Note
Go to the end to download the full example code.
Introduction to foundational models for molecular dynamics¶
- Authors:
Paolo Pegolo @ppegolo
Foundational (or universal) machine-learning interatomic potentials are trained once on broad, chemically diverse datasets, with the goal of describing essentially any system without specific re-parameterization. This recipe illustrates the concept: we take a single foundational model, PET-MAD-XS (which spans 102 elements of the periodic table), and use it, unchanged, to run molecular dynamics on four qualitatively different aqueous systems:
pure liquid water
a NaCl aqueous solution
an ethanol-water mixture
superionic water, an exotic phase found deep inside the ice-giant planets
For each system we provide the LAMMPS input that drives a short constant-temperature
simulation through the metatomic pair style. The first three (water, NaCl,
ethanol-water) are light enough to run live; the fourth (superionic water) is more
demanding, so for it we analyze a pre-computed trajectory.
# sphinx_gallery_thumbnail_number = 3
Setup¶
We download a small archive with the data we need: the starting structures and the
pre-computed trajectory for the superionic system (the first three runs are launched
live below). The LAMMPS dump format stores the full cell information together with
unwrapped Cartesian coordinates (xu yu zu), which makes part of the analysis
below straightforward.
from zipfile import ZipFile
import numpy as np
import matplotlib.pyplot as plt
import ase.io
from ase.geometry.rdf import get_rdf
import chemiscope
import upet
from atomistic_cookbook_utils import download_with_retry, run_command
download_with_retry(
"https://github.com/ppegolo/labcosmo_ictp_school/raw/refs/heads/tmp/water-md.zip",
"data.zip",
)
with ZipFile("data.zip", "r") as z:
z.extractall(".")
PET-MAD-XS through metatomic¶
PET-MAD is a foundational
potential trained on the MAD (Massive Atomic Diversity) dataset, version 1.5, a deliberately heterogeneous collection
of structures spanning 102 elements. PET-MAD-XS (“extra small”) is the lightest
and fastest version: it trades some accuracy for speed, but the same recipe works
unchanged with the larger versions (S, M, L).
The model ships as a single file and is coupled to a simulation engine through metatomic, the software that exposes the same potential to several simulation engines, including i-PI, LAMMPS, gromacs, and ASE through a common API. In every LAMMPS input below the potential is loaded with a single line:
pair_style metatomic pet-mad-xs-v1.5.0.pt device cpu
(use device cuda to run on a GPU instead).
We fetch the model once with upet and save it to the file the LAMMPS inputs load
(pet-mad-xs-v1.5.0.pt); every run below picks it up through the metatomic pair
style.
model_path = "pet-mad-xs-v1.5.0.pt"
upet.save_upet(model="pet-mad", size="xs", version="1.5.0", output=model_path)
Warning: You are sending unauthenticated requests to the HF Hub. Please set a HF_TOKEN to enable higher rate limits and faster downloads.
WARNING:huggingface_hub.utils._http:Warning: You are sending unauthenticated requests to the HF Hub. Please set a HF_TOKEN to enable higher rate limits and faster downloads.
/home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/water-md/lib/python3.12/site-packages/metatrain/pet/model.py:1031: UserWarning: the 'non_conservative_forces' output name is deprecated, please update the model to use 'non_conservative_force' instead
return AtomisticModel(self.eval(), metadata, capabilities)
/home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/water-md/lib/python3.12/site-packages/metatrain/pet/model.py:1031: UserWarning: the 'non_conservative_forces' output name is deprecated, please update the model to use 'non_conservative_force' instead
return AtomisticModel(self.eval(), metadata, capabilities)
/home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/water-md/lib/python3.12/site-packages/metatrain/llpr/model.py:1249: UserWarning: the 'non_conservative_forces' output name is deprecated, please update the model to use 'non_conservative_force' instead
return AtomisticModel(self.eval(), metadata, self.capabilities)
Liquid water at 400 K¶
We start with a simple case: 64 water molecules in a cubic, periodic box, propagated in the canonical (NVT) ensemble. This is the complete LAMMPS input:
# Liquid water NVT at 400 K with PET-MAD-xs
# Atom types: 1=H, 2=O
units metal
atom_style atomic
variable seed index 12345
variable t_target equal 400.0
variable tdamp equal 100*dt # thermostat time constant
variable nsteps equal 500 # 500 * 0.5 fs = 0.25 ps
variable dump_every equal 10
read_data data/water.data
pair_style metatomic pet-mad-xs-v1.5.0.pt device cpu
pair_coeff * * 1 8
timestep 0.0005
neighbor 2.0 bin
neigh_modify one 50000 page 500000
thermo_style custom step temp pe etotal press vol
thermo 10
velocity all create ${t_target} ${seed} mom yes rot yes dist gaussian
reset_timestep 0
fix nve_int all nve
fix thermostat all temp/csvr ${t_target} ${t_target} ${tdamp} ${seed}
print "step temp pe etotal press vol" file water_thermo.out
fix thermofile all print ${dump_every} "$(step) $(temp) $(pe) $(etotal) $(press) $(vol)" append water_thermo.out
dump traj all custom ${dump_every} water_traj.lammpstrj id type element xu yu zu
dump_modify traj element H O sort id
run ${nsteps}
Several of these settings recur in every simulation below and are worth a closer look:
Potential and element map.
pair_style metatomicinstructs LAMMPS to use the metatomic model to compute forces; the singlepair_coeff * * 1 8line is the only chemistry-specific input, mapping LAMMPS atom type 1 to hydrogen (Z=1) and type 2 to oxygen (Z=8).Ensemble.
fix nvepropagates the equations of motion with the velocity-Verlet integrator, whilefix temp/csvradds a stochastic velocity-rescaling thermostat (the Bussi-Donadio-Parrinello, or CSVR, thermostat) on top. Together they sample the canonical ensemble. CSVR reproduces the exact canonical velocity distribution while disturbing the dynamics minimally, which makes it a very common choice, especially when one wants to compute dynamical observables.Thermostat coupling time.
tdamp = 100*dt(here 50 fs) sets how strongly the thermostat couples to the system: 100 times the integration time step is usually loose enough not to damp the physical motion we want to measure, tight enough to keep the temperature steady over the run.Timestep.
timestep 0.0005is 0.5 fs. The fastest motion is the O-H stretch (period ≈ 10 fs), so half a femtosecond samples it about twenty times per oscillation, enough for stable, accurate integration.Temperature. We run at 400 K rather than 300 K because the electronic-structure reference of the MAD dataset (the r2SCAN functional) overstructures liquid water and raises its melting point by a few tens of kelvin. Working slightly above ambient keeps the system liquid and accelerates sampling.
These runs are intentionally short, so they reproduce quickly, but long enough to show some structure and stable dynamics. The only precomputed trajectories are for superionic water, which requires shorter time-steps and longer dynamics.
Each input reads its starting structure from data/ and is launched with a single
command, which we run here:
run_command("lmp -in in_water_nvt.lmp", print_output=True)
LAMMPS (4 Jul 2026)
OMP_NUM_THREADS environment is not set. Defaulting to 1 thread.
using 1 OpenMP thread(s) per MPI task
Reading data file ...
orthogonal box = (0.73005488 0.73005488 0.73005488) to (13.254708 13.254708 13.254708)
1 by 1 by 1 MPI processor grid
reading atoms ...
192 atoms
reading velocities ...
192 velocities
read_data CPU = 0.001 seconds
This is the PET-MAD-XS v1.5.0 model
===================================
A universal interatomic potential for advanced materials modeling based on a
Point-Edge Transformer (PET) architecture, and trained on the MAD dataset.
Model size: xs. Model version: 1.5.0.
Model authors
-------------
- Arslan Mazitov ([email protected])
- Filippo Bigi
- Matthias Kellner
- Paolo Pegolo
- Davide Tisi
- Guillaume Fraux
- Sergey Pozdnyakov
- Philip Loche
- Michele Ceriotti ([email protected])
Model references
----------------
Please cite the following references when using this model:
- about this specific model:
* https://doi.org/10.1038/s41467-025-65662-7
* https://arxiv.org/abs/2601.16195
- about the architecture of this model:
* LLPR (uncertainty method):
https://iopscience.iop.org/article/10.1088/2632-2153/ad805f
* LPR (if using per-atom uncertainty):
https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704
* https://arxiv.org/abs/2305.19302v3
Found 'energy_uncertainty' output, we will check for atoms with high uncertainty on the energy predictions
[W1112 22:35:38.572243866 module.cpp:218] Warning: module does not have '_mts_buffer_names'; falling back to processing all attributes. This is deprecated and will be removed in a future version, update your version of metatensor-learn and use `register_buffer` explicitly to remove this warning. (function operator())
Running simulation on cpu device with float32 data
step temp pe etotal press vol
CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
Your simulation uses code contributions which should be cited:
- LLPR (uncertainty method): https://iopscience.iop.org/article/10.1088/2632-2153/ad805f
- LPR (if using per-atom uncertainty): https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704
- https://arxiv.org/abs/2305.19302v3
- https://doi.org/10.1038/s41467-025-65662-7
- https://arxiv.org/abs/2601.16195
The log file lists these citations in BibTeX format.
CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
Neighbor list info ...
update: every = 1 steps, delay = 0 steps, check = yes
max neighbors/atom: 50000, page size: 500000
master list distance cutoff = 17
ghost atom cutoff = 17
binsize = 8.5, bins = 2 2 2
1 neighbor lists, perpetual/occasional/extra = 1 0 0
(1) pair metatomic, perpetual
attributes: full, newton on, ghost
pair build: full/bin/ghost
stencil: full/ghost/bin/3d
bin: standard
Setting up Verlet run ...
