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Towards Universal Neural Network Potential for Material Discovery Applicable to Arbitrary Combination of 45 Elements

So Takamoto, Chikashi Shinagawa, Daisuke Motoki, Kosuke Nakago, Wenwen Li, Iori Kurata, Taku Watanabe, Yoshihiro Yayama, Hiroki Iriguchi, Yusuke Asano, Tasuku Onodera, Takafumi Ishii, Takao Kudo, Hideki Ono, Ryohto Sawada, Ryuichiro Ishitani, Marc Ong, Taiki Yamaguchi, Toshiki Kataoka, Akihide Hayashi, Nontawat Charoenphakdee, Takeshi Ibuka

arXiv:2106.14583v2cond-mat.mtrl-sciphysics.comp-ph

TL;DR

Computational material discovery needs efficient simulation-based exploration of an enormous chemical space, but most neural network potentials target narrow material classes. This paper develops PFP, a universal potential for arbitrary combinations of 45 elements, and demonstrates quantitatively excellent performance across diverse systems and material-discovery applications.

  • Problem

    Material discovery requires simulation methods capable of searching an astronomically large space of possible material combinations within feasible time.

  • Method

    The authors develop PFP, a single universal neural network potential trained for arbitrary combinations of 45 elements and tested across diverse systems.

  • Results

    PFP achieved quantitatively excellent performance across lithium diffusion, molecular adsorption, alloy transitions, and Fischer–Tropsch catalyst discovery.

  • Takeaways & Limitations

    PFP is versatile for screening a wide range of materials without prior knowledge of target-domain atomic structures, while offering lower computational cost than DFT.

  • Takeaways & Limitations

    The LiFeSO4F and FeSO4F crystal structures were absent from the dataset, which lacked three-body interactions among three different elements in its bulk structures.

Abstract

from arXiv · show

Computational material discovery is under intense study owing to its ability to explore the vast space of chemical systems. Neural network potentials (NNPs) have been shown to be particularly effective in conducting atomistic simulations for such purposes. However, existing NNPs are generally designed for narrow target materials, making them unsuitable for broader applications in material discovery. To overcome this issue, we have developed a universal NNP called PreFerred Potential (PFP), which is able to handle any combination of 45 elements. Particular emphasis is placed on the datasets, which include a diverse set of virtual structures used to attain the universality. We demonstrated the applicability of PFP in selected domains: lithium diffusion in LiFeSO${}_4$F, molecular adsorption in metal-organic frameworks, an order-disorder transition of Cu-Au alloys, and material discovery for a Fischer-Tropsch catalyst. They showcase the power of PFP, and this technology provides a highly useful tool for material discovery.

I. INTRODUCTION · II. RESULTS · A. Lithium diffusion

Material discovery requires simulation methods that can search astronomically large chemical spaces beyond the practical reach of quantum calculations. PFP addresses the generalization gap with a universal 45-element NNP and reproduces one-dimensional lithium diffusion in LiFeSO4F with high quantitative accuracy.

  • I. INTRODUCTION: Astronomically many possible material combinations make computer simulations necessary for searching candidate materials within feasible time.
  • I. INTRODUCTION: Quantum chemical simulations capture atomistic phenomena but require enormous computational resources, limiting their practical use in material discovery.
  • I. INTRODUCTION: Existing NNP datasets based on known structures struggle to generalize to unknown materials, while structure-specific models require recreating datasets and potentials.
  • I. INTRODUCTION: The study improves robustness and generalization by aggressively including unstable structures, irregular elemental substitutions, disordered systems, and varied crystal and molecular structures.
  • I. INTRODUCTION: PFP is a universal NNP capable of handling any combination of 45 elements selected from the periodic table.
  • A. Lithium diffusion: Faster lithium diffusion, corresponding to lower activation energy, is important for increasing lithium-ion battery charge-discharge rates.
  • A. Lithium diffusion: PFP qualitatively reproduces the DFT finding that tavorite-structured LiFeSO4F exhibits one-dimensional lithium diffusion and quantitatively reproduces the result with high accuracy.

