Quantum chemistry datasets

Quantum chemistry is one of the most promising directions for research in quantum algorithms. Here you can explore our available quantum chemistry datasets for some common molecular systems.

Molecules

We provide the electronic structure data for different geometries of the following molecules:

• Linear hydrogen chains: H₂, H₄, H₅, H₆, H₇, H₈, H₁₀.

• Metallic and non-metallic hydrides: LiH, BeH₂, BH₃, NH₃, H₂O, HF.

• Metallic and non-metallic dimers: He₂, Li₂, C₂, N₂, O₂.

• Charged species: HeH⁺, H₃⁺, OH\(^-\), NeH\(^+\).

• Inorganic molecules: CO, CO₂, N₂H₂, N₂H₄, H₂O₂, O₃.

• Organic molecules: CH₄, HCN, C₂H₂, C₂H₄, C₂H₆.

For H₂ and HeH⁺, data is provided for the minimal basis-set STO-3G, the split-valence double-zeta basis set 6-31G, and the correlation-consistent polarized valence double zeta basis set CC-PVDZ. While, for H₃⁺, data is provided for both STO-3G and 6-31G, for He₂, data is present just for 6-31G. For the remaining molecules, data is only available for the minimal basis set, STO-3G. The molecular geometries are defined by bond lengths and bond angles. For each molecule, the available bond lengths and bond lengths are given in the table below. These are written as [minimum bond length, maximum bond length, number of bond lengths] and contain number of bond lengths equispaced values in the given range. In addition to these, we also include the data for the optimal ground-state geometry of each molecule. While for the molecule that require between 22 and 30 qubits, we do not provide VQE or sampling data for any of the geometries, for ones that require between 24 and 30 qubits, we consider only the optimal ground-state geometries. We summarise all of this information for all the molecules below.

Accessing chemistry datasets

The quantum chemistry datasets can be downloaded and loaded to memory using the load() function as follows:

>>> data = qml.data.load("qchem", molname="H2", basis="STO-3G", bondlength=1.1)[0]
>>> print(data)
<Dataset = description: qchem/H2/STO-3G/1.1, attributes: ['molecule', 'hamiltonian', ...]>

Here, the positional argument "qchem" denotes that we are loading a chemistry dataset, while the keyword arguments molname, basis, and bondlength specify the requested dataset. The possible values for these keyword arguments are included in the table below. For more information on using PennyLane functions please see the PennyLane Documentation.