Unit style : metal
Current step : 0
Time step : 5e-04
0 400.00000000000011369 -1009.419189453125 -999.54371437512497778 6880.8960567258991432 1964.7040162035737012
Per MPI rank memory allocation (min/avg/max) = 58.34 | 58.34 | 58.34 Mbytes
Step Temp PotEng TotEng Press Volume
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60 377.42001111670504088 -1008.47088623046875 -999.15288144616499721 15124.637591448228704 1964.7040162035737012
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500 383.1954161697070731 -1007.3896484375 -997.92905648153055154 -254.44980384965245435 1964.7040162035737012
500 383.19542 -1007.3896 -997.92906 -254.4498 1964.704
Loop time of 96.4124 on 1 procs for 500 steps with 192 atoms
Performance: 0.224 ns/day, 107.125 hours/ns, 5.186 timesteps/s, 995.722 atom-step/s
89.5% CPU use with 1 MPI tasks x 1 OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 95.331 | 95.331 | 95.331 | 0.0 | 98.88
Neigh | 1.0358 | 1.0358 | 1.0358 | 0.0 | 1.07
Comm | 0.024334 | 0.024334 | 0.024334 | 0.0 | 0.03
Output | 0.0064362 | 0.0064362 | 0.0064362 | 0.0 | 0.01
Modify | 0.011485 | 0.011485 | 0.011485 | 0.0 | 0.01
Other | | 0.003286 | | | 0.00
Nlocal: 192 ave 192 max 192 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 9642 ave 9642 max 9642 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
FullNghs: 385200 ave 385200 max 385200 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 385200
Ave neighs/atom = 2006.25
Neighbor list builds = 8
Dangerous builds = 0
Total wall time: 0:01:37
CompletedProcess(args=['lmp', '-in', 'in_water_nvt.lmp'], returncode=0, stdout="LAMMPS (4 Jul 2026)\nOMP_NUM_THREADS environment is not set. Defaulting to 1 thread.\n using 1 OpenMP thread(s) per MPI task\nReading data file ...\n orthogonal box = (0.73005488 0.73005488 0.73005488) to (13.254708 13.254708 13.254708)\n 1 by 1 by 1 MPI processor grid\n reading atoms ...\n 192 atoms\n reading velocities ...\n 192 velocities\n read_data CPU = 0.001 seconds\n\nThis is the PET-MAD-XS v1.5.0 model\n===================================\n\nA universal interatomic potential for advanced materials modeling based on a\nPoint-Edge Transformer (PET) architecture, and trained on the MAD dataset.\nModel size: xs. Model version: 1.5.0.\n\nModel authors\n-------------\n\n- Arslan Mazitov ([email protected])\n- Filippo Bigi\n- Matthias Kellner\n- Paolo Pegolo\n- Davide Tisi\n- Guillaume Fraux\n- Sergey Pozdnyakov\n- Philip Loche\n- Michele Ceriotti ([email protected])\n\nModel references\n----------------\n\nPlease cite the following references when using this model:\n- about this specific model:\n * https://doi.org/10.1038/s41467-025-65662-7\n * https://arxiv.org/abs/2601.16195\n- about the architecture of this model:\n * LLPR (uncertainty method):\n https://iopscience.iop.org/article/10.1088/2632-2153/ad805f\n * LPR (if using per-atom uncertainty):\n https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704\n * https://arxiv.org/abs/2305.19302v3\n\nFound 'energy_uncertainty' output, we will check for atoms with high uncertainty on the energy predictions\n[W1112 22:35:38.572243866 module.cpp:218] Warning: module does not have '_mts_buffer_names'; falling back to processing all attributes. This is deprecated and will be removed in a future version, update your version of metatensor-learn and use `register_buffer` explicitly to remove this warning. (function operator())\nRunning simulation on cpu device with float32 data\nstep temp pe etotal press vol\n\nCITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE\n\nYour simulation uses code contributions which should be cited:\n- LLPR (uncertainty method): https://iopscience.iop.org/article/10.1088/2632-2153/ad805f\n- LPR (if using per-atom uncertainty): https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704\n- https://arxiv.org/abs/2305.19302v3\n- https://doi.org/10.1038/s41467-025-65662-7\n- https://arxiv.org/abs/2601.16195\nThe log file lists these citations in BibTeX format.\n\nCITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE\n\nNeighbor list info ...\n update: every = 1 steps, delay = 0 steps, check = yes\n max neighbors/atom: 50000, page size: 500000\n master list distance cutoff = 17\n ghost atom cutoff = 17\n binsize = 8.5, bins = 2 2 2\n 1 neighbor lists, perpetual/occasional/extra = 1 0 0\n (1) pair metatomic, perpetual\n attributes: full, newton on, ghost\n pair build: full/bin/ghost\n stencil: full/ghost/bin/3d\n bin: standard\nSetting up Verlet run ...\n Unit style : metal\n Current step : 0\n Time step : 5e-04\n0 400.00000000000011369 -1009.419189453125 -999.54371437512497778 6880.8960567258991432 1964.7040162035737012\nPer MPI rank memory allocation (min/avg/max) = 58.34 | 58.34 | 58.34 Mbytes\n Step Temp PotEng TotEng Press Volume \n 0 400 -1009.4192 -999.54371 6880.8961 1964.704 \n10 353.47651034321540919 -1008.317138671875 -999.59026750049292787 -1875.0756223653033885 1964.7040162035737012\n 10 353.47651 -1008.3171 -999.59027 -1875.0756 1964.704 \n20 350.42521281030826685 -1008.11572265625 -999.46418401672235632 12577.696343279831126 1964.7040162035737012\n 20 350.42521 -1008.1157 -999.46418 12577.696 1964.704 \n30 336.1002360139348184 -1007.68682861328125 -999.38895485211742198 -3756.7197451692964023 1964.7040162035737012\n 30 336.10024 -1007.6868 -999.38895 -3756.7197 1964.704 \n40 373.63773949462597557 -1008.28289794921875 -999.05827248777018212 13656.7152473466831 1964.7040162035737012\n 40 373.63774 -1008.2829 -999.05827 13656.715 1964.704 \n50 368.59600128231846838 -1007.88623046875 -998.78607890746502562 -6488.2693937542599087 1964.7040162035737012\n 50 368.596 -1007.8862 -998.78608 -6488.2694 1964.704 \n60 377.42001111670504088 -1008.47088623046875 -999.15288144616499721 15124.637591448228704 1964.7040162035737012\n 60 377.42001 -1008.4709 -999.15288 15124.638 1964.704 \n70 360.77919042227858881 -1007.9412841796875 -999.03411942049694972 -5968.3958833969045372 1964.7040162035737012\n 70 360.77919 -1007.9413 -999.03412 -5968.3959 1964.704 \n80 349.77203123083870651 -1008.0147705078125 -999.3793580643085761 14524.144998203531941 1964.7040162035737012\n 80 349.77203 -1008.0148 -999.37936 14524.145 1964.704 \n90 359.54689760107788743 -1007.82354736328125 -998.94680629670210692 -4206.6467043190041295 1964.7040162035737012\n 90 359.5469 -1007.8235 -998.94681 -4206.6467 1964.704 \n100 388.6034627864041795 -1008.54681396484375 -998.9527044349146081 10931.248982186205467 1964.7040162035737012\n 100 388.60346 -1008.5468 -998.9527 10931.249 1964.704 \n110 369.89689135351926552 -1008.023193359375 -998.89092452939667055 -2798.426630698889312 1964.7040162035737012\n 110 369.89689 -1008.0232 -998.89092 -2798.4266 1964.704 \n120 358.43583122643929073 -1007.99346923828125 -999.14415894243393268 11552.504383854700791 1964.7040162035737012\n 120 358.43583 -1007.9935 -999.14416 11552.504 1964.704 \n130 360.78572933201127171 -1007.83673095703125 -998.92940476074045364 -2903.6197654289467209 1964.7040162035737012\n 130 360.78573 -1007.8367 -998.9294 -2903.6198 1964.704 \n140 395.74289786652957446 -1008.54547119140625 -998.77509837846525897 9687.0042892123128695 1964.7040162035737012\n 140 395.7429 -1008.5455 -998.7751 9687.0043 1964.704 \n150 394.10500567597682675 -1008.5372314453125 -998.80729604114208087 -2159.3213168419047179 1964.7040162035737012\n 150 394.10501 -1008.5372 -998.8073 -2159.3213 1964.704 \n160 399.73344786160038211 -1008.686279296875 -998.81738504137433665 8889.0967524455118109 1964.7040162035737012\n 160 399.73345 -1008.6863 -998.81739 8889.0968 1964.704 \n170 393.39304854998289329 -1008.6815185546875 -998.96916043765304494 -2420.761259329470704 1964.7040162035737012\n 170 393.39305 -1008.6815 -998.96916 -2420.7613 1964.704 \n180 391.78834732723043999 -1008.68365478515625 -999.01091463545401439 8432.5562911392844399 1964.7040162035737012\n 180 391.78835 -1008.6837 -999.01091 8432.5563 1964.704 \n190 406.13357187365073742 -1008.752685546875 -998.72578062843160751 -1333.4173700740179811 1964.7040162035737012\n 190 406.13357 -1008.7527 -998.72578 -1333.4174 1964.704 \n200 389.63308430280829953 -1008.7650146484375 -999.14548511444581891 7129.2778736422260408 1964.7040162035737012\n 200 389.63308 -1008.765 -999.14549 7129.2779 1964.704 \n210 394.64274720853410372 -1008.83770751953125 -999.09449598260289349 74.524881759373855061 1964.7040162035737012\n 210 394.64275 -1008.8377 -999.0945 74.524882 1964.704 \n220 381.54878831612228396 -1008.41510009765625 -998.99516122251384331 5540.9455056147453433 1964.7040162035737012\n 220 381.54879 -1008.4151 -998.99516 5540.9455 1964.704 \n230 381.56113794131022132 -1008.43719482421875 -999.01695105303690525 923.45187001665556181 1964.7040162035737012\n 230 381.56114 -1008.4372 -999.01695 923.45187 1964.704 \n240 373.48059786154050244 -1008.4359130859375 -999.21516724519199215 5091.0791300453474832 1964.7040162035737012\n 240 373.4806 -1008.4359 -999.21517 5091.0791 1964.704 \n250 387.02705380540891156 -1008.63494873046875 -999.07975866955109723 1588.9113017713843874 1964.7040162035737012\n 250 387.02705 -1008.6349 -999.07976 1588.9113 1964.704 \n260 356.23139130355502857 -1008.2626953125 -999.46780974545117715 2719.4791534856171893 1964.7040162035737012\n 260 356.23139 -1008.2627 -999.46781 2719.4792 1964.704 \n270 366.61901408075704012 -1008.1405029296875 -999.08916058799889015 4083.6567290128546119 1964.7040162035737012\n 270 366.61901 -1008.1405 -999.08916 4083.6567 1964.704 \n280 368.77457976471407619 -1008.3409423828125 -999.23638195314663335 -1703.554631299625953 1964.7040162035737012\n 280 368.77458 -1008.3409 -999.23638 -1703.5546 1964.704 \n290 370.72648603574856452 -1008.3848876953125 -999.23213726131109524 6641.9899854506256816 1964.7040162035737012\n 290 370.72649 -1008.3849 -999.23214 6641.99 1964.704 \n300 368.67986620939200293 -1008.09234619140625 -998.99012411512819654 -3881.5236584435765508 1964.7040162035737012\n 300 368.67987 -1008.0923 -998.99012 -3881.5237 1964.704 \n310 358.98884329390347148 -1008.02972412109375 -999.16676068302126623 7507.4072714544872724 1964.7040162035737012\n 310 358.98884 -1008.0297 -999.16676 7507.4073 1964.704 \n320 349.97981262145452774 -1007.76055908203125 -999.12001678866556631 -6354.7572427802197126 1964.7040162035737012\n 320 349.97981 -1007.7606 -999.12002 -6354.7572 1964.704 \n330 372.32907062995343495 -1008.10015869140625 -998.90784254685377164 9368.2646881409182242 1964.7040162035737012\n 330 372.32907 -1008.1002 -998.90784 9368.2647 1964.704 \n340 349.43663271529874237 -1007.68450927734375 -999.05737738304333106 -6739.6707301232445388 1964.7040162035737012\n 340 349.43663 -1007.6845 -999.05738 -6739.6707 1964.704 \n350 338.3274197719276799 -1007.50921630859375 -999.15635630318945459 9455.8344396419433906 1964.7040162035737012\n 350 338.32742 -1007.5092 -999.15636 9455.8344 1964.704 \n360 325.71412708702666805 -1007.15118408203125 -999.10972972053014018 -4990.5671701844266863 1964.7040162035737012\n 360 325.71413 -1007.1512 -999.10973 -4990.5672 1964.704 \n370 354.15084755193544197 -1007.5224609375 -998.77894126537069042 7604.5628213891304767 1964.7040162035737012\n 370 354.15085 -1007.5225 -998.77894 7604.5628 1964.704 \n380 370.26932205453937286 -1007.7275390625 -998.58607540725608942 -3773.9854505193738987 1964.7040162035737012\n 380 370.26932 -1007.7275 -998.58608 -3773.9855 1964.704 \n390 370.98158723816379734 -1007.41815185546875 -998.25910330755027644 2424.1003832805395177 1964.7040162035737012\n 390 370.98159 -1007.4182 -998.2591 2424.1004 1964.704 \n400 355.28465088347263645 -1006.99615478515625 -998.22464299666705756 421.10809505087871685 1964.7040162035737012\n 400 355.28465 -1006.9962 -998.22464 421.1081 1964.704 \n410 357.52203384498272953 -1007.2379150390625 -998.4111652013824596 -949.83486119004157899 1964.7040162035737012\n 410 357.52203 -1007.2379 -998.41117 -949.83486 1964.704 \n420 370.23649825866630181 -1007.41839599609375 -998.27774271729515476 1959.5625642427869479 1964.7040162035737012\n 420 370.2365 -1007.4184 -998.27774 1959.5626 1964.704 \n430 361.60696424369689339 -1007.01629638671875 -998.08869497816908734 -4093.7286607283353987 1964.7040162035737012\n 430 361.60696 -1007.0163 -998.08869 -4093.7287 1964.704 \n440 336.39549100029483952 -1006.65399169921875 -998.34882847990627397 4009.8439689740098402 1964.7040162035737012\n 440 336.39549 -1006.654 -998.34883 4009.844 1964.704 \n450 342.11410957188053317 -1006.59759521484375 -998.15124680757060105 -4112.5877294622960108 1964.7040162035737012\n 450 342.11411 -1006.5976 -998.15125 -4112.5877 1964.704 \n460 373.1116772285663501 -1007.12127685546875 -997.9096391810149953 3004.9169817790225352 1964.7040162035737012\n 460 373.11168 -1007.1213 -997.90964 3004.917 1964.704 \n470 358.06668721407288558 -1006.990478515625 -998.15028190101349992 -5493.3630523104202439 1964.7040162035737012\n 470 358.06669 -1006.9905 -998.15028 -5493.3631 1964.704 \n480 374.20418670052868038 -1007.2386474609375 -998.00003716132664522 1194.3189909235295545 1964.7040162035737012\n 480 374.20419 -1007.2386 -998.00004 1194.319 1964.704 \n490 387.95626025605781706 -1007.2105712890625 -997.63244034028059559 -3981.3613706568189627 1964.7040162035737012\n 490 387.95626 -1007.2106 -997.63244 -3981.3614 1964.704 \n500 383.1954161697070731 -1007.3896484375 -997.92905648153055154 -254.44980384965245435 1964.7040162035737012\n 500 383.19542 -1007.3896 -997.92906 -254.4498 1964.704 \nLoop time of 96.4124 on 1 procs for 500 steps with 192 atoms\n\nPerformance: 0.224 ns/day, 107.125 hours/ns, 5.186 timesteps/s, 995.722 atom-step/s\n89.5% CPU use with 1 MPI tasks x 1 OpenMP threads\n\nMPI task timing breakdown:\nSection | min time | avg time | max time |%varavg| %total\n---------------------------------------------------------------\nPair | 95.331 | 95.331 | 95.331 | 0.0 | 98.88\nNeigh | 1.0358 | 1.0358 | 1.0358 | 0.0 | 1.07\nComm | 0.024334 | 0.024334 | 0.024334 | 0.0 | 0.03\nOutput | 0.0064362 | 0.0064362 | 0.0064362 | 0.0 | 0.01\nModify | 0.011485 | 0.011485 | 0.011485 | 0.0 | 0.01\nOther | | 0.003286 | | | 0.00\n\nNlocal: 192 ave 192 max 192 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\nNghost: 9642 ave 9642 max 9642 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\nNeighs: 0 ave 0 max 0 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\nFullNghs: 385200 ave 385200 max 385200 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\n\nTotal # of neighbors = 385200\nAve neighs/atom = 2006.25\nNeighbor list builds = 8\nDangerous builds = 0\nTotal wall time: 0:01:37\n")
As a first sanity check we plot the temperature and potential energy along the trajectory: the thermostat should hold the temperature near its 400 K target (fluctuations are expected, given the small system). After a brief equilibration the potential energy should settle around a stable mean, with no long-term drift.
water_thermo = np.loadtxt("water_thermo.out", skiprows=1)
# columns: step temp pe etotal press vol
time_ps = water_thermo[:, 0] * 0.0005 # step × dt (0.5 fs) in ps
fig, axes = plt.subplots(1, 2, figsize=(10, 4), dpi=200)
axes[0].plot(time_ps, water_thermo[:, 1])
axes[0].set(xlabel="Time (ps)", ylabel="Temperature (K)", title="Temperature")
axes[1].plot(time_ps, water_thermo[:, 2])
axes[1].set(
xlabel="Time (ps)", ylabel="Potential energy (eV)", title="Potential energy"
)
fig.tight_layout()
plt.show()
We can also inspect the trajectory interactively. Water molecules diffuse and the hydrogen-bond network continuously rearranges.
water_traj = ase.io.read("water_traj.lammpstrj", ":", format="lammps-dump-text")
for frame in water_traj:
frame.wrap()
chemiscope.show(
structures=water_traj,
mode="structure",
settings=chemiscope.quick_settings(
trajectory=True,
structure_settings={"playbackDelay": 20, "unitCell": True},
),
)
Adding ions: NaCl in water¶
PET-MAD can handle in principle any stable chemical element. We start by dissolving
two NaCl units (two Na⁺ and two Cl⁻ ions) in 60 water molecules, a roughly 1.8 M
solution. The only change to the LAMMPS input is the element map: the pair_coeff
line now also assigns Na (Z=11) and Cl (Z=17). No new parameters and no retraining
are involved: the same weights describe ion-water and ion-ion interactions out of the
box.
# NaCl aqueous solution NVT at 400 K with PET-MAD-xs
# Atom types: 1=H, 2=O, 3=Na, 4=Cl
units metal
atom_style atomic
variable seed index 23456
variable t_target equal 400.0
variable tdamp equal 100*dt
variable nsteps equal 500 # 500 * 0.5 fs = 0.25 ps
variable dump_every equal 10
read_data data/nacl.data
pair_style metatomic pet-mad-xs-v1.5.0.pt device cpu
pair_coeff * * 1 8 11 17
timestep 0.0005
neighbor 2.0 bin
neigh_modify one 50000 page 500000
thermo_style custom step temp pe etotal press vol
thermo 10
velocity all create ${t_target} ${seed} mom yes rot yes dist gaussian
reset_timestep 0
fix nve_int all nve
fix thermostat all temp/csvr ${t_target} ${t_target} ${tdamp} ${seed}
print "step temp pe etotal press vol" file nacl_thermo.out
fix thermofile all print ${dump_every} "$(step) $(temp) $(pe) $(etotal) $(press) $(vol)" append nacl_thermo.out
dump traj all custom ${dump_every} nacl_traj.lammpstrj id type element xu yu zu
dump_modify traj element H O Na Cl sort id
run ${nsteps}
run_command("lmp -in in_nacl_nvt.lmp", print_output=True)
LAMMPS (4 Jul 2026)
OMP_NUM_THREADS environment is not set. Defaulting to 1 thread.
using 1 OpenMP thread(s) per MPI task
Reading data file ...
orthogonal box = (0.95507965 0.95507965 0.95507965) to (13.141811 13.141811 13.141811)
1 by 1 by 1 MPI processor grid
reading atoms ...
184 atoms
reading velocities ...
184 velocities
read_data CPU = 0.001 seconds
This is the PET-MAD-XS v1.5.0 model
===================================
A universal interatomic potential for advanced materials modeling based on a
Point-Edge Transformer (PET) architecture, and trained on the MAD dataset.
Model size: xs. Model version: 1.5.0.
Model authors
-------------
- Arslan Mazitov ([email protected])
- Filippo Bigi
- Matthias Kellner
- Paolo Pegolo
- Davide Tisi
- Guillaume Fraux
- Sergey Pozdnyakov
- Philip Loche
- Michele Ceriotti ([email protected])
Model references
----------------
Please cite the following references when using this model:
- about this specific model:
* https://doi.org/10.1038/s41467-025-65662-7
* https://arxiv.org/abs/2601.16195
- about the architecture of this model:
* LLPR (uncertainty method):
https://iopscience.iop.org/article/10.1088/2632-2153/ad805f
* LPR (if using per-atom uncertainty):
https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704
* https://arxiv.org/abs/2305.19302v3
Found 'energy_uncertainty' output, we will check for atoms with high uncertainty on the energy predictions
[W1112 22:37:16.728367972 module.cpp:218] Warning: module does not have '_mts_buffer_names'; falling back to processing all attributes. This is deprecated and will be removed in a future version, update your version of metatensor-learn and use `register_buffer` explicitly to remove this warning. (function operator())
Running simulation on cpu device with float32 data
step temp pe etotal press vol
CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
Your simulation uses code contributions which should be cited:
- LLPR (uncertainty method): https://iopscience.iop.org/article/10.1088/2632-2153/ad805f
- LPR (if using per-atom uncertainty): https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704
- https://arxiv.org/abs/2305.19302v3
- https://doi.org/10.1038/s41467-025-65662-7
- https://arxiv.org/abs/2601.16195
The log file lists these citations in BibTeX format.
CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
Neighbor list info ...
update: every = 1 steps, delay = 0 steps, check = yes
max neighbors/atom: 50000, page size: 500000
master list distance cutoff = 17
ghost atom cutoff = 17
binsize = 8.5, bins = 2 2 2
1 neighbor lists, perpetual/occasional/extra = 1 0 0
(1) pair metatomic, perpetual
attributes: full, newton on, ghost
pair build: full/bin/ghost
stencil: full/ghost/bin/3d
bin: standard
Setting up Verlet run ...
