- The paper demonstrates a new technique combining computational and experimental methods to accelerate the discovery and synthesis of ternary metal phosphosulfides.
- The researchers identified 19 previously unreported stable ternary phosphosulfides using high-throughput DFT screening.
- The multi-fidelity ML model achieved a 5-fold cross-validated MAE of 0.17 eV in band gap prediction, outperforming traditional methods and confirming through experimental validation.
This paper presents an integrated computational and experimental workflow for accelerating the discovery of ternary metal phosphosulfides, a chemically diverse but experimentally neglected class of inorganic materials (2601.16693). The work combines high-throughput density functional theory (DFT) screening, multi-fidelity ML for band gap prediction, and combinatorial thin-film synthesis to address two questions: how application-agnostic properties (synthesizability and band gap) vary across the phosphosulfide compositional space, and whether experimental development of phosphosulfides can be accelerated despite the challenges posed by volatile, corrosive, and toxic precursors such as phosphine and sulfur.
Computational screening of structural motifs and stability
The authors classify all known and hypothetical phosphosulfides into two broad categories: thiophosphates, where phosphorus adopts a high positive oxidation state (+4 or +5) within P–S polyanions that do not bond directly to the metal, and non-thiophosphates, where phosphorus bonds to the metal with negative or neutral oxidation states. Thiophosphates dominate the experimentally synthesized set, comprising 85% of the 72 known compounds. A key empirical finding is that the atomic P/S ratio serves as a reliable discriminator: compositions with P/S ≤ 1/3 yield thiophosphates, while P/S > 1/3 yields non-thiophosphates. Phosphorus is never observed in the −3 oxidation state typical of III–V semiconductors, because it always retains bonding to sulfur or other phosphorus atoms.
The structural chemistry of thiophosphate polyanions is systematically cataloged, including the isolated [PS4]³⁻ tetrahedron, corner-sharing [P2S7]⁴⁻ pairs, chains, and rings, edge-sharing [P2S6]²⁻ units, the ethane-like [P2S6]⁴⁻ dimer (which, notably, is the most common motif), and combinations thereof. Non-thiophosphates exhibit three distinct anion motifs: the simple P–S unit, the S–P–P–S unit, and phosphorus nets combined with sulfide anions. The MPS composition is unique among phosphosulfides in allowing both charge-balanced semiconducting compounds and intrinsically charge-imbalanced metallic phases (e.g., NiPS, TiPS, NbPS).
Using 71 structural prototypes derived from Materials Project entries and decorated with metals of compatible oxidation states, the authors computed formation energies and convex hulls for 909 hypothetical ternary phosphosulfides across 50 M-P-S chemical systems using PBEsol. The choice of PBEsol was validated against experimental lattice parameters on a test set of 14 phosphosulfides, where it outperformed both PBE and r²SCAN. Van der Waals corrections were deliberately excluded after test calculations showed a small and consistent shift (−67.6 ± 9 meV/atom) in formation energies, arguing they would not materially alter hull rankings.
A strong correlation between energy above hull (Eh) and synthesizability emerges: 60% of on-hull phosphosulfides have been synthesized, but this drops sharply to 3% in the 50–100 meV/atom range and only 2% above 100 meV/atom. This contrasts sharply with nitrides, where half of synthesized metastable compounds exceed 100 meV/atom [Sun2016b], confirming that phosphosulfides are thermodynamically more demanding targets.
The screen identified 19 previously unreported ternary phosphosulfides predicted to lie exactly on the stability hull (Eh=0), including four Hf-based, three Zr-based, two Sc-based, and two Cs-based compounds, as well as SiP₂S₆ and GePS₃ — the first ternary phosphosulfides ever predicted in the Si-P-S and Ge-P-S systems. An additional 71 metastable candidates lie below 50 meV/atom. These predictions expand the accessible chemical space considerably and provide concrete targets for experimental validation.
Multi-fidelity machine learning for band gap prediction
To overcome the systematic underestimation of band gaps by semilocal functionals without resorting to computationally expensive hybrid calculations across hundreds of compounds, the authors developed a multi-fidelity deep learning pipeline built on permutation-invariant transformers. Unlike prior approaches requiring structural input [chenLearningPropertiesOrdered2021], this model operates from chemical composition alone plus a band gap value at one of seven fidelity levels (six DFT functionals plus experiment).
The architecture comprises two components: a base model trained on ~350,000 entries spanning PBE, PBE+U, PBEsol, SCAN, GLLB-SC, HSE, and experimental datasets, which learns fidelity-aware elemental embeddings via attention; and a translation layer (an MLP) that takes the source-fidelity gap value together with learned global representation vectors at source and target fidelities to predict the band gap at the target level. Hyperparameter optimization was performed over ~130 Optuna trials using held-out HSE performance as the selection metric.
On a held-out test set of 479 materials, the PBEsol-to-experimental translation model achieves a 5-fold cross-validated MAE of 0.17 eV with R2=0.876. This substantially outperforms a simpler second-order polynomial regression fitted to 39 ternary phosphosulfides with available HSE data (MAE = 0.41 eV on their four synthesized compounds). Validation against the authors' own thin-film samples shows the ML model achieving an MAE of 0.24 eV versus experiment on those four compounds, compared to 1.24 eV for raw PBEsol and 0.14 eV for direct HSE06 calculation. This confirms the practical utility of the approach: near-HSE accuracy at PBEsol computational cost.
