RXN-MFBench: Reaction Multi-Fidelity Benchmark

Code and models: Romarin87/RXN-MFBench.

Datasets of nonperiodic molecules containing carbon, hydrogen, nitrogen, and oxygen, provided as DeepMD HDF5 files, labeled Extended XYZ files, raw reaction-geometry archives, and fixed-geometry reference HDF5 files.

The associated models are intended for nonperiodic, neutral, closed-shell CHON chemistry.

Coordinates are in Å throughout. DeepMD and Extended XYZ labels use total energies in eV and forces in eV/Å. The three *reference.hdf5 files retain the original atomic units: energies in hartree, forces in hartree/bohr, and Hessians in hartree/bohr². Forces are the negative energy gradient, F = −∇E.

Models and interfaces

Release models-v1.0.0 provides 52 model files across DPA2, DPA3, DPA4-Neo, and MACE. Each architecture has one GFN2-xTB pretrained model and protocols S, F, D, and DF, each with seeds 123, 456, and 789. The F and DF runs share the released pretrained starting model for their architecture. The higher-fidelity target is ωB97X-D/def2-TZVP.

Protocol	Training target and initialization	Inference
pretrain	GFN2-xTB total energies and forces	Direct low-fidelity prediction
S	DFT total energies and forces, from scratch	Direct target-level prediction
F	GFN2-xTB pretraining, then DFT total-energy and force fine-tuning	Direct target-level prediction
D	DFT − GFN2-xTB energy and force residuals, from scratch	Learned residual + online GFN2-xTB
DF	GFN2-xTB pretraining, then energy and force residual fine-tuning	Learned residual + online GFN2-xTB

For D and DF, the interfaces add the predicted energy and force residuals to an online GFN2-xTB calculation at the same geometry: E = E(GFN2-xTB) + ΔE and F = F(GFN2-xTB) + ΔF.

See the model documentation for downloads and checksums, the ASE interface for DeePMD and MACE energy/force calculations, and the ASH interface for DeePMD energy/gradient calculations. ASH reaction-path examples cover NEB, transition-state optimization, and IRC.

Repository layout

Data files are grouped by dataset under data/. Paths in the table and Python examples below are relative to the repository root. Files from the same dataset share a directory even when they use different formats.

RXN-MFBench/
├── README.md
└── data/
    ├── RXN-xTB/       # three GFN2-xTB split files
    ├── RXN-xTB-AL/    # DFT training file
    ├── Val/           # R/TS/P energy and force evaluation
    ├── Val-path/      # interior IRC energy and force evaluation
    ├── GDB-10-rxn/    # labeled IRC frames, raw geometries, R/TS/P energies and forces
    ├── GDB-17-rxn/    # labeled IRC frames and raw geometries
    ├── MDCD-NN/       # fixed-geometry energy, force, Hessian, frequency references
    └── Val-Hessian/   # fixed-geometry energy, force, Hessian, frequency references

Files

File	Contents	Frames or reactions	Reference method
data/RXN-xTB/RXN-xTB_train.deepmd.hdf5	Training split	14,082,895 frames	GFN2-xTB
data/RXN-xTB/RXN-xTB_validation.deepmd.hdf5	Validation split	1,760,362 frames	GFN2-xTB
data/RXN-xTB/RXN-xTB_test.deepmd.hdf5	Test split	1,760,359 frames	GFN2-xTB
data/RXN-xTB-AL/RXN-xTB-AL_training.deepmd.hdf5	DFT training data	198,622 frames	ωB97X-D/def2-TZVP
data/Val/Val.deepmd.hdf5	RGD1-derived evaluation data	30,036 frames	ωB97X-D/def2-TZVP
data/Val-path/Val-path.extxyz	DFT evaluation: interior IRC configurations	5,000 frames from 500 reactions	ωB97X-D/def2-TZVP
data/GDB-10-rxn/GDB-10-rxn_irc_path.extxyz	Labeled IRC geometries	7,790 frames from 779 reactions	ωB97X-D/def2-TZVP
data/GDB-17-rxn/GDB-17-rxn_irc_path.extxyz	Labeled IRC geometries	1,740 frames from 174 reactions	ωB97X-D/def2-TZVP
data/GDB-10-rxn/GDB-10-rxn_raw.tar.gz	Raw reaction geometries	779 reaction directories	Geometry only
data/GDB-17-rxn/GDB-17-rxn_raw.tar.gz	Raw reaction geometries	174 reaction directories	Geometry only
data/MDCD-NN/MDCD-NN_reference.hdf5	Fixed R/TS/P geometries, energies, forces, and Hessians	300 structures from 100 reactions	ωB97X-D/def2-TZVP
data/Val-Hessian/Val-Hessian_reference.hdf5	Fixed R/TS/P geometries, energies, forces, and Hessians	300 structures from 100 reactions	ωB97X-D/def2-TZVP
data/GDB-10-rxn/GDB-10-rxn_stationary_reference.hdf5	Fixed R/TS/P geometries, energies, and forces	2,337 structures from 779 reactions	ωB97X-D/def2-TZVP

data/Val/Val.deepmd.hdf5 derives from 10,012 RGD1 reaction records and contains 10,012 reactant, 10,012 transition-state, and 10,012 product geometries. Shared endpoint geometries mean that source reaction-record counts should not be interpreted as counts of unique molecules.