Unit style : metal
Current step : 0
Time step : 5e-04
0 400.0000000000003979 -959.44195556640625 -949.98011295240621621 6335.7549538093817318 1809.9298793830914747
Per MPI rank memory allocation (min/avg/max) = 60.24 | 60.24 | 60.24 Mbytes
Step Temp PotEng TotEng Press Volume
0 400 -959.44196 -949.98011 6335.755 1809.9299
10 357.76270136866310168 -958.8070068359375 -950.34427090216308898 -4157.8629208241200104 1809.9298793830914747
10 357.7627 -958.80701 -950.34427 -4157.8629 1809.9299
20 368.2313956257402765 -958.78961181640625 -950.07924303904542285 6893.2132518616199377 1809.9298793830914747
20 368.2314 -958.78961 -950.07924 6893.2133 1809.9299
30 377.54361026649974065 -958.9130859375 -949.98244038684254065 -3363.3847967695915031 1809.9298793830914747
30 377.54361 -958.91309 -949.98244 -3363.3848 1809.9299
40 401.97242399286898262 -959.4512939453125 -949.94279441784101436 3892.1394653452580314 1809.9298793830914747
40 401.97242 -959.45129 -949.94279 3892.1395 1809.9299
50 390.11838080151500208 -958.847412109375 -949.61931530944389124 -3125.7976544292077961 1809.9298793830914747
50 390.11838 -958.84741 -949.61932 -3125.7977 1809.9299
60 386.20364715920112531 -958.65234375 -949.51684843406712844 4062.0612724453812916 1809.9298793830914747
60 386.20365 -958.65234 -949.51685 4062.0613 1809.9299
70 353.71238858351682666 -958.32366943359375 -949.956742055095674 865.02153831453586008 1809.9298793830914747
70 353.71239 -958.32367 -949.95674 865.02154 1809.9299
80 359.76838551701052893 -958.33544921875 -949.82526961561291046 1907.8110746174854739 1809.9298793830914747
80 359.76839 -958.33545 -949.82527 1907.8111 1809.9299
90 352.06678692479886195 -957.8079833984375 -949.47998207968964834 3620.8438756366390407 1809.9298793830914747
90 352.06679 -957.80798 -949.47998 3620.8439 1809.9299
100 358.18235134928096386 -958.34326171875 -949.87059912980157605 2566.473967981273745 1809.9298793830914747
100 358.18235 -958.34326 -949.8706 2566.474 1809.9299
110 363.88334083473250757 -958.43194580078125 -949.82442854869429993 1234.8566694970288609 1809.9298793830914747
110 363.88334 -958.43195 -949.82443 1234.8567 1809.9299
120 373.82342524926855276 -958.70703125 -949.86438521216257413 2094.8943130351972286 1809.9298793830914747
120 373.82343 -958.70703 -949.86439 2094.8943 1809.9299
130 368.08427457452256704 -958.3759765625 -949.66908787571878747 -378.42231312886991645 1809.9298793830914747
130 368.08427 -958.37598 -949.66909 -378.42231 1809.9299
140 368.27450218901969947 -958.5618896484375 -949.85050120228322612 3698.8597652647417817 1809.9298793830914747
140 368.2745 -958.56189 -949.8505 3698.8598 1809.9299
150 363.86393982424090154 -958.3436279296875 -949.73656960087021162 -1021.8411772040705046 1809.9298793830914747
150 363.86394 -958.34363 -949.73657 -1021.8412 1809.9299
160 376.88530236228092463 -958.6251220703125 -949.71004853410818214 3818.0540117032560374 1809.9298793830914747
160 376.8853 -958.62512 -949.71005 3818.054 1809.9299
170 370.01742805759852217 -958.29583740234375 -949.54322073054856901 -1560.5347033240848305 1809.9298793830914747
170 370.01743 -958.29584 -949.54322 -1560.5347 1809.9299
180 375.20697524693821379 -958.2528076171875 -949.37743424853374563 7268.9324810175121456 1809.9298793830914747
180 375.20698 -958.25281 -949.37743 7268.9325 1809.9299
190 368.71585445181131035 -958.04571533203125 -949.32388687175728137 -1773.6827925224718001 1809.9298793830914747
190 368.71585 -958.04572 -949.32389 -1773.6828 1809.9299
200 395.51712363634868552 -958.24554443359375 -948.8897424961210163 7414.0000078246730482 1809.9298793830914747
200 395.51712 -958.24554 -948.88974 7414 1809.9299
210 408.67912003430245704 -958.3060302734375 -948.63888648995600761 -5245.7495408454005883 1809.9298793830914747
210 408.67912 -958.30603 -948.63889 -5245.7495 1809.9299
220 390.90929619250670157 -958.05902099609375 -948.81221540378624013 9910.7577994477378525 1809.9298793830914747
220 390.9093 -958.05902 -948.81222 9910.7578 1809.9299
230 364.84071214120450577 -957.48834228515625 -948.8581787915068162 -2397.5339159197751542 1809.9298793830914747
230 364.84071 -957.48834 -948.85818 -2397.5339 1809.9299
240 386.76912590282285009 -957.663330078125 -948.51445858500790109 8076.86192415374353 1809.9298793830914747
240 386.76913 -957.66333 -948.51446 8076.8619 1809.9299
250 370.72894673783054031 -957.7017822265625 -948.93233486034409907 -2306.3223410830269131 1809.9298793830914747
250 370.72895 -957.70178 -948.93233 -2306.3223 1809.9299
260 383.43137578340559912 -958.25836181640625 -949.18844348907600761 6073.1066072935045668 1809.9298793830914747
260 383.43138 -958.25836 -949.18844 6073.1066 1809.9299
270 373.25424608491709932 -958.096923828125 -949.26774149946822945 508.04752117434082948 1809.9298793830914747
270 373.25425 -958.09692 -949.26774 508.04752 1809.9299
280 368.81270525464429966 -958.204345703125 -949.48022627521743289 2777.0725966917971164 1809.9298793830914747
280 368.81271 -958.20435 -949.48023 2777.0726 1809.9299
290 376.21677847444868803 -958.04461669921875 -949.14535683254041487 1492.4762343307020274 1809.9298793830914747
290 376.21678 -958.04462 -949.14536 1492.4762 1809.9299
300 374.30667327966455105 -958.2183837890625 -949.36430670920719876 -645.28430971218278955 1809.9298793830914747
300 374.30667 -958.21838 -949.36431 -645.28431 1809.9299
310 361.44552299349192026 -958.01593017578125 -949.46607854553292327 3105.0892987513620938 1809.9298793830914747
310 361.44552 -958.01593 -949.46608 3105.0893 1809.9299
320 349.80745753863863001 -957.9735107421875 -949.69895297110224419 -379.13226111580485167 1809.9298793830914747
320 349.80746 -957.97351 -949.69895 -379.13226 1809.9299
330 355.28235181499576356 -957.98529052734375 -949.58122628633054774 1854.6336502830301924 1809.9298793830914747
330 355.28235 -957.98529 -949.58123 1854.6337 1809.9299
340 381.020044753571824 -958.40716552734375 -949.39428628674988886 -839.95248540467298426 1809.9298793830914747
340 381.02004 -958.40717 -949.39429 -839.95249 1809.9299
350 373.81607171690615132 -957.98480224609375 -949.14233015317097397 2729.9399222625347647 1809.9298793830914747
350 373.81607 -957.9848 -949.14233 2729.9399 1809.9299
360 386.35484846762648203 -958.3848876953125 -949.2458157719212295 911.84361643808006193 1809.9298793830914747
360 386.35485 -958.38489 -949.24582 911.84362 1809.9299
370 366.83628494289740729 -958.5029296875 -949.82556170441466747 -2075.2851000857053805 1809.9298793830914747
370 366.83628 -958.50293 -949.82556 -2075.2851 1809.9299
380 380.42193095523185775 -958.48736572265625 -949.4886346286252774 4381.8674187077322131 1809.9298793830914747
380 380.42193 -958.48737 -949.48863 4381.8674 1809.9299
390 347.34769606009774634 -957.6953125 -949.47893941885956792 -2456.6105419831615109 1809.9298793830914747
390 347.3477 -957.69531 -949.47894 -2456.6105 1809.9299
400 352.97610167536896597 -957.91729736328125 -949.5677865618922624 7865.9368940733102136 1809.9298793830914747
400 352.9761 -957.9173 -949.56779 7865.9369 1809.9299
410 353.10666018450081083 -957.73779296875 -949.38519385719769161 -4989.7809190577308982 1809.9298793830914747
410 353.10666 -957.73779 -949.38519 -4989.7809 1809.9299
420 369.12890951348498447 -958.27557373046875 -949.54397461523365109 8734.8565660249405482 1809.9298793830914747
420 369.12891 -958.27557 -949.54397 8734.8566 1809.9299
430 341.24601204841138724 -957.774658203125 -949.70261805648192421 -5312.7471148321346845 1809.9298793830914747
430 341.24601 -957.77466 -949.70262 -5312.7471 1809.9299
440 338.93406866984810222 -957.77581787109375 -949.75846583540180745 10912.954742425434233 1809.9298793830914747
440 338.93407 -957.77582 -949.75847 10912.955 1809.9299
450 347.03217177807630378 -957.72894287109375 -949.52003339269685966 -5333.438674577346319 1809.9298793830914747
450 347.03217 -957.72894 -949.52003 -5333.4387 1809.9299
460 356.21562833728677333 -957.97454833984375 -949.54840780990741678 8940.4830165785897407 1809.9298793830914747
460 356.21563 -957.97455 -949.54841 8940.483 1809.9299
470 370.31347369663683367 -958.25762939453125 -949.49800987962828458 -3376.2427915034259058 1809.9298793830914747
470 370.31347 -958.25763 -949.49801 -3376.2428 1809.9299
480 366.28611203962304899 -958.01123046875 -949.34687660921781571 6831.6791024523818123 1809.9298793830914747
480 366.28611 -958.01123 -949.34688 6831.6791 1809.9299
490 366.20898906280382334 -957.9986572265625 -949.336127680701793 -1089.3675463962440517 1809.9298793830914747
490 366.20899 -957.99866 -949.33613 -1089.3675 1809.9299
500 365.27188681451849561 -958.096923828125 -949.45656106723049561 4678.6586299143518772 1809.9298793830914747
500 365.27189 -958.09692 -949.45656 4678.6586 1809.9299
Loop time of 97.3972 on 1 procs for 500 steps with 184 atoms
Performance: 0.222 ns/day, 108.219 hours/ns, 5.134 timesteps/s, 944.586 atom-step/s
88.4% CPU use with 1 MPI tasks x 1 OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 96.421 | 96.421 | 96.421 | 0.0 | 99.00
Neigh | 0.93273 | 0.93273 | 0.93273 | 0.0 | 0.96
Comm | 0.0245 | 0.0245 | 0.0245 | 0.0 | 0.03
Output | 0.0062822 | 0.0062822 | 0.0062822 | 0.0 | 0.01
Modify | 0.0094216 | 0.0094216 | 0.0094216 | 0.0 | 0.01
Other | | 0.003157 | | | 0.00
Nlocal: 184 ave 184 max 184 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 9765 ave 9765 max 9765 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
FullNghs: 383610 ave 383610 max 383610 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 383610
Ave neighs/atom = 2084.837
Neighbor list builds = 7
Dangerous builds = 0
Total wall time: 0:01:38
CompletedProcess(args=['lmp', '-in', 'in_nacl_nvt.lmp'], returncode=0, stdout="LAMMPS (4 Jul 2026)\nOMP_NUM_THREADS environment is not set. Defaulting to 1 thread.\n using 1 OpenMP thread(s) per MPI task\nReading data file ...\n orthogonal box = (0.95507965 0.95507965 0.95507965) to (13.141811 13.141811 13.141811)\n 1 by 1 by 1 MPI processor grid\n reading atoms ...\n 184 atoms\n reading velocities ...\n 184 velocities\n read_data CPU = 0.001 seconds\n\nThis is the PET-MAD-XS v1.5.0 model\n===================================\n\nA universal interatomic potential for advanced materials modeling based on a\nPoint-Edge Transformer (PET) architecture, and trained on the MAD dataset.\nModel size: xs. Model version: 1.5.0.\n\nModel authors\n-------------\n\n- Arslan Mazitov ([email protected])\n- Filippo Bigi\n- Matthias Kellner\n- Paolo Pegolo\n- Davide Tisi\n- Guillaume Fraux\n- Sergey Pozdnyakov\n- Philip Loche\n- Michele Ceriotti ([email protected])\n\nModel references\n----------------\n\nPlease cite the following references when using this model:\n- about this specific model:\n * https://doi.org/10.1038/s41467-025-65662-7\n * https://arxiv.org/abs/2601.16195\n- about the architecture of this model:\n * LLPR (uncertainty method):\n https://iopscience.iop.org/article/10.1088/2632-2153/ad805f\n * LPR (if using per-atom uncertainty):\n https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704\n * https://arxiv.org/abs/2305.19302v3\n\nFound 'energy_uncertainty' output, we will check for atoms with high uncertainty on the energy predictions\n[W1112 22:37:16.728367972 module.cpp:218] Warning: module does not have '_mts_buffer_names'; falling back to processing all attributes. This is deprecated and will be removed in a future version, update your version of metatensor-learn and use `register_buffer` explicitly to remove this warning. (function operator())\nRunning simulation on cpu device with float32 data\nstep temp pe etotal press vol\n\nCITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE\n\nYour simulation uses code contributions which should be cited:\n- LLPR (uncertainty method): https://iopscience.iop.org/article/10.1088/2632-2153/ad805f\n- LPR (if using per-atom uncertainty): https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704\n- https://arxiv.org/abs/2305.19302v3\n- https://doi.org/10.1038/s41467-025-65662-7\n- https://arxiv.org/abs/2601.16195\nThe log file lists these citations in BibTeX format.