B. Molecular adsorption in metal-organic framework

PFP was tested on metal-organic frameworks excluded from its training dataset, where it reproduced experimental crystal structures and water–metal-center interactions with generally close agreement to literature results.

  • Motivation: MOFs provide a demanding test for PFP because their diverse organic–inorganic chemistry and crystalline pore structures are difficult for conventional potentials to reproduce without parameter finetuning.DFT can address these difficulties but requires tremendous computational costs.
  • Out-of-domain evaluation: None of the selected MOF structures were included in PFP’s training dataset, making the geometry-optimization tests out-of-domain evaluations.Starting crystalline structures came from the Cambridge Structure Database and were cleaned by removing physically adsorbed pore molecules.
  • Crystal-structure optimization: +4.5% and +3.4% mean absolute errors in MOF cell volume were obtained with and without dispersion corrections, respectively, while predicted lattice parameters agreed well with experiment.Individual cell parameters are provided in Supplementary Data 15.
  • Water adsorption: The largest water-binding-energy deviation occurred for Mg at more than 10%, whereas all other selected MOFs remained within a few percentage points on average.For the MOF-74 series, agreement with literature was better using PFP+D3, consistent with the vdw-DF functional used in reported calculations.
  • Generalization: PFP predicted metal-center–water interactions in MOFs and metal-organic complexes absent from training by learning from isolated-molecule and periodic-solid energies and forces.The passage states that neither the MOFs nor the examined metal-organic complexes were explicitly included in the training dataset.

C. Cu-Au alloy order-disorder transition · D. Material discovery for a Fischer–Tropsch catalyst

PFP was applied to Cu-Au order-disorder transitions across three compositions and to Fischer–Tropsch catalyst modeling. It reproduced composition-dependent transition behavior and predicted reaction activation energies with high fidelity, enabling promoter screening that identified V as especially effective.

  • C. Cu-Au alloy order-disorder transition: PFP simulations examined CuAu3, CuAu, and Cu3Au using 4 × 4 × 4 expanded unit cells as starting geometries for Metropolis Monte Carlo sampling.The simulations targeted transition temperatures between ordered and disordered phases.
  • C. Cu-Au alloy order-disorder transition: Order parameters showed a clear transition from ordered low-temperature structures to dispersed, disordered configurations as temperature increased.Voronoi weighted Steinhardt parameters were used to characterize the resulting structures.
  • C. Cu-Au alloy order-disorder transition: 300–400 K for CuAu3, 800–900 K for CuAu, and 600–700 K for Cu3Au were the calculated transition temperatures, consistent with reported composition-dependent trends.Reported transition temperatures were CuAu3, 440–480 K; CuAu, 670–700 K; Cu3Au, 660–670 K.
  • D. Material discovery for a Fischer–Tropsch catalyst: PFP was used to study methanation and CO dissociation on Co surfaces within the Fischer–Tropsch reaction, which synthesizes hydrocarbons from hydrogen and carbon monoxide.The study focused on methanation reactions and CO dissociation processes on Co surfaces.
  • D. Material discovery for a Fischer–Tropsch catalyst: 0.98 correlation coefficient and 0.097 eV mean absolute error were obtained when PFP activation energies were compared with reported values for methanation reactions on Co(0001).The calculations included zero-point energy corrections and used CI-NEB with 14 images for each process.
  • D. Material discovery for a Fischer–Tropsch catalyst: PFP screened Ag, Ce, K, Li, Mg, Mn, Na, Pt, Ru, V, and Zn as promoter elements for CO dissociation on Co surfaces.The screening addressed the critical CO dissociation step and sought reductions from the approximately 1 eV barrier reported for pure Co surfaces.
  • D. Material discovery for a Fischer–Tropsch catalyst: Approximately 40% reduction in the activation barrier was found with V, while the other promoters had minor effects; CO bridged Co and V sites on Co(1121).The lowest-energy V-promoted configuration placed the CO molecule across Co and V bridge sites.