Molecule	Basis set(s)	#Qubits	Bond length (Å), Bond angle (°)	Optimal geometry (Å, °)
H\(_2\)	STO\(\text{-}\)3G / 6\(\text{-}\)31G / CC\(\text{-}\)PVDZ	4 / 8 / 20	H\(_A-\)H\(_B\) \(\in\ [0.5, 2.1, 41]\) Å H\(_A-\)H\(_B\) \(\in\ [0.5, 2.1, 41]\) Å H\(_A-\)H\(_B\) \(\in\ [0.5, 2.5, 11]\) Å	H\(_A-\)H\(_B = 0.742\) Å
HeH\(^+\)	STO\(\text{-}\)3G / 6\(\text{-}\)31G / CC\(\text{-}\)PVDZ	4 / 8 / 20	He\(-\)H \(\in\ [0.5, 2.1, 41]\) Å He\(-\)H \(\in\ [0.5, 2.1, 41]\) Å He\(-\)H \(\in\ [0.5, 2.5, 11]\) Å	He\(-\)H\(= 0.775\) Å
H\(_3^+\)	STO\(\text{-}\)3G / 6\(\text{-}\)31G	6 / 12	H\(_A-\)H\(_B\) \(\in\ [0.5, 2.1, 41]\) Å, \(\measuredangle\) HHH \(= 60^{\circ}\)	H\(_A-\)H\(_B = 0.874\) Å, \(\measuredangle\) HHH \(= 60^{\circ}\)
H\(_4\)	STO\(\text{-}\)3G	8	H\(_A-\)H\(_B\) \(\in\ [0.5, 1.3, 41]\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)	H\(_A-\)H\(_B = 0.88\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)
He\(_2\)	6\(\text{-}\)31G	8	He\(-\)He \(\in\ [0.5, 6.5, 41]\) Å	He\(-\)He\(= 5.200\) Å
H\(_5\)	STO\(\text{-}\)3G	10	H\(_A-\)H\(_B\) \(\in\ [0.5, 1.5, 11]\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)	H\(_A-\)H\(_B = 1.0\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)
LiH	STO\(\text{-}\)3G	12	Li\(-\)H \(\in\ [0.9, 2.1, 41]\) Å	Li\(-\)H \(= 1.57\) Å
HF	STO\(\text{-}\)3G	12	H\(-\)F \(\in\ [0.5, 2.1, 41]\) Å	H\(-\)F \(= 0.917\) Å
OH\(^-\)	STO\(\text{-}\)3G	12	O\(-\)H \(\in\ [0.5, 2.1, 41]\) Å	O\(-\)H \(= 0.964\) Å
NeH\(^+\)	STO\(\text{-}\)3G	12	Ne\(-\)H \(\in\ [0.5, 2.5, 11]\) Å	Ne\(-\)H \(= 0.991\) Å
H\(_6\)	STO\(\text{-}\)3G	12	H\(_A-\)H\(_B\) \(\in\ [0.5, 1.3, 41]\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)	H\(_A-\)H\(_B = 0.92\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)
BeH\(_2\)	STO\(\text{-}\)3G	14	Be\(-\)H \(\in\ [0.5, 2.1, 41]\) Å, \(\measuredangle\) HBeH \(= 180^{\circ}\)	Be\(-\)H \(=1.330\) Å, \(\measuredangle\) HBeH \(= 180^{\circ}\)
H\(_2\)O	STO\(\text{-}\)3G	14	H\(-\)O \(\in [0.5, 2.1, 41]\) Å, \(\measuredangle\) HOH \(= 104.5^{\circ}\)	H\(-\)O \(=0.958\) Å, \(\measuredangle\) HOH \(= 104.5^{\circ}\)
H\(_7\)	STO\(\text{-}\)3G	14	H\(_A-\)H\(_B\) \(\in\ [0.5, 1.5, 11]\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)	H\(_A-\)H\(_B = 1.0\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)
BH\(_3\)	STO\(\text{-}\)3G	16	B\(-\)H \(\in\ [0.5, 2.1, 41]\) Å, \(\measuredangle\) HBH \(= 120^{\circ}\)	B\(-\)H \(=1.189\) Å, \(\measuredangle\) HBH \(= 120^{\circ}\)
NH\(_3\)	STO\(\text{-}\)3G	16	N\(-\)H \(\in\ [0.5, 2.1, 41]\) Å, \(\measuredangle\) HNH \(= 106.8^{\circ}\)	N\(-\)H \(=1.110\) Å, \(\measuredangle\) HNH \(= 106.8^{\circ}\)
H\(_8\)	STO\(\text{-}\)3G	16	H\(_A-\)H\(_B\) \(\in\ [0.5, 0.9, 41]\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)	N/A