\n\nCITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE\n\nNeighbor list info ...\n update: every = 1 steps, delay = 0 steps, check = yes\n max neighbors/atom: 50000, page size: 500000\n master list distance cutoff = 17\n ghost atom cutoff = 17\n binsize = 8.5, bins = 2 2 2\n 1 neighbor lists, perpetual/occasional/extra = 1 0 0\n (1) pair metatomic, perpetual\n attributes: full, newton on, ghost\n pair build: full/bin/ghost\n stencil: full/ghost/bin/3d\n bin: standard\nSetting up Verlet run ...\n Unit style : metal\n Current step : 0\n Time step : 5e-04\n0 400.0000000000003979 -959.44195556640625 -949.98011295240621621 6335.7549538093817318 1809.9298793830914747\nPer MPI rank memory allocation (min/avg/max) = 60.24 | 60.24 | 60.24 Mbytes\n Step Temp PotEng TotEng Press Volume \n 0 400 -959.44196 -949.98011 6335.755 1809.9299 \n10 357.76270136866310168 -958.8070068359375 -950.34427090216308898 -4157.8629208241200104 1809.9298793830914747\n 10 357.7627 -958.80701 -950.34427 -4157.8629 1809.9299 \n20 368.2313956257402765 -958.78961181640625 -950.07924303904542285 6893.2132518616199377 1809.9298793830914747\n 20 368.2314 -958.78961 -950.07924 6893.2133 1809.9299 \n30 377.54361026649974065 -958.9130859375 -949.98244038684254065 -3363.3847967695915031 1809.9298793830914747\n 30 377.54361 -958.91309 -949.98244 -3363.3848 1809.9299 \n40 401.97242399286898262 -959.4512939453125 -949.94279441784101436 3892.1394653452580314 1809.9298793830914747\n 40 401.97242 -959.45129 -949.94279 3892.1395 1809.9299 \n50 390.11838080151500208 -958.847412109375 -949.61931530944389124 -3125.7976544292077961 1809.9298793830914747\n 50 390.11838 -958.84741 -949.61932 -3125.7977 1809.9299 \n60 386.20364715920112531 -958.65234375 -949.51684843406712844 4062.0612724453812916 1809.9298793830914747\n 60 386.20365 -958.65234 -949.51685 4062.0613 1809.9299 \n70 353.71238858351682666 -958.32366943359375 -949.956742055095674 865.02153831453586008 1809.9298793830914747\n 70 353.71239 -958.32367 -949.95674 865.02154 1809.9299 \n80 359.76838551701052893 -958.33544921875 -949.82526961561291046 1907.8110746174854739 1809.9298793830914747\n 80 359.76839 -958.33545 -949.82527 1907.8111 1809.9299 \n90 352.06678692479886195 -957.8079833984375 -949.47998207968964834 3620.8438756366390407 1809.9298793830914747\n 90 352.06679 -957.80798 -949.47998 3620.8439 1809.9299 \n100 358.18235134928096386 -958.34326171875 -949.87059912980157605 2566.473967981273745 1809.9298793830914747\n 100 358.18235 -958.34326 -949.8706 2566.474 1809.9299 \n110 363.88334083473250757 -958.43194580078125 -949.82442854869429993 1234.8566694970288609 1809.9298793830914747\n 110 363.88334 -958.43195 -949.82443 1234.8567 1809.9299 \n120 373.82342524926855276 -958.70703125 -949.86438521216257413 2094.8943130351972286 1809.9298793830914747\n 120 373.82343 -958.70703 -949.86439 2094.8943 1809.9299 \n130 368.08427457452256704 -958.3759765625 -949.66908787571878747 -378.42231312886991645 1809.9298793830914747\n 130 368.08427 -958.37598 -949.66909 -378.42231 1809.9299 \n140 368.27450218901969947 -958.5618896484375 -949.85050120228322612 3698.8597652647417817 1809.9298793830914747\n 140 368.2745 -958.56189 -949.8505 3698.8598 1809.9299 \n150 363.86393982424090154 -958.3436279296875 -949.73656960087021162 -1021.8411772040705046 1809.9298793830914747\n 150 363.86394 -958.34363 -949.73657 -1021.8412 1809.9299 \n160 376.88530236228092463 -958.6251220703125 -949.71004853410818214 3818.0540117032560374 1809.9298793830914747\n 160 376.8853 -958.62512 -949.71005 3818.054 1809.9299 \n170 370.01742805759852217 -958.29583740234375 -949.54322073054856901 -1560.5347033240848305 1809.9298793830914747\n 170 370.01743 -958.29584 -949.54322 -1560.5347 1809.9299 \n180 375.20697524693821379 -958.2528076171875 -949.37743424853374563 7268.9324810175121456 1809.9298793830914747\n 180 375.20698 -958.25281 -949.37743 7268.9325 1809.9299 \n190 368.71585445181131035 -958.04571533203125 -949.32388687175728137 -1773.6827925224718001 1809.9298793830914747\n 190 368.71585 -958.04572 -949.32389 -1773.6828 1809.9299 \n200 395.51712363634868552 -958.24554443359375 -948.8897424961210163 7414.0000078246730482 1809.9298793830914747\n 200 395.51712 -958.24554 -948.88974 7414 1809.9299 \n210 408.67912003430245704 -958.3060302734375 -948.63888648995600761 -5245.7495408454005883 1809.9298793830914747\n 210 408.67912 -958.30603 -948.63889 -5245.7495 1809.9299 \n220 390.90929619250670157 -958.05902099609375 -948.81221540378624013 9910.7577994477378525 1809.9298793830914747\n 220 390.9093 -958.05902 -948.81222 9910.7578 1809.9299 \n230 364.84071214120450577 -957.48834228515625 -948.8581787915068162 -2397.5339159197751542 1809.9298793830914747\n 230 364.84071 -957.48834 -948.85818 -2397.5339 1809.9299 \n240 386.76912590282285009 -957.663330078125 -948.51445858500790109 8076.86192415374353 1809.9298793830914747\n 240 386.76913 -957.66333 -948.51446 8076.8619 1809.9299 \n250 370.72894673783054031 -957.7017822265625 -948.93233486034409907 -2306.3223410830269131 1809.9298793830914747\n 250 370.72895 -957.70178 -948.93233 -2306.3223 1809.9299 \n260 383.43137578340559912 -958.25836181640625 -949.18844348907600761 6073.1066072935045668 1809.9298793830914747\n 260 383.43138 -958.25836 -949.18844 6073.1066 1809.9299 \n270 373.25424608491709932 -958.096923828125 -949.26774149946822945 508.04752117434082948 1809.9298793830914747\n 270 373.25425 -958.09692 -949.26774 508.04752 1809.9299 \n280 368.81270525464429966 -958.204345703125 -949.48022627521743289 2777.0725966917971164 1809.9298793830914747\n 280 368.81271 -958.20435 -949.48023 2777.0726 1809.9299 \n290 376.21677847444868803 -958.04461669921875 -949.14535683254041487 1492.4762343307020274 1809.9298793830914747\n 290 376.21678 -958.04462 -949.14536 1492.4762 1809.9299 \n300 374.30667327966455105 -958.2183837890625 -949.36430670920719876 -645.28430971218278955 1809.9298793830914747\n 300 374.30667 -958.21838 -949.36431 -645.28431 1809.9299 \n310 361.44552299349192026 -958.01593017578125 -949.46607854553292327 3105.0892987513620938 1809.9298793830914747\n 310 361.44552 -958.01593 -949.46608 3105.0893 1809.9299 \n320 349.80745753863863001 -957.9735107421875 -949.69895297110224419 -379.13226111580485167 1809.9298793830914747\n 320 349.80746 -957.97351 -949.69895 -379.13226 1809.9299 \n330 355.28235181499576356 -957.98529052734375 -949.58122628633054774 1854.6336502830301924 1809.9298793830914747\n 330 355.28235 -957.98529 -949.58123 1854.6337 1809.9299 \n340 381.020044753571824 -958.40716552734375 -949.39428628674988886 -839.95248540467298426 1809.9298793830914747\n 340 381.02004 -958.40717 -949.39429 -839.95249 1809.9299 \n350 373.81607171690615132 -957.98480224609375 -949.14233015317097397 2729.9399222625347647 1809.9298793830914747\n 350 373.81607 -957.9848 -949.14233 2729.9399 1809.9299 \n360 386.35484846762648203 -958.3848876953125 -949.2458157719212295 911.84361643808006193 1809.9298793830914747\n 360 386.35485 -958.38489 -949.24582 911.84362 1809.9299 \n370 366.83628494289740729 -958.5029296875 -949.82556170441466747 -2075.2851000857053805 1809.9298793830914747\n 370 366.83628 -958.50293 -949.82556 -2075.2851 1809.9299 \n380 380.42193095523185775 -958.48736572265625 -949.4886346286252774 4381.8674187077322131 1809.9298793830914747\n 380 380.42193 -958.48737 -949.48863 4381.8674 1809.9299 \n390 347.34769606009774634 -957.6953125 -949.47893941885956792 -2456.6105419831615109 1809.9298793830914747\n 390 347.3477 -957.69531 -949.47894 -2456.6105 1809.9299 \n400 352.97610167536896597 -957.91729736328125 -949.5677865618922624 7865.9368940733102136 1809.9298793830914747\n 400 352.9761 -957.9173 -949.56779 7865.9369 1809.9299 \n410 353.10666018450081083 -957.73779296875 -949.38519385719769161 -4989.7809190577308982 1809.9298793830914747\n 410 353.10666 -957.73779 -949.38519 -4989.7809 1809.9299 \n420 369.12890951348498447 -958.27557373046875 -949.54397461523365109 8734.8565660249405482 1809.9298793830914747\n 420 369.12891 -958.27557 -949.54397 8734.8566 1809.9299 \n430 341.24601204841138724 -957.774658203125 -949.70261805648192421 -5312.7471148321346845 1809.9298793830914747\n 430 341.24601 -957.77466 -949.70262 -5312.7471 1809.9299 \n440 338.93406866984810222 -957.77581787109375 -949.75846583540180745 10912.954742425434233 1809.9298793830914747\n 440 338.93407 -957.77582 -949.75847 10912.955 1809.9299 \n450 347.03217177807630378 -957.72894287109375 -949.52003339269685966 -5333.438674577346319 1809.9298793830914747\n 450 347.03217 -957.72894 -949.52003 -5333.4387 1809.9299 \n460 356.21562833728677333 -957.97454833984375 -949.54840780990741678 8940.4830165785897407 1809.9298793830914747\n 460 356.21563 -957.97455 -949.54841 8940.483 1809.9299 \n470 370.31347369663683367 -958.25762939453125 -949.49800987962828458 -3376.2427915034259058 1809.9298793830914747\n 470 370.31347 -958.25763 -949.49801 -3376.2428 1809.9299 \n480 366.28611203962304899 -958.01123046875 -949.34687660921781571 6831.6791024523818123 1809.9298793830914747\n 480 366.28611 -958.01123 -949.34688 6831.6791 1809.9299 \n490 366.20898906280382334 -957.9986572265625 -949.336127680701793 -1089.3675463962440517 1809.9298793830914747\n 490 366.20899 -957.99866 -949.33613 -1089.3675 1809.9299 \n500 365.27188681451849561 -958.096923828125 -949.45656106723049561 4678.6586299143518772 1809.9298793830914747\n 500 365.27189 -958.09692 -949.45656 4678.6586 1809.9299 \nLoop time of 97.3972 on 1 procs for 500 steps with 184 atoms\n\nPerformance: 0.222 ns/day, 108.219 hours/ns, 5.134 timesteps/s, 944.586 atom-step/s\n88.4% CPU use with 1 MPI tasks x 1 OpenMP threads\n\nMPI task timing breakdown:\nSection | min time | avg time | max time |%varavg| %total\n---------------------------------------------------------------\nPair | 96.421 | 96.421 | 96.421 | 0.0 | 99.00\nNeigh | 0.93273 | 0.93273 | 0.93273 | 0.0 | 0.96\nComm | 0.0245 | 0.0245 | 0.0245 | 0.0 | 0.03\nOutput | 0.0062822 | 0.0062822 | 0.0062822 | 0.0 | 0.01\nModify | 0.0094216 | 0.0094216 | 0.0094216 | 0.0 | 0.01\nOther | | 0.003157 | | | 0.00\n\nNlocal: 184 ave 184 max 184 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\nNghost: 9765 ave 9765 max 9765 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\nNeighs: 0 ave 0 max 0 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\nFullNghs: 383610 ave 383610 max 383610 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\n\nTotal # of neighbors = 383610\nAve neighs/atom = 2084.837\nNeighbor list builds = 7\nDangerous builds = 0\nTotal wall time: 0:01:38\n")
Does that hold up quantitatively? The standard structural probe of solvation is the ion-oxygen radial distribution function g(r): the density of water oxygens at a distance r from each ion, normalized to the bulk density. A tall first peak followed by a deep minimum is the fingerprint of a well-defined hydration shell, and that first minimum sets the shell radius.