III. DISCUSSION … 1. Systems and Structures

PFP is a universal neural network potential for arbitrary combinations of 45 elements, combining broad elemental coverage, unanticipated phenomena, quantitative accuracy, low computational cost, and applicability to material discovery. Its original dataset spans diverse systems and structures, with DFT-derived energies and forces supporting universal-potential construction.

  • III. DISCUSSION: PFP operates on systems containing any combination of 45 elements.
  • III. DISCUSSION: A single PFP model describes diverse phenomena with high quantitative accuracy and low computational cost.
  • III. DISCUSSION: The Fischer–Tropsch catalyst study demonstrates PFP in an actual material discovery task.
  • III. DISCUSSION: PFP simultaneously handles diverse elements, unanticipated phenomena, and substantially faster computation than DFT.
  • III. DISCUSSION: PFP enables material screening without prior knowledge of target-domain atomic structures.
  • 1. Systems and Structures: The dataset was generated to cover diverse systems and provide data necessary for constructing a universal potential.
  • 1. Systems and Structures: The original dataset covers molecular, crystal, slab, cluster, adsorption, and disordered systems, sampling optimized, vibrational, and molecular-dynamics structures.
  • 1. Systems and Structures: Molecular and crystal datasets contain DFT-derived structures, total energies, and forces, while crystal data also include atomic charges.

2. Training with multiple datasets · 3. DFT calculation conditions

PFP was trained concurrently on multiple datasets with differing DFT conditions by conditioning training and inference on explicit DFT labels. The datasets used distinct molecular and crystal DFT protocols, including unrestricted or restricted molecular calculations and spin-polarized crystal calculations with PBE, PAW, and plane waves.

  • 2. Training with multiple datasets: The OC20 dataset was added to the molecular and crystal datasets as an additional training dataset.This created a combined training setting involving multiple datasets generated under different DFT conditions.
  • 2. Training with multiple datasets: Different DFT conditions made naïve dataset merging ineffective because overlapping regions could produce inconsistent energy surfaces.The authors nevertheless sought to combine the datasets to improve generalization because each was well sampled in its area of strength.
  • 2. Training with multiple datasets: Explicit DFT-condition labels enabled concurrent training on mutually contradictory datasets and selection of the inferred condition during inference.The method assigns labels during both training and inference, allowing the model to distinguish datasets generated under different conditions.
  • 2. Training with multiple datasets: The simultaneous-training mechanism is expected to become more important as datasets grow larger.The authors identify future dataset expansion as a motivation for supporting simultaneous training under different DFT conditions.
  • 2. Training with multiple datasets: The crystal dataset was treated as the basic dataset, and all reported applications used their corresponding calculation mode.This establishes the crystal dataset as the reference mode for the applications presented in the study.
  • 3. DFT calculation conditions: Molecular DFT used ωB97X-D with 6-31G(d) in Gaussian 16, using unrestricted symmetry-broken calculations for wavefunction symmetry breaking and restricted calculations for geometry optimization.Only singlet or
  • 3. DFT calculation conditions: Crystal DFT used spin-polarized PBE in VASP 5.4.4 with GPU acceleration, the PAW method, and a plane-wave basis.The protocol was designed for a wide variety of systems, including insulators, semiconductors, and metals, under the same conditions.
  • 3. DFT calculation conditions: Crystal calculations used Gaussian smearing with a smearing width of 0.05 eV and GGA+U with Dudarev U−J parameters for all structures, including metals.Both parallel and antiparallel magnetic configurations were calculated to consider ferromagnetism and anti-ferromagnetism.

B. Trained properties … 2. NNP characteristics

PFP is trained on system energies, atomic forces, and supplementary atomic charges using a modified TeaNet architecture. Its design combines short-range repulsion modeling, auxiliary charge prediction, E(3) invariance, locality, extensivity, and higher-order differentiability to support stable atomistic calculations.