CH\(_4\)	STO\(\text{-}\)3G	18	C\(-\)H \(\in\ [0.5, 2.5, 11]\) Å, \(\measuredangle\) HCH \(= 109.5^{\circ}\)	C\(-\)H \(=1.086\) Å, \(\measuredangle\) HCH \(= 109.5^{\circ}\)
Li\(_2\)	STO\(\text{-}\)3G	20	Li\(-\)Li \(\in\ [1.5, 3.5, 11]\) Å,	Li\(-\)Li \(=2.679\) Å
C\(_2\)	STO\(\text{-}\)3G	20	C\(-\)C \(\in\ [0.5, 2.5, 11]\) Å,	C\(-\)C \(=1.246\) Å
N\(_2\)	STO\(\text{-}\)3G	20	N\(-\)N \(\in\ [0.5, 2.5, 11]\) Å,	N\(-\)N \(=1.120\) Å
O\(_2\)	STO\(\text{-}\)3G	20	O\(-\)O \(\in\ [0.5, 2.5, 11]\) Å,	O\(-\)O \(=1.220\) Å
CO	STO\(\text{-}\)3G	20	C\(-\)O \(\in\ [0.5, 2.5, 11]\) Å,	C\(-\)O \(=1.128\) Å
H\(_{10}\)	STO\(\text{-}\)3G	20	H\(_A-\)H\(_B\) \(= 1.0\) Å, \(\measuredangle\) HHH \(= 180^{\circ}\)	N/A
HCN	STO\(\text{-}\)3G	22	\(\measuredangle\) HCN \(\in\ [0, \pi]^{\circ}\), C\(-\)N \(= 1.156\) Å	\(\measuredangle\) HCN \(= \pi^{\circ}\), C\(-\)N \(=1.156\) Å
H\(_2\)CO	STO\(\text{-}\)3G	24	C\(-\)O \(= 0.9167\) Å, \(\measuredangle\) OCH \(= 102.3^{\circ}\)	C\(-\)O \(= 0.9167\) Å, \(\measuredangle\) OCH \(= 102.3^{\circ}\)
H\(_2\)O\(_2\)	STO\(\text{-}\)3G	24	O\(_A-\)O\(_B\) \(= 1.475\) Å, \(\measuredangle\) OOH \(= 94.8^{\circ}\)	O\(_A-\)O\(_B\) \(= 1.475\) Å, \(\measuredangle\) OOH \(= 94.8^{\circ}\)
N\(_2\)H\(_2\)	STO\(\text{-}\)3G	24	N\(_A-\)N\(_B\) \(= 1.247\) Å, \(\measuredangle\) NNH \(= 106.9^{\circ}\)	N\(_A-\)N\(_B\) \(= 1.247\) Å, \(\measuredangle\) NNH \(= 106.9^{\circ}\)
C\(_2\)H\(_2\)	STO\(\text{-}\)3G	24	C\(_A-\)C\(_B\) \(= 1.203\) Å, \(\measuredangle\) HCC \(= 180.0^{\circ}\)	C\(_A-\)C\(_B\) \(= 1.203\) Å, \(\measuredangle\) HCC \(= 180.0^{\circ}\)
C\(_2\)H\(_4\)	STO\(\text{-}\)3G	28	C\(_A-\)C\(_B\) \(= 1.339\) Å, \(\measuredangle\) CCH \(= 121.2^{\circ}\) \(\measuredangle\) HCH \(= 117.6^{\circ}\)	C\(_A-\)C\(_B\) \(= 1.339\) Å, \(\measuredangle\) CCH \(= 121.2^{\circ}\) \(\measuredangle\) HCH \(= 117.6^{\circ}\)
N\(_2\)H\(_4\)	STO\(\text{-}\)3G	28	N\(_A-\)N\(_B\) \(= 1.446\) Å, \(\measuredangle\) NNH \(= 108.9^{\circ}\) \(\measuredangle\) HNH \(= 106.0^{\circ}\)	N\(_A-\)N\(_B\) \(= 1.446\) Å, \(\measuredangle\) NNH \(= 108.9^{\circ}\) \(\measuredangle\) HNH \(= 106.0^{\circ}\)
C\(_2\)H\(_6\)	STO\(\text{-}\)3G	30	C\(_A-\)C\(_B\) \(= 1.535\) Å, \(\measuredangle\) CCH \(= 110.9^{\circ}\) \(\measuredangle\) HCH \(= 108.0^{\circ}\)	C\(_A-\)C\(_B\) \(= 1.535\) Å, \(\measuredangle\) CCH \(= 110.9^{\circ}\) \(\measuredangle\) HCH \(= 108.0^{\circ}\)
CO\(_2\)	STO\(\text{-}\)3G	30	C\(-\)O \(= 1.162\) Å, \(\measuredangle\) OCO \(= 180.0^{\circ}\)	C\(-\)O \(= 1.162\) Å, \(\measuredangle\) OCO \(= 180^{\circ}\)
O\(_3\)	STO\(\text{-}\)3G	30	O\(_A-\)O\(_B\)\(= 1.278\) Å, \(\measuredangle\) OOO \(= 116.8^{\circ}\)	O\(_A-\)O\(_B\) \(= 1.278\) Å, \(\measuredangle\) OOO \(= 116.8^{\circ}\)