DeepMD HDF5 layout and loading

In the five *.deepmd.hdf5 files, each composition group contains:

• type_map.raw: element mapping ['C', 'H', 'N', 'O'].
• type.raw: per-atom indices into that mapping.
• nopbc: nonperiodic-system marker.
• set.* groups containing coord.npy, energy.npy, and force.npy.

Coordinates and forces use atom-major Cartesian order: x₁, y₁, z₁, x₂, y₂, z₂, …. Composition-group, set, and row order is a storage arrangement, not an ordering of reactant/transition-state/product triplets.

Use dpdata to read these files with its deepmd/hdf5 format. Each file contains multiple composition groups, which are loaded as a MultiSystems collection of LabeledSystem objects:

import dpdata

systems = dpdata.MultiSystems().from_deepmd_hdf5("data/Val/Val.deepmd.hdf5")
print("Total frames:", systems.get_nframes())  # 30036

for system in systems:
    atom_names = system["atom_names"]
    atom_types = system["atom_types"]
    coordinates = system["coords"]   # (nframes, natoms, 3), Å
    energies = system["energies"]    # (nframes,), eV
    forces = system["forces"]        # (nframes, natoms, 3), eV/Å

MultiSystems loads the selected file into memory. For a large file, load an individual composition group with dpdata.LabeledSystem("data/<dataset>/file.deepmd.hdf5#group_name", fmt="deepmd/hdf5"), replacing group_name with its actual HDF5 group name. Interpret atom_types using the atom_names returned by dpdata.

GDB labeled frames and raw geometries

Each GDB Extended XYZ file contains exactly 10 labeled frames per reaction. Its Properties fields include species, pos, and forces, with an energy value stored for each frame. These files can be read with ASE:

from ase.io import iread

for atoms in iread("data/GDB-10-rxn/GDB-10-rxn_irc_path.extxyz", format="extxyz"):
    coordinates = atoms.get_positions()     # Å
    energy = atoms.get_potential_energy()   # eV
    forces = atoms.get_forces()             # eV/Å

The raw archives use these case-sensitive directory layouts:

data/GDB-10-rxn/GDB-10-rxn_raw.tar.gz: raw/Reaction<number>/{R,P,TS,IRC}.xyz
data/GDB-17-rxn/GDB-17-rxn_raw.tar.gz: raw/reaction<number>/{R,P,TS,IRC}.xyz

R.xyz, P.xyz, and TS.xyz each contain a single reactant, product, or transition-state geometry; IRC.xyz contains the full reaction path. These raw files contain geometry only. DFT labels are provided for the selected Extended XYZ frames, not every point along each full IRC path.

Every labeled GDB frame exactly matches coordinates on its corresponding raw IRC path. Extended XYZ file order is not guaranteed to follow IRC path order.

Val-path IRC configurations

data/Val-path/Val-path.extxyz contains 5,000 DFT-labeled interior IRC configurations from 500 reactions in the fixed higher-fidelity validation reaction split. Each reaction contributes ten frames, five per IRC branch, evaluated at ωB97X-D/def2-TZVP for neutral singlets under nonperiodic conditions. Coordinates are in Å, total energies in eV, and forces in eV/Å.

Frames form consecutive ten-frame reaction blocks, ordered point_01–point_10: the first five belong to branch 1 and the last five to branch 2. Branch labels do not specify a fixed reactant/product orientation. Each branch contributes the nearest accepted interior IRC points to fractions j/6, for j = 1, …, 5, of its recorded endpoint reaction coordinate.

Of the 500 source IRC calculations, 190 reached the configured point limit. The dataset represents selected interior configurations; connectivity-based endpoint acceptance does not certify optimized endpoint minima.

Use the ASE iread(..., format="extxyz") example above with data/Val-path/Val-path.extxyz; retrieve labels with get_potential_energy() and get_forces().

Fixed-geometry energy, force, and Hessian references

The three *reference.hdf5 files use a dedicated HDF5 schema, CHON-stationary-reference-v1, read with h5py. The DeepMD/dpdata example above applies to the *.deepmd.hdf5 files.

