materials-chemistry/ai produced the result/arXiv 2024 · v2
Random atoms settle into molecules and crystals on a learned energy surface
Researchers trained a neural network interatomic potential to reproduce made-up forces that appear when known structures are jostled. Random clumps of atoms were then relaxed on that learned surface to produce molecules and crystals.
spectrum · one line per step, placed by what the step does · bright lines used AI
Response Matching for generating materials and molecules
arXiv, 2024
doi:10.48550/arxiv.2405.09057 · record aix-00113 v2 · checked 2026-10-08
- AI was for
- Candidate generation, Structure determination
- Model family
- Multilayer perceptron
- Checked by
- Benchmark15 tested, 8 worked
- Code
- not reported
The finding the paper is about came from the AI.
What this research was about
Atoms in a stable molecule or crystal sit in an arrangement where the forces pulling on each one cancel out. Chemists picture this as a landscape, the potential energy surface, in which stable structures are the valleys. Working out which arrangement a given set of elements will adopt usually means searching that landscape, and the search is expensive because every trial arrangement has to be evaluated by quantum mechanical calculation. Generating plausible new molecules or crystal structures from scratch is hard for the same reason: there are vastly more ways to scatter atoms in a box than there are arrangements a chemist would recognise as real.
This work takes a different route to the landscape. Instead of computing real energies, the researchers built an artificial one whose valleys sit at the structures they already know, then let random configurations roll downhill into it.
Where AI came in
The researchers took equilibrium structures from two public collections, QM7b organic molecules and MP-20 crystals from the Materials Project, plus a single cubic diamond cell. They nudged the atoms off their resting positions and distorted the crystal cells, and for each nudged structure they wrote down invented forces and stresses: a spring pulling each atom back towards where it started, plus a short-range push keeping atoms apart. A CACE interatomic potential, a model that turns a description of each atom's surroundings into an energy through a multilayer perceptron, was trained from scratch to predict those invented forces. No real energies or measured properties went into the training targets.
The trained model then served as the generator. Atoms of a chosen composition were dropped at random positions in a box, and the FIRE optimiser relaxed positions and cell until the model's forces faded, so the structure settled into a valley of this pseudo energy surface. Every molecule and crystal reported is the output of that relaxation, standing in for the quantum mechanical simulation that would otherwise supply the forces. Molecules were then checked by PoseBusters feasibility tests, with validity rates from 80% to 100% depending on composition. On the fifteen test compounds, the known structure was recovered for eight, against eleven reported for the DiffCSP method.
Written by AIxSci from the checked record below, to give context for readers outside the field. It is not part of the record.
The work
Technical · from the record
Response Matching trains a machine learning interatomic potential (CACE) to predict the fictitious forces and stresses that arise when equilibrium structures are randomly displaced and their cells distorted, then generates new molecules and crystals by relaxing random atomic configurations on the resulting pseudo potential energy surface with the FIRE optimiser. Separate models were trained on 7,211 QM7b molecules, 27,136 MP-20 Materials Project structures, and a single cubic diamond configuration. Generated molecules were checked with PoseBusters, where the sanitisation (validity) rate ranged from 80% to 100% depending on composition; on the compound set used by DiffCSP the ground-truth structure was recovered for eight compounds, against a reported 11/15 for DiffCSP. Relaxing random carbon configurations under the single-diamond model yielded cubic and hexagonal diamond, diamonds with stacking faults, and graphite structures.