  • B. Trained properties: PFP training uses system energy and atomic forces, with atomic charges included as supplementary information about local atomic environments.Charges are not directly used to calculate energy or simulate dynamics.
  • 1. Neural network architecture: PFP uses TeaNet, a graph neural network that message-passes scalar, vector, and 2nd-order tensor values while maintaining required equivariances.The tensor representation captures higher-order geometric features.
  • 1. Neural network architecture: A Morse-style two-body potential is added to TeaNet to reproduce rapidly increasing energy from short-range nuclear repulsion.The term addresses atom pairs much closer than their stable bond distance, including structures that may arise during structure sampling.
  • 1. Neural network architecture: Morse-style potential parameters are trained independently for every possible element combination and added separately to the energy term to improve practical convenience.This treatment avoids the training difficulty associated with extremely large values.
  • 1. Neural network architecture: The architecture outputs atomic charges alongside total energy through the GNN forward path, without an explicit Coulombic interaction term.The charges support post-processing molecular dynamics and increase the number of learned properties.
  • 2. NNP characteristics: PFP is invariant to E(3) transformations and uses fully local interactions, preserving rotational, translational, and mirror-image reversal invariance.Local information cannot propagate over an infinite distance.
  • 2. NNP characteristics: PFP preserves spatial invariances for separated subsystems and extensive energy behavior, including additive energies for separated systems and system-size changes.These properties are described as beneficial for improving generalization.
  • 2. NNP characteristics: PFP remains differentiable to higher order with respect to atomic positions, producing a smooth energy surface relevant to relaxation, NEB, and long-time dynamics calculations.Smoothness is directly related to calculation stability.

V. DATA AVAILABILITY

The paper provides source data, simulation scripts, output data, and the HME21 atomic structure dataset as supplementary materials.

  • Supplementary Script 1 includes simulation scripts and output data corresponding to the results section.
  • Supplementary Script 2 provides the HME21 atomic structure dataset, a portion of the PFP dataset.

VI. CODE AVAILABILITY

The paper provides the NNP architecture benchmark code and TeaNet implementation with trained parameters in Supplementary Script 3, while PFP itself is proprietary and not open-source.

  • Code availability: Supplementary Script 3 provides code for the NNP architecture benchmark using HME21, including the TeaNet implementation with trained parameters.PFP is distributed through proprietary software, with its name and service URL anonymized during peer review.
  • Code availability: PFP can be used to reproduce the reported results through software-as-a-service, although its code and trained parameters are not open-source.The manuscript states that code availability is conditional on acceptance.

VII. AUTHOR CONTRIBUTIONS

The author contributions are anonymized during peer review.

  • Author contributions are anonymized during the peer review process.

Supplementary Information

The supplementary analyses benchmark PFP on challenging adsorbed-structure prediction, test its transferability to realistic molecular and surface components, and show limitations of OC20-only training for material discovery. They also report substantial computational speed advantages and describe diverse dataset components and generation procedures.

  • NN architecture benchmark: OC20 adsorbed-structure prediction was used as a challenging benchmark for evaluating the PFP architecture, with S2EF 2M training data and a held-out validation set.The baseline SchNet and DimeNet++ values came from test datasets, whereas PFP was evaluated on validation data.
  • Silicon crystal properties: Both DimeNet++ and OC20-trained PFP failed to identify diamond as silicon’s most stable structure, predicting BCC and FCC, respectively.The reported inconsistency may not matter when simulating silicon in the diamond-structure phase, but it demonstrates a limitation for material discovery.
  • Regression benchmark: PFP predicted energy and force with high accuracy for adsorbed structures and normal-mode-sampled molecules that were excluded from training.The regression benchmark also included disordered structures generated by melting randomly assembled periodic systems at approximately 10000 K and then 2000 K.
  • Computational efficiency: 20-million times faster than DFT: PFP evaluated energy and forces for 3000 Pt atoms in 0.3 s, versus an estimated typical DFT time of approximately 2 months.The PFP timing was measured on a single NVIDIA V100 GPU using the stated benchmark setup.

