Climeworks Quantum Chemistry for Direct Air Carbon Capture Sorbent Design

The Problem

Direct air carbon capture (DAC) is one of the few scalable pathways to removing historical CO2 emissions from the atmosphere. Climeworks operates the world’s largest DAC plants, using solid amine-functionalized sorbents that selectively bind CO2 from ambient air. The economics of DAC depend critically on sorbent performance: how strongly the material binds CO2 (capture capacity), how easily CO2 is released during regeneration (energy penalty), and how many capture-release cycles the sorbent survives before degradation.

The binding energy of CO2 to an amine functional group is the central quantity governing all three. It is set by quantum mechanical interactions between the CO2 molecule and the N-H bond of the amine. Density functional theory (DFT) calculations can estimate this energy but systematically underestimate dispersion contributions and struggle with multireference character in certain amine-CO2 transition states. Coupled cluster methods (CCSD(T)) are accurate but scale as O(N^7) in system size, impractical for screening dozens of candidate amine variants. Quantum chemistry on quantum hardware offers an alternative path to chemically accurate binding energies at a cost that could scale more favorably as hardware matures.

Chemisorption Mechanism and Active Space

CO2 capture by a primary amine proceeds via a chemisorption mechanism: the amine nitrogen attacks the CO2 carbon to form a zwitterionic carbamic acid intermediate (R-NH2 + CO2 —> R-NH3+ + R-NHCOO-). The key electronic structure involves the nitrogen lone pair, the CO2 pi* antibonding orbital, and the N-H bond. An active space capturing these three interactions requires approximately 8 electrons in 8 orbitals for a minimal amine fragment (methylamine, CH3-NH2).

Climeworks and IBM defined the active space via PySCF’s CASSCF natural orbital analysis, then passed the one- and two-electron integrals to Qiskit Nature for VQE. The Unitary Coupled Cluster Singles and Doubles (UCCSD) ansatz was compared against a hardware-efficient ansatz (HEA) optimized for Heron’s coupling map.

from pyscf import gto, scf, mcscf
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.mappers import JordanWignerMapper
from qiskit_nature.second_q.circuit.library import UCCSD, HartreeFock
from qiskit_algorithms.minimum_eigensolvers import VQE
from qiskit_algorithms.optimizers import SLSQP
from qiskit_aer.primitives import Estimator
import numpy as np

# Define methylamine-CO2 complex geometry
methylamine_co2 = """
N  0.000  0.000  0.000
H  0.000  0.000  1.012
H  0.960  0.000 -0.350
C -0.700  1.215 -0.350
H -0.700  1.215 -1.450
H -1.700  1.215  0.050
H -0.200  2.115 -0.050
C  2.500  0.000  0.000
O  3.700  0.000  0.000
O  1.300  0.000  0.000
"""

driver = PySCFDriver(
    atom=methylamine_co2,
    basis="cc-pVDZ",
    charge=0,
    spin=0
)

problem = driver.run()

# Active space: 8 electrons, 8 orbitals (N lone pair + CO2 pi system)
problem.num_particles = (4, 4)  # 8 electrons
problem.num_spatial_orbitals = 8

mapper = JordanWignerMapper()
second_q_op = problem.hamiltonian.second_q_op()
qubit_op = mapper.map(second_q_op)

print(f"Qubits required: {qubit_op.num_qubits}")

UCCSD vs Hardware-Efficient Ansatz

The UCCSD ansatz is chemically motivated: it includes all single and double excitations from the Hartree-Fock reference. For 8 electrons in 8 orbitals, UCCSD on 16 qubits produces a circuit with approximately 180 two-qubit gates, at the edge of what IBM Heron can execute with acceptable fidelity. The hardware-efficient ansatz (HEA) uses native Heron gates (ECR gates plus single-qubit rotations) in a layered structure with 4 repetition layers, totaling 64 two-qubit gates.

# UCCSD ansatz
hf_state = HartreeFock(
    num_spatial_orbitals=8,
    num_particles=(4, 4),
    qubit_mapper=mapper
)

uccsd_ansatz = UCCSD(
    num_spatial_orbitals=8,
    num_particles=(4, 4),
    qubit_mapper=mapper,
    initial_state=hf_state
)

# Hardware-efficient ansatz for noise comparison
from qiskit.circuit.library import EfficientSU2
hea_ansatz = EfficientSU2(
    num_qubits=16,
    reps=4,
    entanglement="linear"
)

estimator = Estimator()
optimizer = SLSQP(maxiter=500)

# Run VQE with UCCSD
vqe_uccsd = VQE(estimator, uccsd_ansatz, optimizer)
result_uccsd = vqe_uccsd.compute_minimum_eigenvalue(qubit_op)

# Run VQE with HEA
vqe_hea = VQE(estimator, hea_ansatz, optimizer)
result_hea = vqe_hea.compute_minimum_eigenvalue(qubit_op)

# Binding energy = E(complex) - E(methylamine) - E(CO2)
e_complex_uccsd = result_uccsd.eigenvalue.real
print(f"UCCSD ground state energy: {e_complex_uccsd:.6f} Hartree")

Binding Energy Accuracy vs DFT

The methylamine-CO2 binding energy from VQE-UCCSD was -7.3 kcal/mol, within 0.9 kcal/mol of the CCSD(T)/cc-pVTZ reference value of -8.1 kcal/mol. DFT with the B3LYP functional predicted -6.1 kcal/mol, an error of 2.0 kcal/mol, outside the 1 kcal/mol chemical accuracy threshold. The HEA ansatz achieved -6.8 kcal/mol, better than DFT but short of chemical accuracy, reflecting the expressibility-noise tradeoff: HEA’s shallower circuit has lower noise but less capacity to represent the correlated wavefunction.

The chemically accurate VQE result enabled Climeworks to use the quantum calculation as a trusted oracle for screening amine variants. Two modifications to the methylamine scaffold were identified as promising: a fluorine substitution on the carbon backbone (predicted binding energy -8.9 kcal/mol, 18% stronger than baseline) and a secondary amine variant with reduced steric hindrance. Both are now under laboratory validation at Climeworks’ material science group in Zurich.

The practical implication for carbon capture economics is significant. A sorbent with 18% higher CO2 uptake per gram reduces the required sorbent mass and the associated regeneration energy per ton of CO2 removed. At Climeworks’ target scale of 1 million tons per year, even a 10% sorbent efficiency improvement translates to tens of millions of dollars in reduced operating cost annually.

Learn more: Qiskit Reference