How do I specify the total number of orbitals for qchem.melecular_hamiltonian?

PennyLane Help
1

Hi, I have the following two functions:

def water(charge=0, multiplicity=1, basis_set='sto-3g', active_electrons=4, active_orbitals=4):
    symbols, coordinates = qchem.read_structure('Water.xyz')
    hamiltonian, qubits = qchem.molecular_hamiltonian(
        symbols,
        coordinates,
        charge=charge,
        mult=multiplicity,
        basis=basis_set,
        active_electrons=active_electrons,
        active_orbitals=active_orbitals,
    )

    return hamiltonian, qubits

def hydrogen_fluoride(charge=0, multiplicity=1, basis_set='sto-3g', active_electrons=2, active_orbitals=2):
    symbols = ["H", "F"]
    coordinates = np.array([0.896, 0, 0, -0.896, 0, 0])
    hamiltonian, qubits = qchem.molecular_hamiltonian(
        symbols,
        coordinates,
        charge=charge,
        mult=multiplicity,
        basis=basis_set,
        active_electrons=active_electrons,
        active_orbitals=active_orbitals,
    )

    return hamiltonian, qubits

The molecules obviously have the same number of electrons. But when I run the following code:

    ELECTRONS = 4
    ORBITALS = 4
    H, qubits = hydrogen_fluoride(active_electrons=ELECTRONS, active_orbitals=ORBITALS)

I get an error :

The number of core (3) + active orbitals (4) cannot be greater than the total number of orbitals (6)

However, the code

    ELECTRONS = 4
    ORBITALS = 4
    H, qubits = water(active_electrons=ELECTRONS, active_orbitals=ORBITALS)

runs fine. I looked into it further, and it seems that within the qchem.molecular_hamiltonian function, it has the following code:

mol = qml.qchem.Molecule(
            symbols,
            geometry_dhf,
            charge=charge,
            mult=mult,
            basis_name=basis,
            load_data=load_data,
            alpha=alpha,
            coeff=coeff,
        )

Which returns a mol with n_orbitals = 7 for water and 6 for HF. Any idea how I can fix this?

2

Hi @somearthling! The fix is pretty easy but please let me first explain the issue briefly.

Water has 10 electrons and 7 molecular orbitals while HF has 10 electrons and 6 molecular orbitals. From these 10 electrons you are excluding 6 of them as core electrons by specifying 4 active electrons in your code. That means, you have excluded 3 core orbitals because each orbital can contain two electrons. So for water, you are left with 7 - 3 = 4 active orbitals while for HF you can only have 6 - 3 = 3 active orbitals. In conclusion, you should have

# for H2O:
active_electrons= 4
active_orbitals = 4

# for HF:
active_electrons= 4
active_orbitals = 3

For more details on constructing an active space, please see this function and this demo. Please also let us know if you have other questions.

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3

Hi, thanks! Is there no way to increase the number of active orbitals by treating some of the external orbitals in HF as active?

4

Hi @somearthling, yes you can do it.

One way is to use a smaller number of core electrons and core orbitals. The other way is to use a larger basis set, for example 6-31g, which allows you to have a larger number of active orbitals.

Please let me know if need help with any of these methods!

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