A. Lithium diffusion … Cu-Au alloy

PFP’s application comparisons reveal both useful performance and domain-specific limitations: competing models fail or cannot be evaluated for several tasks, while dataset coverage and functional differences constrain interpretation.

  • A. Lithium diffusion: LiFeSO4F and FeSO4F are absent from the explicit crystal-structure dataset, whose bulk structures contain only single-element and binary-element systems.Multielement local environments may instead resemble structures in the disordered dataset.
  • C. Cu-Au alloy order-disorder transition: Ordered and deformed Cu-Au lattices are included in the dataset, but the simulated disordered crystal lattice was not explicitly included.This limits direct assessment of the model’s representation of the disorder transition.
  • D. Material discovery for a Fischer–Tropsch catalyst: The section includes a comparison of PFP applications with the OC20 DimeNet++ model.The comparison is presented as DATA 12.
  • D. Material discovery for a Fischer–Tropsch catalyst: The Fischer–Tropsch comparison used the Open Catalyst Project baseline, whose publicly available dimenetpp all model was trained on all OC20 S2EF data.The implementation was modified for differentiable cell inputs and increased neighbor limits from 50 to 150.
  • D. Material discovery for a Fischer–Tropsch catalyst: The PFP and OC20 comparisons use different DFT functionals—PBE for PFP and RPBE for OC20—so direct comparison requires careful consideration.The catalyst effects shown in the results were not explicitly included in the dataset.
  • A. Lithium diffusion: PFP’s lithium-diffusion comparison shows that dimenetpp all sometimes fails to reproduce the energy barrier along identical NEB images.Lithium diffusion in the bulk structure is outside the scope of OC20 tasks.
  • B. Molecular adsorption in metal-organic framework: DimeNet++ structural optimization did not converge for the MOF comparison, preventing evaluation of volume change rate and adsorption energy.The relevant dataset contains artificial molecules with intramolecular, but not intermolecular, interactions.
  • Cu-Au alloy order-disorder transition: 10−7 eV/atom order formation energy for CuAu rocksalt from dimenetpp all contrasts with the 0.1 eV/atom order DFT value using PBE.The bulk energy was therefore considered inappropriate for reproducing transition phenomena.

Fischer–Tropsch catalyst … DATA 16: METROPOLIS SAMPLING METHOD

The supplementary sections assess PFP for Fischer–Tropsch catalyst calculations and detail simulation protocols for lithium diffusion, MOF optimization, MOF cell-parameter comparison, and Cu–Au Metropolis sampling. PFP produced reasonable NEB diagrams despite differing energies, while dimenetpp all struggled to generate physically reasonable adsorbed structures.

  • Fischer–Tropsch catalyst: PFP and dimenetpp all produced relatively reasonable NEB diagrams despite differing energy values, indicating an interpolation region of the OC20 dataset.The same optimization method and NEB conditions were used for both potentials.
  • Fischer–Tropsch catalyst: dimenetpp all failed to reproduce a reasonable adsorption process, and evaluated structure b at -6.15 eV as more stable than structure c at -1.56 eV.Structure b resulted from optimizing a molecule attached to an optimized surface, whereas structure c was optimized from the molecule placed on the bare surface.
  • DATA 13: MOLECULAR DYNAMICS SIMULATION OF LITHIUM DIFFUSION: Lithium-diffusion trajectories used 100 ps NVT simulations at 300 K, 325 K, 350 K, 375 K, and 400 K, with eight independent trajectories sampled per temperature.Initial momenta followed the Maxwell–Boltzmann distribution, and the lithium atom was verified to travel only along [111].
  • DATA 13: MOLECULAR DYNAMICS SIMULATION OF LITHIUM DIFFUSION: Diffusion coefficients were obtained from the [111]-direction mean squared distance by sampling trajectories every 0.01 ps and fitting the MSD’s linear coefficient over time spans from 0.05 ps to 10 ps.Sampling began 20 ps after the initial state and continued for 80 ps; the Arrhenius plot used the fitted diffusion coefficients.
  • DATA 14: COMPUTATIONAL DETAILS OF MOF: Representative MOF crystal structures were optimized with PFP after CSD-based cleaning that removed physically adsorbed pore molecules while retaining water chemically bound to metal centers.The cleaned structures were called “hydrated” structures, with additional procedures including hydrogen addition and removal of unspecified atoms.
  • DATA 15: COMPARISON OF INDIVIDUAL CELL PARAMETERS OF MOFS CALCULATED BY PFP: Table S5 compares selected MOF unit-cell parameters and volumes after PFP and PFP+D3 optimization against experimental CSD structures using the relative volumetric error ∆Vexp.Each experimental crystal structure was identified by its Cambridge Structure Database identifier.
  • DATA 16: METROPOLIS SAMPLING METHOD: Cu–Au alloy order-disorder simulations used Metropolis sampling in which an arbitrary atom pair was swapped, the structure relaxed, and the energy change ∆E recorded.Because relaxation was computationally expensive, optimization was performed only every 100 steps.
  • DATA 16: METROPOLIS SAMPLING METHOD: The Metropolis acceptance procedure computed exp (−∆E/kBT) and compared it with a uniformly distributed random number between 0 and 1.This comparison followed each recorded energy change in the sampling protocol.