Band gap landscape of phosphosulfides
Applying the ML model to the screened set reveals distinct optoelectronic signatures for the two phosphosulfide classes. Thiophosphates cluster predominantly in the 2.3–3.0 eV range with a slight preference for indirect gaps; remarkably, the median difference between the lowest direct gap and the fundamental gap is only 23 meV among indirect-gap thiophosphates, meaning the direct transition lies within thermal energy at room temperature. The peak of this distribution coincides with the maximum observed across all sulfide compounds generally [Varley2017], lending credibility to the methodology. Thiophosphates also show very low propensity toward metallicity. Together, these properties position them as plausible candidates for LEDs, photocatalysis, and solar fuel applications targeting yellow-blue spectral regions.
Non-thiophosphates exhibit a trimodal distribution corresponding to their three anion motifs: the P-S unit peaks near 1.2 eV (indirect by ~0.4 eV), the S-P-P-S motif near 1.7 eV, and P-net-based structures cluster near zero gap (metallic). The authors note a limitation here: the ML model sometimes predicts spurious sub-0.2 eV band openings in compounds that are metallic at PBEsol, particularly charge-imbalanced MPS phases. Since the uncertainty of the model itself is ~0.2 eV, all such cases are conservatively labeled as metals. More broadly, distinguishing true metals from narrow-gap semiconductors remains difficult even experimentally, as illustrated by the Cu₃₋ₓP controversy [crovettoCu3xPSemiconductorMetal2023].
Collectively, phosphosulfides span nearly the full range of useful band gaps up to ~3.6 eV, though ultra-wide gaps above that threshold are absent. The authors acknowledge that non-thiophosphates may be underrepresented because the screening relied on only a handful of structural prototypes, reflecting limited prior research attention; no quaternary non-thiophosphates have been reported, and none involve metals outside the d-block.
Combinatorial thin-film synthesis via DADMARS
The most distinctive contribution is the demonstration that high-throughput experimentation can be extended to phosphosulfide chemistry through directional-and-diffuse multi-anion reactive sputtering (DADMARS). This technique combines magnetron-sputtered metal sources (Cu, Ag), reactive PH₃ gas, and a thermally cracked sulfur beam in a single Ar discharge, generating intentional spatial composition gradients across large substrates (~10 × 8 cm²). Each combinatorial run yields roughly 100 distinct compositions, characterized automatically by EDX mapping, θ-2θ XRD, and spectrophotometric band gap extraction via Tauc analysis.
In just four combinatorial experiments, without pre-existing synthesis recipes, the authors synthesized four single-phase thin-film compounds — Cu₃PS₄, Ag₃PS₄, Cu₇PS₆, and Ag₇PS₆ — all previously unreported in thin-film form. Notably, Ag₃PS₄ and Ag₇PS₆ were obtained simultaneously in a single run. All films are air-stable visible-band-gap semiconductors, with measured optical gaps of 2.5, 2.4, 1.9, and 1.9 eV respectively. Cu₇PS₆ lies 51 meV/atom above the hull computationally, suggesting possible disorder stabilization analogous to Cu₇PSe₆ [Foster2013].
These results carry significant methodological weight beyond phosphosulfides themselves. Many inorganic material families outside oxides, nitrides, and intermetallics require volatile or hazardous precursors, and serial bulk synthesis has been a major bottleneck. The demonstration that DADMARS can produce crystalline, phase-pure films of challenging multi-anion compounds in a single deposition cycle suggests a viable route for accelerated exploration of "difficult" chemistries more broadly. Data management was handled through a NOMAD Oasis instance with automated workflows, keeping human intervention to validation steps.
Limitations and open questions
Several caveats bear on the strength of the results. First, the computational screening was restricted to 71 structural prototypes drawn exclusively from experimentally known phosphosulfide structures; genuinely novel structure types would be invisible to this approach, and the authors concede that many chemically plausible non-thiophosphates may have been misclassified as unstable simply because appropriate prototypes were not considered. Second, oxidation state assignment for non-thiophosphates proved unreliable under automated tools and required extensive manual curation, reflecting genuine chemical ambiguity in this class. Third, the ML band gap model cannot reliably separate metals from very narrow-gap semiconductors, and its uncertainty (~0.2 eV) is comparable to typical experimental error in Tauc-based gap determination (±0.1 eV), so fine distinctions near the metal/semiconductor boundary remain unresolved. Fourth, Hubbard U corrections and spin-orbit coupling were omitted throughout, justified by consistency with the training database rather than by physical arguments specific to phosphosulfides. Finally, only two ternary systems (Cu-P-S and Ag-P-S) were experimentally validated; generalization of the DADMARS throughput claims to other metal phosphosulfides, particularly those involving refractory or open-shell transition metals, remains to be demonstrated. Whether additional synthesizable non-thiophosphates await discovery given better structural priors is left explicitly open.
Conclusion
This paper delivers three coordinated advances: a systematic map of stability, structure, and band gaps across 909 hypothetical ternary phosphosulfides yielding 19 new on-hull compound predictions including the first Si- and Ge-based members; a composition-only multi-fidelity ML model translating PBEsol gaps to experimental fidelity with 0.17 eV cross-validated MAE; and proof that combinatorial thin-film synthesis compatible with hazardous precursor chemistry can deliver multiple phase-pure phosphosulfide compounds per experimental run. The combination demonstrates that theory-AI-experiment workflows are practicable not only for well-behaved oxide systems but also for chemically demanding multi-anion semiconductors, provided the synthesis infrastructure is purpose-built.