a, 0]) - GTO(gamma, [0, -a, 0])
5. GTO(gamma, [0, 0, a]) - GTO(gamma, [0, 0, -a])

Where GTO are Gaussian Type Orbitals and alpha/beta/gamma are the GTO parameters and "a" is the delocalization.

Hi,
Neat work!
I just tried to do some benchmark of Quiqbox.jl against openfermion, but got some unit issues. For H2 molecule with bond length of 0.275 angstrom, the Hartree Fock energy calculated from openfermion is -0.46576 Ha, while the result I got from Quiqbox.jl is -2.53861 Ha. I think it must be a unit issues, but I'm not sure where it is. The piece of code I used for the calculation is as below:

using Quiqbox

function calc_H2()
    bond_length = 0.275
    nuc = ["H", "H"]
    nucCoords = [[0.0, 0.0, 0.0], [0.0, 0.0, bond_length]]
    bs = genBasisFunc.(nucCoords, ("STO-3G", "H") |> Ref) |> flatten

    resRHF = runHF(bs, nuc, nucCoords)
    println("Quiqbox:")
    println("bond length = ", bond_length)
    @show resRHF.Ehf
    println()
end 


using PyCall
py"""
from openfermion.chem import MolecularData
from openfermionpyscf import run_pyscf
def get_H2():
    bond_length = 0.275
    geometry = [
                ["H", [0.0, 0.0, 0.0]],
                ["H", [0.0, 0.0, bond_length]],
            ]

    basis = "sto3g"
    spin = 0

    molecule_of = MolecularData(
        geometry,
        basis,
        multiplicity=2 * spin + 1
    )
    molecule_of = run_pyscf(
        molecule_of,
        run_scf=1,
        run_ccsd=0,
        run_fci=0
    )
    print("openfermion:")
    print('At bond length of {} angstrom, molecular hydrogen has:'.format(
        bond_length))
    print('Hartree-Fock energy of {} Hartree.'.format(molecule_of.hf_energy))
""" 


calc_H2()
py"get_H2"()

The result is as below:

Quiqbox:
bond length = 0.275
resRHF.Ehf = -2.538611549467369

openfermion:
At bond length of 0.275 angstrom, molecular hydrogen has:
Hartree-Fock energy of -0.46576369202200985 Hartree.

For more detailed examples of openfermion, please refer to this

Thanks a lot in advance!

Hi,
I would like to get the Hamiltonian in the second quantization after HF calculation, i.e. the coefficient matrix of the Hamiltonian in the Fock space given the basis set calculated by HF method. This is the first step of post-HF method, including FCI and quantum computing algorithms(such as VQE) I'm working on.

I did a little bit of review of the Quiqbox.jl code, and found that maybe I can do it using functions provided by src/Integrals/OneBody.jl and src/Integrals/TwoBody.jl, following the Slater's rules.

Do you have any suggestions for this, and what is the easiest way to achieve this in Quiqbox.jl ?

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