nacl_traj = ase.io.read("nacl_traj.lammpstrj", ":", format="lammps-dump-text")
g_na = []
r_na = []
g_cl = []
r_cl = []
for frame in nacl_traj:
g_na_, r_na_ = get_rdf(frame, 6.0, 100, elements=["Na", "O"])
g_cl_, r_cl_ = get_rdf(frame, 6.0, 100, elements=["Cl", "O"])
g_na.append(g_na_)
r_na.append(r_na_)
g_cl.append(g_cl_)
r_cl.append(r_cl_)
g_na = np.array(g_na).mean(axis=0)
r_na = np.array(r_na).mean(axis=0)
g_cl = np.array(g_cl).mean(axis=0)
r_cl = np.array(r_cl).mean(axis=0)
fig, ax = plt.subplots(figsize=(7, 4), dpi=200)
ax.plot(r_na, g_na, color="tab:orange", label="Na⁺-O")
ax.plot(r_cl, g_cl, color="tab:green", label="Cl⁻-O")
ax.axvline(3.1, color="tab:orange", ls="--", lw=0.8)
ax.axvline(3.8, color="tab:green", ls="--", lw=0.8)
ax.set(xlabel="r (Å)", ylabel="g(r)", title="Ion-oxygen radial distribution")
ax.legend()
plt.show()
If sampled for longer, g(r) of both ions would show a structured first peak and a clear first minimum (dashed lines, near 3.1 Å for Na⁺ and 3.8 Å for Cl⁻). Counting the water oxygens inside those radii every frame gives a coordination number, which we attach to the trajectory and show on the map beside the structure below. It fluctuates around 5-6 for Na⁺ and about 7 for Cl⁻. The default chemiscope visualization shows the Na⁺ coordination as the y-axis, but you can switch to the Cl⁻ one with the dropdown menu.
def first_shell_count(
traj: list[ase.Atoms], ion: str, cutoff: float, other: str = "O"
) -> np.ndarray:
"""
Mean number of other atoms within cutoff of each ion.
:param traj: trajectory to analyze
:param ion: element symbol of the ion (e.g. "Na" or "Cl")
:param cutoff: shell radius in Å
:param other: element symbol of the other species (default: "O")
:return: array of shape (n_frames,) with the average count per ion at each frame
"""
sym = np.array(traj[0].get_chemical_symbols())
i_ion = np.where(sym == ion)[0]
i_other = np.where(sym == other)[0]
counts = []
for frame in traj:
d = frame.get_all_distances(mic=True)[i_ion, :][:, i_other]
counts.append((d < cutoff).sum(axis=1).mean())
return np.array(counts)
n_na = first_shell_count(nacl_traj, "Na", 3.1)
n_cl = first_shell_count(nacl_traj, "Cl", 3.8)
time_ps = np.arange(len(nacl_traj)) * 0.0005 * 10 # 0.5 fs step, dumped every 10
for frame in nacl_traj:
frame.wrap()
chemiscope.show(
structures=nacl_traj,
properties={
"time [ps]": {"target": "structure", "values": time_ps},
"Na+ first-shell waters": {"target": "structure", "values": n_na},
"Cl- first-shell waters": {"target": "structure", "values": n_cl},
},
mode="default",
settings=chemiscope.quick_settings(
trajectory=True,
x="time [ps]",
y="Na+ first-shell waters",
structure_settings={"playbackDelay": 20, "unitCell": True},
map_settings={"markerOutline": False},
),
)
An organic mixture: ethanol-water¶
Ethanol (C₂H₅OH) adds a third element, carbon. For LAMMPS this is simply a third
atom type, and the pair_coeff line grows by one entry to map C (Z=6). The model
handles the new C-H, C-C, C-O and carbon-water interactions with no extra input. This
kind of mixed organic/aqueous environment is common in chemistry, but can be tedious
to parameterize with traditional force fields.
# Ethanol-water mixture NVT at 400 K with PET-MAD-xs
# Atom types: 1=H, 2=O, 3=C
units metal
atom_style atomic
variable seed index 34567
variable t_target equal 400.0
variable tdamp equal 100*dt
variable nsteps equal 500 # 500 * 0.5 fs = 0.25 ps
variable dump_every equal 10
read_data data/ethanol_water.data
pair_style metatomic pet-mad-xs-v1.5.0.pt device cpu
pair_coeff * * 1 8 6
timestep 0.0005
neighbor 2.0 bin
neigh_modify one 50000 page 500000
thermo_style custom step temp pe etotal press vol
thermo 10
velocity all create ${t_target} ${seed} mom yes rot yes dist gaussian
reset_timestep 0
fix nve_int all nve
fix thermostat all temp/csvr ${t_target} ${t_target} ${tdamp} ${seed}
print "step temp pe etotal press vol" file ethanol_thermo.out
fix thermofile all print ${dump_every} "$(step) $(temp) $(pe) $(etotal) $(press) $(vol)" append ethanol_thermo.out
dump traj all custom ${dump_every} ethanol_traj.lammpstrj id type element xu yu zu
dump_modify traj element H O C sort id
run ${nsteps}
run_command("lmp -in in_ethanol_nvt.lmp", print_output=True)
LAMMPS (4 Jul 2026)
OMP_NUM_THREADS environment is not set. Defaulting to 1 thread.
using 1 OpenMP thread(s) per MPI task
Reading data file ...
orthogonal box = (0.56573683 0.56573683 0.56573683) to (13.499283 13.499283 13.499283)
1 by 1 by 1 MPI processor grid
reading atoms ...
192 atoms
reading velocities ...
192 velocities
read_data CPU = 0.001 seconds
This is the PET-MAD-XS v1.5.0 model
===================================
A universal interatomic potential for advanced materials modeling based on a
Point-Edge Transformer (PET) architecture, and trained on the MAD dataset.
Model size: xs. Model version: 1.5.0.
Model authors
-------------
- Arslan Mazitov ([email protected])
- Filippo Bigi
- Matthias Kellner
- Paolo Pegolo
- Davide Tisi
- Guillaume Fraux
- Sergey Pozdnyakov
- Philip Loche
- Michele Ceriotti ([email protected])
Model references
----------------
Please cite the following references when using this model:
- about this specific model:
* https://doi.org/10.1038/s41467-025-65662-7
* https://arxiv.org/abs/2601.16195
- about the architecture of this model:
* LLPR (uncertainty method):
https://iopscience.iop.org/article/10.1088/2632-2153/ad805f
* LPR (if using per-atom uncertainty):
https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704
* https://arxiv.org/abs/2305.19302v3
Found 'energy_uncertainty' output, we will check for atoms with high uncertainty on the energy predictions
[W1112 22:38:58.854822627 module.cpp:218] Warning: module does not have '_mts_buffer_names'; falling back to processing all attributes. This is deprecated and will be removed in a future version, update your version of metatensor-learn and use `register_buffer` explicitly to remove this warning. (function operator())
Running simulation on cpu device with float32 data
step temp pe etotal press vol
CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
Your simulation uses code contributions which should be cited:
- LLPR (uncertainty method): https://iopscience.iop.org/article/10.1088/2632-2153/ad805f
- LPR (if using per-atom uncertainty): https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704
- https://arxiv.org/abs/2305.19302v3
- https://doi.org/10.1038/s41467-025-65662-7
- https://arxiv.org/abs/2601.16195
The log file lists these citations in BibTeX format.
CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
Neighbor list info ...
update: every = 1 steps, delay = 0 steps, check = yes
max neighbors/atom: 50000, page size: 500000
master list distance cutoff = 17
ghost atom cutoff = 17
binsize = 8.5, bins = 2 2 2
1 neighbor lists, perpetual/occasional/extra = 1 0 0
(1) pair metatomic, perpetual
attributes: full, newton on, ghost
pair build: full/bin/ghost
stencil: full/ghost/bin/3d
bin: standard
Setting up Verlet run ...
