uMLIP-RSS Workflow for Chiral Materials Discovery

• The uMLIP-RSS workflow integrates uMLIPs with RSS to perform high-throughput chiral crystal search, reducing 20 million seeds to 142 viable candidates.
• It employs rigorous filters including force relaxation, hull screening, spglib symmetry checks, and phonon stability to ensure thermodynamic and dynamical plausibility.
• The pipeline’s scalable approach accelerates discovery in ternary chiral materials with potential applications in nonlinear optics and superconductivity.

Searching arXiv for the primary paper and closely related work on RSS and ML interatomic potentials. The uMLIP-RSS workflow is a hybrid crystal-structure-discovery pipeline that integrates universal machine learning interatomic potentials (uMLIPs) for high-throughput structure optimization with Random Structure Search (RSS) for broad exploration of candidate configurations. In the formulation developed for ternary chiral materials discovery, the workflow performs massive variable-composition crystal structure prediction across ternary systems while explicitly targeting chiral space groups. Applied at scale, it optimized and screened over 20 million randomly generated chiral structures, identified numerous potentially stable phases outside the existing database, and, after first-principles validation, yielded 142 thermodynamically viable compounds, of which 128 are strictly chiral (Song et al., 6 Aug 2025).

1. Definition, scope, and target search space

In this workflow, the target systems are three ternary families: $\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{X}_{1-3}$, $\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$, and $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$. The structural search is restricted to 64 Sohncke, or chiral, space groups, specified as numbers 3–5, 16–24, …, 207–214. For each composition and each space group, the RSS stage generates up to 30 random structures, imposes Wyckoff-site occupancy, enforces multiplicity parameter $\mu = 1 \ldots 8$, and caps the total number of atoms at 24. If no valid assignment is found after scanning $\mu$ and atom-count combinations, that space group is skipped (Song et al., 6 Aug 2025).

This design couples compositional variability with symmetry-restricted sampling. The search space is therefore not a generic unconstrained crystal-structure search, but a chiral, variable-composition search over explicitly enumerated ternary families. A plausible implication is that chirality is imposed at the generation stage rather than recovered only after relaxation, which reduces wasted screening effort on obviously irrelevant symmetry sectors.

2. Random Structure Search construction

The RSS component samples both symmetry and atomic arrangement. A space group is selected from the 64 Sohncke groups, and, for each Wyckoff-site combination consistent with stoichiometry and multiplicity $\mu$, atoms are placed at random positions in the asymmetric unit subject to minimal distance constraints, given in the detailed overview as approximately $> 1.5\,\text{\AA}$. Space-group operations are then applied to generate the full cell, and structures violating cell-edge or close-pair cutoffs are rejected. The compositional loop spans allowed element triplets drawn from preselected sets, with stoichiometric ratio $1:1:1$ and unit-cell multiplicities $\mu = 1 \ldots 8$ used to increase structural diversity (Song et al., 6 Aug 2025).

The algorithmic controls reported for this stage are explicit. The number of random samples per composition–space-group pair is 30, the multiplicity range is $1 \ldots 8$, the atom-count cap is $\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$0, and the maximum number of attempts per pair is approximately 100 before skipping to the next group. These controls define the practical envelope within which the exploratory part of the pipeline remains tractable at the 20-million-structure scale.

3. uMLIP relaxation and first-pass screening

After random generation, each structure is relaxed with the universal ML interatomic potential mattersim-v1.0.0-1M until the maximum atomic force satisfies $\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$1. For each unique composition, the lowest-energy uMLIP-relaxed structure is retained. The workflow then computes the energy above convex hull, $\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$2, against Materials Project reference data and applies a cutoff $\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$3. Post-optimization structures that become centrosymmetric are discarded using spglib symmetry analysis. This stage yields approximately $\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$4 distinct candidate compositions (Song et al., 6 Aug 2025).

A second screening pass evaluates dynamical stability through phonon dispersion calculations using mattersim-v1.0.0-5M. Any structure with imaginary, or negative-frequency, phonon modes is rejected, leaving approximately $\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$5 dynamically stable candidates. The integration summary also states the dynamical-stability requirement as no imaginary phonon frequencies below approximately $\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$6 (Song et al., 6 Aug 2025).

Stage	Operation	Criterion / outcome
Initial relaxation	uMLIP relaxation with mattersim-v1.0.0-1M	$\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$7
Thermodynamic filter	Hull screening	$\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$8
Symmetry filter	spglib analysis	noncentrosymmetric only
Dynamical filter	uMLIP phonons with mattersim-v1.0.0-5M	no imaginary modes
First-pass outcome	Candidate pool	$\mathrm{A}_{1-3}\mathrm{M}_{1-3}\mathrm{B}_{1-3}$9, then $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$0

The first-pass screening is therefore hierarchical rather than monolithic: local relaxation, hull filtering, symmetry filtering, and phonon stability are applied sequentially. This arrangement separates geometric plausibility, thermodynamic plausibility, symmetry retention, and dynamical plausibility into distinct tests.

4. Homologous substitution and DFT validation

The surviving candidates are expanded by homologous substitution. The workflow performs element substitutions on each site; the examples given are $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$1, $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$2, and $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$3. These derived structures are relaxed with uMLIP to the stricter threshold $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$4, filtered by $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$5, symmetrized, and phonon-screened again. Approximately 277 structures pass to density functional theory (Song et al., 6 Aug 2025).

