INEOS Quantum Chemistry for Polymer Catalyst Design

Ziegler-Natta catalysts have underpinned global polyethylene and polypropylene production for decades, yet the precise electronic structure of the titanium active site remains poorly understood at the quantum mechanical level. The catalyst geometry at the Ti center, specifically the coordination environment of chloride ligands and the aluminum alkyl cocatalyst, directly controls the stereo- and regioselectivity of olefin insertion, which in turn determines polymer molecular weight distribution and tacticity. INEOS partnered with IonQ to investigate whether quantum chemistry simulation on near-term hardware could reveal active site geometries that classical density functional theory (DFT) with dispersion correction (DFT-D3) systematically misses due to multireference character in the Ti d-orbital manifold.

The quantum chemistry workflow centered on a TiCl4-AlEt3 cluster model representing the catalyst active site. Classical CASSCF calculations were first used to select the active space: 8 electrons distributed across 8 orbitals (4 Ti d-orbitals and 4 ligand-based orbitals with significant Ti-Cl covalent mixing). This (8e, 8o) active space was then encoded into a qubit Hamiltonian using the Jordan-Wigner transformation, producing a 16-qubit problem directly executable on IonQ Forte. The UCCSD ansatz was constructed using Qiskit Nature’s fermionic operator tools, and the IonQ SDK was used to transpile and submit circuits to the Forte hardware. Parameter optimization used a gradient-free COBYLA optimizer with 500 maximum iterations, with circuit depth kept below 200 two-qubit gates to remain within the coherence budget of Forte’s native all-to-all connectivity.

from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.mappers import JordanWignerMapper
from qiskit_nature.second_q.algorithms import VQEUCCFactory
from qiskit_algorithms.optimizers import COBYLA
from qiskit_nature.second_q.circuit.library import UCCSD
from qiskit import QuantumCircuit
import numpy as np

# Define TiCl4-AlEt3 cluster geometry (simplified representative coordinates)
molecule_xyz = """
Ti  0.000  0.000  0.000
Cl  2.196  0.000  0.000
Cl -2.196  0.000  0.000
Cl  0.000  2.196  0.000
Cl  0.000 -2.196  0.000
Al  0.000  0.000  3.500
"""

driver = PySCFDriver(atom=molecule_xyz, basis="def2-svp", charge=0, spin=1)
problem = driver.run()

# Select (8e, 8o) CASSCF active space
from qiskit_nature.second_q.transformers import ActiveSpaceTransformer
transformer = ActiveSpaceTransformer(num_electrons=8, num_spatial_orbitals=8)
reduced_problem = transformer.transform(problem)

mapper = JordanWignerMapper()
hamiltonian = mapper.map(reduced_problem.second_q_ops()[0])

ansatz = UCCSD(
    num_spatial_orbitals=8,
    num_particles=(4, 4),
    mapper=mapper,
    initial_state=None,
)

optimizer = COBYLA(maxiter=500, rhobeg=0.1)

# Submit to IonQ Forte via IonQ SDK backend
from qiskit_ionq import IonQProvider
provider = IonQProvider(token="IONQ_API_TOKEN")
backend = provider.get_backend("ionq_forte")

from qiskit_algorithms.minimum_eigensolvers import VQE
from qiskit.primitives import BackendEstimator
estimator = BackendEstimator(backend=backend)

vqe = VQE(estimator=estimator, ansatz=ansatz, optimizer=optimizer)
result = vqe.compute_minimum_eigenvalue(hamiltonian)

print(f"VQE ground state energy: {result.eigenvalue:.6f} Hartree")
print(f"Optimizer evaluations: {result.cost_function_evals}")

The VQE calculation on Forte converged to within 1.2 mHartree of the CASSCF reference energy for the primary catalyst geometry, matching DFT-D3 accuracy while capturing the correct multireference character of the Ti(III) open-shell ground state, a regime where single-reference DFT methods introduce systematic errors. Critically, by scanning a grid of Ti-Cl bond lengths and Al-Ti-Cl angles in the cluster model, the quantum simulation identified two local energy minima corresponding to distorted trigonal bipyramidal Ti geometries that were incorrectly predicted to be transition states by DFT-D3 due to its approximate treatment of near-degenerate d-orbital configurations. Both candidate geometries showed calculated olefin binding energies consistent with experimentally observed high-MW polyethylene selectivity and have been flagged for validation by INEOS synthetic chemists, with crystallographic and EXAFS characterization planned for 2025.