How AI was used
Equilibrium structures from QM7b, MP-20 and a single diamond configuration were perturbed by random atomic displacements (maximum 1.6 Å for molecules, 0.8 Å for crystals and diamond) and, for periodic systems, cell distortion of up to 0.1. For each perturbed structure, fictitious forces were assigned from a harmonic spring to the equilibrium position plus a short-range pairwise repulsion, and fictitious stresses from an isotropic elastic stress-strain relation, with the force constant, repulsion parameters and moduli set as hyperparameters. A CACE interatomic potential without message passing was then trained from scratch on these pseudo forces and stresses using a weighted force-plus-stress objective, with no energies or molecular properties in the training targets; cutoff radii, angular and body orders and element-embedding dimensions are reported per system, as are parameter counts. The trained potential defines a pseudo potential energy surface used as the denoising model: atoms of a chosen composition are placed at random positions in a box, periodic for crystals and non-periodic for molecules, with a minimum interatomic distance constraint and an initial molar volume set from linear regression of volume on composition for crystals, and both atomic positions and cell are relaxed with the FIRE optimiser until pseudo forces are negligible. Resulting structures were passed to PoseBusters feasibility checks, to pymatgen's StructureMatcher against ground-truth structures, and to a pseudo excess energy convex hull for the Li-S system; the learned element embedding matrix was examined by principal component analysis.
The shape of the work
Structural · the record, drawn
no AI
Assemble equilibrium training structures
Obtaining raw data, whether by measurement, download or retrieval.
The training set contains 27,136 structures.where the paper describes this · verbatim
no AI
Noise structures and compute fictitious responses
Cleaning, filtering, normalising or labelling data already obtained.
random displacements with a maximum magnitude of 1.6 Å were added to all the atoms in the original moleculeswhere the paper describes this · verbatim
AI
Train interatomic potential as denoising model
Fitting model parameters, including fine-tuning an existing model.
A CACE potential was used to learn the these pseudo forces and stresses.where the paper describes this · verbatim
no AI
Initialise random candidate configurations
Producing candidate objects that did not previously exist.
we randomly placed atoms of specific compositions in a box with periodic conditionswhere the paper describes this · verbatim
AI
Relax on pseudo energy surface (denoising)
Iterative search over a space. The AI stood in for simulation.
We then relax both the atomic positions and simulation cell using the FIRE (Fast Inertial Relaxation Engine) optimizerwhere the paper describes this · verbatim
no AI
Check feasibility and match to known structures
Testing outputs against ground truth.
Here we use a set of comprehensive and stringent criteria offered by PoseBusterswhere the paper describes this · verbatim
no AI
Rank Li-S candidates by pseudo excess energy
Reducing a candidate set by filtering or ranking, in a single pass.
we plotted the pseudo convex hull using the pseudo excess energywhere the paper describes this · verbatim
no AI
Inspect learned element embeddings
Extracting understanding from model behaviour.
we performed a principal component analysis (PCA) and plotted the first two principal component axes in Fig. 3where the paper describes this · verbatim
What the record says
Technical · every part carries its own basis
+ in the paper~ our reading− not reported
How to read the quotations. A quotation shows where the paper describes something. It does not quote every value beside it: one passage locates a part of the work, and values without their own quotation are our reading of that passage.
All generated molecules and crystals are produced by relaxing random configurations on a learned pseudo potential energy surface, so the reported structures exist only as model output
a CACE potential was employed to learn these pseudo forceswhere the paper describes this · verbatim
For eight of these compounds (Ag6O2, Bi2F8, Co2Sb2, Co4B2, Cr4Si4, KZnF3, Sr2O4, YMg3), we found the ground truth structures.where the paper describes this · verbatim
The training time took two days on an A10 card.where the paper describes this · verbatim
What this paper did not report
Technical · absence is published deliberately
- CodeWhether the code is available is not stated.
- Trained model weightsWhether the trained model is available is not stated.
- DataWhether the data are available is not stated.
- Version of CACE (Cartesian Atomic Cluster Expansion) potential, used without message passingWhich version of the model was used is not stated.
- What step 3 replacedThe paper gives no basis for what the AI stood in for.
About this article
Record aix-00113, version 2, checked by a person on 2026-10-08. The record describes the paper; it does not assess whether the paper's findings are right. The paper is published under CC-BY; quotations are at most 25 words. How we work · Report an error