Final validation is carried out by DFT re-optimization in Quantum Espresso using PBE-ONCV. The reported typical force convergence is $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$6–$\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$7. After re-optimizing the structures, the workflow recomputes $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$8 against Materials Project and applies the cutoff $\mathrm{M}_{1-3}\mathrm{X}_{1-3}\mathrm{S}_{1-3}$9. A final symmetry analysis retains only noncentrosymmetric, chiral space groups, producing 142 thermodynamically viable compounds, of which 128 are strictly chiral (Song et al., 6 Aug 2025).

The reported application space of these validated materials includes topological characteristics, nonlinear optics, and superconductivity. The final set also includes materials exhibiting the nonlinear Hall effect driven by berry curvature dipole, quantum metric and symmetry-enforced six-fold topological points, long Fermi arcs, and large magnetoresistance. Because these statements are tied to the final validated set, they characterize the downstream functional relevance of the pipeline output rather than merely the raw search space.

5. Algorithmic and theoretical basis of the hybrid loop

The uMLIP component is formulated as an atom-wise energy model,

$\mu = 1 \ldots 8$0

where $\mu = 1 \ldots 8$1 is a descriptor vector encoding the local environment of atom $\mu = 1 \ldots 8$2 within a cutoff $\mu = 1 \ldots 8$3, and $\mu = 1 \ldots 8$4 are trainable parameters. The corresponding forces are obtained analytically:

$\mu = 1 \ldots 8$5

The detailed overview further notes that many uMLIPs employ variants of atom-centered symmetry functions, Smooth Overlap of Atomic Positions (SOAP), or equivariant message-passing features, and gives a SOAP example based on local atomic density expansion (Song et al., 6 Aug 2025).

The training objective given in the overview combines energy and force errors,

$\mu = 1 \ldots 8$6

with $\mu = 1 \ldots 8$7 described as typical in order to ensure accurate forces. The same overview explicitly distinguishes these as typical modern-uMLIP choices where the paper itself is silent on exact hyperparameters (Song et al., 6 Aug 2025).

Operationally, the hybrid loop is defined composition by composition. For each composition and each chiral space group, the workflow generates random structures, relaxes them with uMLIP, records $\mu = 1 \ldots 8$8, selects $\mu = 1 \ldots 8$9 as the lowest-energy relaxed structure, discards it if $\mu$0 or if it is centrosymmetric, rejects it if it has imaginary uMLIP phonons, and otherwise adds it to survivors. Homologous substitutions are then generated from survivors, re-relaxed at the stricter force threshold, re-screened by hull, symmetry, and phonons, and finally re-optimized and re-screened at the DFT level before final output (Song et al., 6 Aug 2025).

This hybridization separates global exploration from expensive electronic-structure validation. RSS supplies broad configurational coverage, whereas the uMLIP stages compress the candidate set before DFT is applied.

6. Throughput, efficiency, and terminological scope

The scale of the workflow is central to its definition. The reported throughput includes approximately 20 million random-structure relaxations, a uMLIP relaxation rate of approximately $\mu$1–$\mu$2 structures per GPU-hour, and roughly one structure per $\mu$3. By contrast, pure DFT-RSS is stated to achieve approximately 10–20 relaxations per CPU-core-hour, implying a slowdown greater than $\mu$4. The end-to-end campaign is reported as approximately 10 GPU-weeks plus approximately 10,000 CPU-hours for DFT validation (Song et al., 6 Aug 2025).

The success-rate cascade is likewise explicit: 20,000,000 initial structures are reduced to 3,554 after initial RSS-to-uMLIP screening, then to 142 after phonon screening, substitution, and DFT, with a final chiral set of 128 stable chiral phases. The corresponding percentages are reported as $\mu$5, $\mu$6, and $\mu$7 relative to seeds. A plausible implication is that the workflow is intentionally high-rejection: breadth is concentrated at the generation stage, while the later stages enforce increasingly strict physical and symmetry constraints (Song et al., 6 Aug 2025).

A recurring source of confusion is the acronym “RSS.” In the present workflow, RSS means Random Structure Search. This is distinct from the use of RSS as received signal strength in localization literature, including user positioning in distributed massive MIMO (Prasad et al., 2018), hybrid TDOA/RSS localization in visible-light systems (Kazikli et al., 2018), and trajectory map-matching in urban road networks based on RSS measurements (Xing et al., 3 Feb 2025). The term “uMLIP-RSS workflow” therefore refers here to a materials-discovery pipeline for crystal structure prediction rather than to signal-based positioning or tracking.

7. Scientific significance and limitations of interpretation

Within the reported study, the workflow is presented as a scalable route for discovering chiral inorganic crystals with topological characteristics that are scarce in the existing database. Its scientific significance lies in coupling variable-composition random generation, symmetry-aware filtering, high-throughput uMLIP relaxation, phonon-based dynamical screening, homologous substitution, and DFT validation into one pipeline capable of exploring tens of millions of candidates (Song et al., 6 Aug 2025).

At the same time, the workflow should not be interpreted as eliminating the need for first-principles verification. The reported procedure retains DFT re-optimization, $\mu$8 evaluation, and final symmetry analysis as the decisive validation stage. This indicates that uMLIP-RSS is a discovery and down-selection workflow rather than a replacement for DFT. A plausible implication is that its principal contribution is computational triage at extreme scale: it makes a 20-million-structure search tractable while preserving first-principles confirmation for the final candidate set.