DATA 17: HIGH-TEMPERATURE MULTI-ELEMENT DATASET DESCRIPTION · DATA 19: STATISTICAL INFORMATION OF PFP DATASET · DATA 20: PFP MOLECULE MODE WITH OUT-OF-DOMAIN ELEMENTS

The supplementary sections describe HME21, a high-temperature multi-element subset of PFP intended for dataset analysis and benchmarking, report statistical information for PFP molecule and crystal datasets, and examine molecule-mode transferability for phenol and phenoxide structures. They find that TeaNet performs well on HME21 and that molecule-mode Li and Na behavior imitates crystal mode while benzene-ring bond-distance ratios remain mostly constant.

  • DATA 17: HIGH-TEMPERATURE MULTI-ELEMENT DATASET DESCRIPTION: HME21 is a high-temperature multi-element 2021 atomic-structure subset of the PFP dataset.It corresponds to the disordered dataset and contains structures sampled through high-temperature molecular dynamics.
  • DATA 17: HIGH-TEMPERATURE MULTI-ELEMENT DATASET DESCRIPTION: HME21 is provided to enable further analysis of PFP and serve as a benchmark for future universal NNP development.The dataset’s structural diversity, including element-type counts and neighboring-atom variety, is presented as relevant to the reported molecular-dynamics results.
  • DATA 17: HIGH-TEMPERATURE MULTI-ELEMENT DATASET DESCRIPTION: HME21 contains disordered, high-temperature-sampled structures that are far from stable and carry less molecule- or crystal-specific prior knowledge.The structures were sampled from the entire disordered dataset and randomly split.
  • DATA 17: HIGH-TEMPERATURE MULTI-ELEMENT DATASET DESCRIPTION: TeaNet performed well on both energy and force metrics in the HME21 multi-element NNP architecture benchmark.This result indicates that TeaNet is suitable for multielement structures with unstable coordination.
  • DATA 19: STATISTICAL INFORMATION OF PFP DATASET: Table S7 reports statistical information for the PFP molecule and PFP crystal datasets.The table includes ranges, means, and standard deviations for atom counts, element counts, energies, and forces.
  • DATA 20: PFP MOLECULE MODE WITH OUT-OF-DOMAIN ELEMENTS: Domain transferability was examined by comparing PFP molecule-mode and crystal-mode estimates for phenol, lithium phenoxide, and sodium phenoxide.In crystal mode, all elements are included in the dataset, so the three molecules are expected to be in-domain.
  • DATA 20: PFP MOLECULE MODE WITH OUT-OF-DOMAIN ELEMENTS: Li and Na positions were consistent between molecule and crystal modes, indicating that molecule-mode Li and Na behavior imitates crystal mode.Bond-distance ratios in the benzene ring were mostly constant between the two modes.
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