Each file stores an ordered UTF-8 structure_ids array and groups at structures/<reaction_id>/<state>, where state is R, TS, or P. The array contains consecutive R/TS/P triplets; follow this array when reading the original benchmark order. Each group identifies a neutral singlet, nonperiodic structure and preserves its original atom order. The numeric fields are:

Field	Shape	Units	Availability
atomic_numbers	(N,)	atomic number	All three files
coordinates_angstrom	(N, 3)	Å	All three files
energy_hartree	scalar	hartree	All three files
forces_hartree_per_bohr	(N, 3)	hartree/bohr	All three files
hessian_hartree_per_bohr2	(3N, 3N)	hartree/bohr²	MDCD-NN and Val-Hessian
frequencies_cm_minus1	(3N−6,) or (3N−5,)	cm⁻¹	MDCD-NN and Val-Hessian

Each numeric dataset also has a units attribute. Hessians are full, symmetric Cartesian second-derivative matrices in x₁,y₁,z₁,x₂,y₂,z₂,… order, without mass weighting or translation/rotation projection. Their atom order and coordinate frame match the coordinates and forces in the same group. The separately stored Gaussian harmonic frequencies are diagnostic quantities, not the eigenvalues of this unmass-weighted matrix. Fixed-geometry calculations may have imaginary frequencies; all structures and their signed frequencies are retained.

import h5py

with h5py.File("data/MDCD-NN/MDCD-NN_reference.hdf5", "r") as data:
    for structure_id in data["structure_ids"].asstr()[:]:
        group = data["structures"][structure_id]
        reaction_id = group.attrs["reaction_id"]
        state = group.attrs["state"]
        atomic_numbers = group["atomic_numbers"][:]
        coordinates = group["coordinates_angstrom"][:]
        energy = group["energy_hartree"][()]             # hartree
        forces = group["forces_hartree_per_bohr"][:]     # hartree/bohr
        if "hessian_hartree_per_bohr2" in group:
            hessian = group["hessian_hartree_per_bohr2"][:]  # hartree/bohr²

The same example reads data/Val-Hessian/Val-Hessian_reference.hdf5 and data/GDB-10-rxn/GDB-10-rxn_stationary_reference.hdf5 by changing the file path. All three files provide identifiers, atomic numbers, coordinates, energies, and forces; Hessians and frequencies are available in MDCD-NN and Val-Hessian. To convert to eV-based units, multiply energy by the file attribute hartree_to_eV, forces by hartree_to_eV / bohr_to_angstrom, and Hessians by hartree_to_eV / bohr_to_angstrom**2. The stored atomic-unit values retain the precision available in their reference sources.

MDCD-NN

The 100 reactions are neutral_001–neutral_100, with R/TS/P geometries from MDCD-NN, revision 31d7b2a10cacec07e885f799d7548c95682676eb. The upstream geometry level is described as gCP(TZ)-ωB97X-D4/def2-TZVP. The energies, forces, and Hessians in this release were calculated in this work with Gaussian at ωB97X-D/def2-TZVP (wb97xd def2tzvp freq nosymm) at those fixed geometries.

Val-Hessian

The 100 reactions were selected from the existing 500-reaction Val-path cohort using proportional heavy-atom-count stratification and seed 20260929. The file contains the preserved source R/TS/P geometries with ωB97X-D/def2-TZVP energy, force, and Hessian labels from fixed-geometry frequency calculations. These are the reference R/TS/P structures, rather than the ten interior IRC configurations per reaction in data/Val-path/Val-path.extxyz. Reaction IDs are retained as MR_<number>_<number>.

GDB-10 fixed-geometry energies and forces

The 779 reactions contain one R/TS/P triplet each, ordered by numeric Reaction<number> ID. Coordinates are taken from the corresponding Gaussian Input orientation tables; energies and forces are from the ωB97X-D/def2-TZVP single-point calculations at those geometries (wb97xd def2tzvp force nosymm). The file provides fixed-geometry energy and force references, including the energies used for reaction-energy and forward-barrier evaluation, alongside the separately supplied IRC-frame dataset.

Every one of the 2,337 structures includes forces_hartree_per_bohr with shape (N, 3). These values are taken directly from the Gaussian Forces (Hartrees/Bohr) table, preserving its nine-decimal-place printed precision in float64 storage. The sign is the physical force, F = −∇E. Atom order and the Input-orientation coordinate frame match atomic_numbers and coordinates_angstrom; all logs contain a single Input orientation and a single force table.

For each triplet, the reaction energy is E(P) − E(R) and the forward barrier is E(TS) − E(R). The full 779-reaction cohort includes Reaction7714, whose reference forward barrier is negative; it is retained as in the complete reference cohort. Structure labels describe the source R/TS/P assignment and do not certify stationary points at the single-point label level.