Unit style : metal
Current step : 0
Time step : 5e-04
0 400 -1028.9742431640625 -1019.0987680860624778 717.51682503471897689 2163.4799322060885061
Per MPI rank memory allocation (min/avg/max) = 48.77 | 48.77 | 48.77 Mbytes
Step Temp PotEng TotEng Press Volume
0 400 -1028.9742 -1019.0988 717.51683 2163.4799
10 349.42218400918369525 -1027.592529296875 -1018.9657541221674819 -3486.295519217384026 2163.4799322060885061
10 349.42218 -1027.5925 -1018.9658 -3486.2955 2163.4799
20 355.95343052041005194 -1027.8218994140625 -1019.0338763339801744 2142.6315074866952273 2163.4799322060885061
20 355.95343 -1027.8219 -1019.0339 2142.6315 2163.4799
30 334.17441061579535244 -1027.2874755859375 -1019.0371479265834296 -2718.7649894840965317 2163.4799322060885061
30 334.17441 -1027.2875 -1019.0371 -2718.765 2163.4799
40 362.92848731804122053 -1027.7923583984375 -1018.8321303194236407 -1187.041094676281773 2163.4799322060885061
40 362.92849 -1027.7924 -1018.8321 -1187.0411 2163.4799
50 353.89805323155746919 -1027.4453125 -1018.7080339878975792 -4482.7427147296430121 2163.4799322060885061
50 353.89805 -1027.4453 -1018.708 -4482.7427 2163.4799
60 374.43759758289479578 -1027.9898681640625 -1018.7454952560723314 -1737.8300076318919309 2163.4799322060885061
60 374.4376 -1027.9899 -1018.7455 -1737.83 2163.4799
70 365.46118474268536147 -1027.596435546875 -1018.5736784921181197 -1459.8112919911534391 2163.4799322060885061
70 365.46118 -1027.5964 -1018.5737 -1459.8113 2163.4799
80 358.77885252725923237 -1027.21728515625 -1018.3595061146340868 1656.1738239276116929 2163.4799322060885061
80 358.77885 -1027.2173 -1018.3595 1656.1738 2163.4799
90 381.5412394442068944 -1027.7908935546875 -1018.3711410512862585 -1895.7055939821452739 2163.4799322060885061
90 381.54124 -1027.7909 -1018.3711 -1895.7056 2163.4799
100 382.82974346116475317 -1027.853759765625 -1018.4021957889552823 -1163.6294116432820829 2163.4799322060885061
100 382.82974 -1027.8538 -1018.4022 -1163.6294 2163.4799
110 377.19127754355292836 -1027.6220703125 -1018.3097126599491276 -3631.747488323052039 2163.4799322060885061
110 377.19128 -1027.6221 -1018.3097 -3631.7475 2163.4799
120 363.76280905215696748 -1027.15673828125 -1018.1759118935053721 4850.1819746739256516 2163.4799322060885061
120 363.76281 -1027.1567 -1018.1759 4850.182 2163.4799
130 349.80128802047227055 -1026.5670166015625 -1017.9308818463163107 -2141.191830946088885 2163.4799322060885061
130 349.80129 -1026.567 -1017.9309 -2141.1918 2163.4799
140 356.03468912810456004 -1026.57373046875 -1017.7837012202797951 7723.7641925793359405 2163.4799322060885061
140 356.03469 -1026.5737 -1017.7837 7723.7642 2163.4799
150 368.82244122990658752 -1026.542236328125 -1017.4364942616923599 -4841.5642811041252571 2163.4799322060885061
150 368.82244 -1026.5422 -1017.4365 -4841.5643 2163.4799
160 381.17826948844231083 -1026.6846923828125 -1017.2739011312918365 5882.3535690258449904 2163.4799322060885061
160 381.17827 -1026.6847 -1017.2739 5882.3536 2163.4799
170 373.09475217817521298 -1026.7027587890625 -1017.4915389718920551 -4756.6325068653186463 2163.4799322060885061
170 373.09475 -1026.7028 -1017.4915 -4756.6325 2163.4799
180 390.22774885981755233 -1026.848388671875 -1017.2141776503520987 6978.2788193237747691 2163.4799322060885061
180 390.22775 -1026.8484 -1017.2142 6978.2788 2163.4799
190 394.16298286034293596 -1027.242919921875 -1017.5115531371063753 -1389.0215714746984759 2163.4799322060885061
190 394.16298 -1027.2429 -1017.5116 -1389.0216 2163.4799
200 400.3763384996685204 -1027.137939453125 -1017.2531730714390505 3610.2662469872020665 2163.4799322060885061
200 400.37634 -1027.1379 -1017.2532 3610.2662 2163.4799
210 405.17908337292556098 -1026.8817138671875 -1016.8783740172469834 -815.07385519534466312 2163.4799322060885061
210 405.17908 -1026.8817 -1016.8784 -815.07386 2163.4799
220 420.06102594271851558 -1027.5062255859375 -1017.1354701035963899 -2095.6330720881628622 2163.4799322060885061
220 420.06103 -1027.5062 -1017.1355 -2095.6331 2163.4799
230 392.82501159946372127 -1027.119384765625 -1017.4210507354611082 904.63580205286200453 2163.4799322060885061
230 392.82501 -1027.1194 -1017.4211 904.6358 2163.4799
240 381.13616863211842656 -1027.0189208984375 -1017.6091690618102348 -1332.7090621924232892 2163.4799322060885061
240 381.13617 -1027.0189 -1017.6092 -1332.7091 2163.4799
250 392.56812876433696147 -1027.026611328125 -1017.3346193980517 5603.8152747003068725 2163.4799322060885061
250 392.56813 -1027.0266 -1017.3346 5603.8153 2163.4799
260 394.15127369798324253 -1027.01123046875 -1017.2801527678340108 -1792.4369270820300244 2163.4799322060885061
260 394.15127 -1027.0112 -1017.2802 -1792.4369 2163.4799
270 380.18425905731237435 -1026.7059326171875 -1017.319682178766584 2910.4201382769119846 2163.4799322060885061
270 380.18426 -1026.7059 -1017.3197 2910.4201 2163.4799
280 374.36736908290595238 -1026.6458740234375 -1017.4032349649507978 -3824.572998811407615 2163.4799322060885061
280 374.36737 -1026.6459 -1017.4032 -3824.573 2163.4799
290 391.94811032393681671 -1027.187255859375 -1017.5105713709418751 -2012.1581118069761942 2163.4799322060885061
290 391.94811 -1027.1873 -1017.5106 -2012.1581 2163.4799
300 376.63468544542109839 -1026.712646484375 -1017.4140303603084021 -2754.1609311017150503 2163.4799322060885061
300 376.63469 -1026.7126 -1017.414 -2754.1609 2163.4799
310 360.6546755000569533 -1026.343994140625 -1017.4399034914624735 794.33858852195555755 2163.4799322060885061
310 360.65468 -1026.344 -1017.4399 794.33859 2163.4799
320 385.50406291861162345 -1026.5064697265625 -1016.988880312011247 3231.3733342119239751 2163.4799322060885061
320 385.50406 -1026.5065 -1016.9889 3231.3733 2163.4799
330 377.58400538937860347 -1026.158935546875 -1016.8368819591894407 1455.0140582805966005 2163.4799322060885061
330 377.58401 -1026.1589 -1016.8369 1455.0141 2163.4799
340 396.18316493284191893 -1026.6485595703125 -1016.8673171412689271 1650.3635382130985363 2163.4799322060885061
340 396.18316 -1026.6486 -1016.8673 1650.3635 2163.4799
350 387.84398511650863384 -1026.211181640625 -1016.6358226176993185 -5903.019574067890062 2163.4799322060885061
350 387.84399 -1026.2112 -1016.6358 -5903.0196 2163.4799
360 410.46447057194217223 -1026.40625 -1016.2724208761558202 1430.7218597770468023 2163.4799322060885061
360 410.46447 -1026.4062 -1016.2724 1430.7219 2163.4799
370 385.92954467507394156 -1025.6885986328125 -1016.1605046320560177 -2691.767405219664397 2163.4799322060885061
370 385.92954 -1025.6886 -1016.1605 -2691.7674 2163.4799
380 416.70756587828037709 -1026.1011962890625 -1015.8132333349500414 4342.3765654897742934 2163.4799322060885061
380 416.70757 -1026.1012 -1015.8132 4342.3766 2163.4799
390 409.72420781272143131 -1025.88134765625 -1015.765794648480437 -3450.7249787115588333 2163.4799322060885061
390 409.72421 -1025.8813 -1015.7658 -3450.725 2163.4799
400 394.80920947988295211 -1025.70263671875 -1015.95531544679136 2652.5861336972902791 2163.4799322060885061
400 394.80921 -1025.7026 -1015.9553 2652.5861 2163.4799
410 422.82324586378160802 -1026.1741943359375 -1015.7352432686203656 -225.36224076115135517 2163.4799322060885061
410 422.82325 -1026.1742 -1015.7352 -225.36224 2163.4799
420 413.89894493054578106 -1026.1680908203125 -1015.9494690316322476 2078.2117382508563423 2163.4799322060885061
420 413.89894 -1026.1681 -1015.9495 2078.2117 2163.4799
430 395.27518527021993577 -1025.7569580078125 -1015.9981324050927469 1347.8967052914140368 2163.4799322060885061
430 395.27519 -1025.757 -1015.9981 1347.8967 2163.4799
440 380.74592536404071552 -1025.70556640625 -1016.3054491637934689 -2874.8196658917681816 2163.4799322060885061
440 380.74593 -1025.7056 -1016.3054 -2874.8197 2163.4799
450 400.66887351650512983 -1026.021240234375 -1016.1292515470184981 581.92806061408475671 2163.4799322060885061
450 400.66887 -1026.0212 -1016.1293 581.92806 2163.4799
460 398.14875522088902926 -1025.8626708984375 -1016.0329006246359995 -1075.0429855684494669 2163.4799322060885061
460 398.14876 -1025.8627 -1016.0329 -1075.043 2163.4799
470 380.37486801224810051 -1025.5836181640625 -1016.1926618406812395 3332.0170868604695897 2163.4799322060885061
470 380.37487 -1025.5836 -1016.1927 3332.0171 2163.4799
480 422.64425955235878973 -1026.5401611328125 -1016.1056290026398301 650.47644334875144523 2163.4799322060885061
480 422.64426 -1026.5402 -1016.1056 650.47644 2163.4799
490 411.69368051031727873 -1026.0535888671875 -1015.8894121630631844 -1347.8853738152106416 2163.4799322060885061
490 411.69368 -1026.0536 -1015.8894 -1347.8854 2163.4799
500 409.15463300468798025 -1025.697998046875 -1015.5965070936599659 4266.4235048339542118 2163.4799322060885061
500 409.15463 -1025.698 -1015.5965 4266.4235 2163.4799
Loop time of 94.1532 on 1 procs for 500 steps with 192 atoms
Performance: 0.229 ns/day, 104.615 hours/ns, 5.310 timesteps/s, 1.020 katom-step/s
88.7% CPU use with 1 MPI tasks x 1 OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 93.192 | 93.192 | 93.192 | 0.0 | 98.98
Neigh | 0.91859 | 0.91859 | 0.91859 | 0.0 | 0.98
Comm | 0.023645 | 0.023645 | 0.023645 | 0.0 | 0.03
Output | 0.0064293 | 0.0064293 | 0.0064293 | 0.0 | 0.01
Modify | 0.0095891 | 0.0095891 | 0.0095891 | 0.0 | 0.01
Other | | 0.003215 | | | 0.00
Nlocal: 192 ave 192 max 192 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 9037 ave 9037 max 9037 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
FullNghs: 349944 ave 349944 max 349944 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 349944
Ave neighs/atom = 1822.625
Neighbor list builds = 8
Dangerous builds = 0
Total wall time: 0:01:35