Data features

For each of the molecules mentioned above, the following characteristics can be extracted for each geometry:

Molecular data

Information regarding the molecule, including its complete classical description and the Hartree Fock state.

Name	Type	Description
molecule	Molecule	PennyLane Molecule object containing description for the system and basis set
hf_state	numpy.ndarray	Hartree-Fock state of the chemical system represented by a binary vector

Hamiltonian data

Hamiltonian for the molecular system under Jordan-Wigner transformation and its properties.

Name	Type	Description
hamiltonian	Hamiltonian	Hamiltonian of the system in the Pauli basis
sparse_hamiltonian	scipy.sparse.csr_array	Sparse matrix representation of a Hamiltonian in the computational basis
fci_energy	float	Ground-state energy of the molecule obtained from exact diagonalization
fci_spectrum	numpy.ndarray	First \(2\times\)num_qubits eigenvalues obtained from exact diagonalization

Groupings data

Groupings of the Hamiltonian terms for facilitating simultaneous measurements of all observables within a group.

Name	Type	Description
qwc_groupings	tuple(list[tensor_like], list[list[Operator]], list[tensor_like]])	List of grouped qubit-wise commuting Hamiltonian terms obtained using optimize_measurements()
basis_rot_groupings	tuple(list[tensor_like], list[list[Operator]], list[tensor_like]])	List of grouped Hamiltonian terms obtained using basis_rotation()

Auxiliary observables

The supplementary operators required to obtain additional properties of the molecule such as its dipole moment, spin, etc.

Name	Type	Description
dipole_op	Hamiltonian	Qubit dipole moment operators for the chemical system
number_op	Hamiltonian	Qubit particle number operator for the chemical system
spin2_op	Hamiltonian	Qubit operator for computing total spin \(S^2\) for the chemical system
spinz_op	Hamiltonian	Qubit operator for computing total spin’s projection in the \(Z\) direction

Tapering data

Features based on \(Z_2\) symmetries of the molecular Hamiltonian for performing tapering.

Name	Type	Description
symmetries	list[Hamiltonian]	Symmetries required for tapering molecular Hamiltonian
paulix_ops	list[PauliX]	Supporting PauliX ops required to build Clifford \(U\) for tapering
optimal_sector	numpy.ndarray	Eigensector of the tapered qubits that would contain the ground state

Tapered observables data

Tapered observables and Hartree-Fock state based on the \(Z_2\) symmetries of the molecular Hamiltonian.

Name	Type	Description
tapered_hamiltonian	Hamiltonian	Tapered Hamiltonian
tapered_hf_state	numpy.ndarray	Tapered Hartree-Fock state of the molecule
tapered_dipole_op	Hamiltonian	Tapered dipole moment operator
tapered_num_op	Hamiltonian	Tapered number operator
tapered_spin2_op	Hamiltonian	Tapered total spin operator
tapered_spinz_op	Hamiltonian	Tapered spin projection operator

VQE data

Variational data obtained by using AdaptiveOptimizer to minimize ground state energy.

Note

This data is only available for molecules with basis sets that require 20 or fewer qubits.

Name	Type	Description
vqe_gates	list[Operation]	SingleExcitation and DoubleExcitation gates for the optimized circuit
vqe_params	numpy.ndarray	Optimal parameters for the gates that prepares ground state
vqe_energy	float	Energy obtained from the state prepared by the optimized circuit

Samples data

Samples data obtained from the optimized variational circuit with available Hamiltonian groupings.

Note

This data is only available for molecules with basis sets that require 20 or fewer qubits.

Name	Type	Description
qwc_samples	list[dict]	List of samples for each grouping of the qubit-wise commuting Hamiltonian terms
basis_rot_samples	list[dict]	List of samples for each grouping of the basis-rotated Hamiltonian terms

datasets_qchem

 

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