CompletedProcess(args=['lmp', '-in', 'in_ethanol_nvt.lmp'], returncode=0, stdout="LAMMPS (4 Jul 2026)\nOMP_NUM_THREADS environment is not set. Defaulting to 1 thread.\n using 1 OpenMP thread(s) per MPI task\nReading data file ...\n orthogonal box = (0.56573683 0.56573683 0.56573683) to (13.499283 13.499283 13.499283)\n 1 by 1 by 1 MPI processor grid\n reading atoms ...\n 192 atoms\n reading velocities ...\n 192 velocities\n read_data CPU = 0.001 seconds\n\nThis is the PET-MAD-XS v1.5.0 model\n===================================\n\nA universal interatomic potential for advanced materials modeling based on a\nPoint-Edge Transformer (PET) architecture, and trained on the MAD dataset.\nModel size: xs. Model version: 1.5.0.\n\nModel authors\n-------------\n\n- Arslan Mazitov ([email protected])\n- Filippo Bigi\n- Matthias Kellner\n- Paolo Pegolo\n- Davide Tisi\n- Guillaume Fraux\n- Sergey Pozdnyakov\n- Philip Loche\n- Michele Ceriotti ([email protected])\n\nModel references\n----------------\n\nPlease cite the following references when using this model:\n- about this specific model:\n * https://doi.org/10.1038/s41467-025-65662-7\n * https://arxiv.org/abs/2601.16195\n- about the architecture of this model:\n * LLPR (uncertainty method):\n https://iopscience.iop.org/article/10.1088/2632-2153/ad805f\n * LPR (if using per-atom uncertainty):\n https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704\n * https://arxiv.org/abs/2305.19302v3\n\nFound 'energy_uncertainty' output, we will check for atoms with high uncertainty on the energy predictions\n[W1112 22:38:58.854822627 module.cpp:218] Warning: module does not have '_mts_buffer_names'; falling back to processing all attributes. This is deprecated and will be removed in a future version, update your version of metatensor-learn and use `register_buffer` explicitly to remove this warning. (function operator())\nRunning simulation on cpu device with float32 data\nstep temp pe etotal press vol\n\nCITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE\n\nYour simulation uses code contributions which should be cited:\n- LLPR (uncertainty method): https://iopscience.iop.org/article/10.1088/2632-2153/ad805f\n- LPR (if using per-atom uncertainty): https://pubs.acs.org/doi/10.1021/acs.jctc.3c00704\n- https://arxiv.org/abs/2305.19302v3\n- https://doi.org/10.1038/s41467-025-65662-7\n- https://arxiv.org/abs/2601.16195\nThe log file lists these citations in BibTeX format.\n\nCITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE\n\nNeighbor list info ...\n update: every = 1 steps, delay = 0 steps, check = yes\n max neighbors/atom: 50000, page size: 500000\n master list distance cutoff = 17\n ghost atom cutoff = 17\n binsize = 8.5, bins = 2 2 2\n 1 neighbor lists, perpetual/occasional/extra = 1 0 0\n (1) pair metatomic, perpetual\n attributes: full, newton on, ghost\n pair build: full/bin/ghost\n stencil: full/ghost/bin/3d\n bin: standard\nSetting up Verlet run ...\n Unit style : metal\n Current step : 0\n Time step : 5e-04\n0 400 -1028.9742431640625 -1019.0987680860624778 717.51682503471897689 2163.4799322060885061\nPer MPI rank memory allocation (min/avg/max) = 48.77 | 48.77 | 48.77 Mbytes\n Step Temp PotEng TotEng Press Volume \n 0 400 -1028.9742 -1019.0988 717.51683 2163.4799 \n10 349.42218400918369525 -1027.592529296875 -1018.9657541221674819 -3486.295519217384026 2163.4799322060885061\n 10 349.42218 -1027.5925 -1018.9658 -3486.2955 2163.4799 \n20 355.95343052041005194 -1027.8218994140625 -1019.0338763339801744 2142.6315074866952273 2163.4799322060885061\n 20 355.95343 -1027.8219 -1019.0339 2142.6315 2163.4799 \n30 334.17441061579535244 -1027.2874755859375 -1019.0371479265834296 -2718.7649894840965317 2163.4799322060885061\n 30 334.17441 -1027.2875 -1019.0371 -2718.765 2163.4799 \n40 362.92848731804122053 -1027.7923583984375 -1018.8321303194236407 -1187.041094676281773 2163.4799322060885061\n 40 362.92849 -1027.7924 -1018.8321 -1187.0411 2163.4799 \n50 353.89805323155746919 -1027.4453125 -1018.7080339878975792 -4482.7427147296430121 2163.4799322060885061\n 50 353.89805 -1027.4453 -1018.708 -4482.7427 2163.4799 \n60 374.43759758289479578 -1027.9898681640625 -1018.7454952560723314 -1737.8300076318919309 2163.4799322060885061\n 60 374.4376 -1027.9899 -1018.7455 -1737.83 2163.4799 \n70 365.46118474268536147 -1027.596435546875 -1018.5736784921181197 -1459.8112919911534391 2163.4799322060885061\n 70 365.46118 -1027.5964 -1018.5737 -1459.8113 2163.4799 \n80 358.77885252725923237 -1027.21728515625 -1018.3595061146340868 1656.1738239276116929 2163.4799322060885061\n 80 358.77885 -1027.2173 -1018.3595 1656.1738 2163.4799 \n90 381.5412394442068944 -1027.7908935546875 -1018.3711410512862585 -1895.7055939821452739 2163.4799322060885061\n 90 381.54124 -1027.7909 -1018.3711 -1895.7056 2163.4799 \n100 382.82974346116475317 -1027.853759765625 -1018.4021957889552823 -1163.6294116432820829 2163.4799322060885061\n 100 382.82974 -1027.8538 -1018.4022 -1163.6294 2163.4799 \n110 377.19127754355292836 -1027.6220703125 -1018.3097126599491276 -3631.747488323052039 2163.4799322060885061\n 110 377.19128 -1027.6221 -1018.3097 -3631.7475 2163.4799 \n120 363.76280905215696748 -1027.15673828125 -1018.1759118935053721 4850.1819746739256516 2163.4799322060885061\n 120 363.76281 -1027.1567 -1018.1759 4850.182 2163.4799 \n130 349.80128802047227055 -1026.5670166015625 -1017.9308818463163107 -2141.191830946088885 2163.4799322060885061\n 130 349.80129 -1026.567 -1017.9309 -2141.1918 2163.4799 \n140 356.03468912810456004 -1026.57373046875 -1017.7837012202797951 7723.7641925793359405 2163.4799322060885061\n 140 356.03469 -1026.5737 -1017.7837 7723.7642 2163.4799 \n150 368.82244122990658752 -1026.542236328125 -1017.4364942616923599 -4841.5642811041252571 2163.4799322060885061\n 150 368.82244 -1026.5422 -1017.4365 -4841.5643 2163.4799 \n160 381.17826948844231083 -1026.6846923828125 -1017.2739011312918365 5882.3535690258449904 2163.4799322060885061\n 160 381.17827 -1026.6847 -1017.2739 5882.3536 2163.4799 \n170 373.09475217817521298 -1026.7027587890625 -1017.4915389718920551 -4756.6325068653186463 2163.4799322060885061\n 170 373.09475 -1026.7028 -1017.4915 -4756.6325 2163.4799 \n180 390.22774885981755233 -1026.848388671875 -1017.2141776503520987 6978.2788193237747691 2163.4799322060885061\n 180 390.22775 -1026.8484 -1017.2142 6978.2788 2163.4799 \n190 394.16298286034293596 -1027.242919921875 -1017.5115531371063753 -1389.0215714746984759 2163.4799322060885061\n 190 394.16298 -1027.2429 -1017.5116 -1389.0216 2163.4799 \n200 400.3763384996685204 -1027.137939453125 -1017.2531730714390505 3610.2662469872020665 2163.4799322060885061\n 200 400.37634 -1027.1379 -1017.2532 3610.2662 2163.4799 \n210 405.17908337292556098 -1026.8817138671875 -1016.8783740172469834 -815.07385519534466312 2163.4799322060885061\n 210 405.17908 -1026.8817 -1016.8784 -815.07386 2163.4799 \n220 420.06102594271851558 -1027.5062255859375 -1017.1354701035963899 -2095.6330720881628622 2163.4799322060885061\n 220 420.06103 -1027.5062 -1017.1355 -2095.6331 2163.4799 \n230 392.82501159946372127 -1027.119384765625 -1017.4210507354611082 904.63580205286200453 2163.4799322060885061\n 230 392.82501 -1027.1194 -1017.4211 904.6358 2163.4799 \n240 381.13616863211842656 -1027.0189208984375 -1017.6091690618102348 -1332.7090621924232892 2163.4799322060885061\n 240 381.13617 -1027.0189 -1017.6092 -1332.7091 2163.4799 \n250 392.56812876433696147 -1027.026611328125 -1017.3346193980517 5603.8152747003068725 2163.4799322060885061\n 250 392.56813 -1027.0266 -1017.3346 5603.8153 2163.4799 \n260 394.15127369798324253 -1027.01123046875 -1017.2801527678340108 -1792.4369270820300244 2163.4799322060885061\n 260 394.15127 -1027.0112 -1017.2802 -1792.4369 2163.4799 \n270 380.18425905731237435 -1026.7059326171875 -1017.319682178766584 2910.4201382769119846 2163.4799322060885061\n 270 380.18426 -1026.7059 -1017.3197 2910.4201 2163.4799 \n280 374.36736908290595238 -1026.6458740234375 -1017.4032349649507978 -3824.572998811407615 2163.4799322060885061\n 280 374.36737 -1026.6459 -1017.4032 -3824.573 2163.4799 \n290 391.94811032393681671 -1027.187255859375 -1017.5105713709418751 -2012.1581118069761942 2163.4799322060885061\n 290 391.94811 -1027.1873 -1017.5106 -2012.1581 2163.4799 \n300 376.63468544542109839 -1026.712646484375 -1017.4140303603084021 -2754.1609311017150503 2163.4799322060885061\n 300 376.63469 -1026.7126 -1017.414 -2754.1609 2163.4799 \n310 360.6546755000569533 -1026.343994140625 -1017.4399034914624735 794.33858852195555755 2163.4799322060885061\n 310 360.65468 -1026.344 -1017.4399 794.33859 2163.4799 \n320 385.50406291861162345 -1026.5064697265625 -1016.988880312011247 3231.3733342119239751 2163.4799322060885061\n 320 385.50406 -1026.5065 -1016.9889 3231.3733 2163.4799 \n330 377.58400538937860347 -1026.158935546875 -1016.8368819591894407 1455.0140582805966005 2163.4799322060885061\n 330 377.58401 -1026.1589 -1016.8369 1455.0141 2163.4799 \n340 396.18316493284191893 -1026.6485595703125 -1016.8673171412689271 1650.3635382130985363 2163.4799322060885061\n 340 396.18316 -1026.6486 -1016.8673 1650.3635 2163.4799 \n350 387.84398511650863384 -1026.211181640625 -1016.6358226176993185 -5903.019574067890062 2163.4799322060885061\n 350 387.84399 -1026.2112 -1016.6358 -5903.0196 2163.4799 \n360 410.46447057194217223 -1026.40625 -1016.2724208761558202 1430.7218597770468023 2163.4799322060885061\n 360 410.46447 -1026.4062 -1016.2724 1430.7219 2163.4799 \n370 385.92954467507394156 -1025.6885986328125 -1016.1605046320560177 -2691.767405219664397 2163.4799322060885061\n 370 385.92954 -1025.6886 -1016.1605 -2691.7674 2163.4799 \n380 416.70756587828037709 -1026.1011962890625 -1015.8132333349500414 4342.3765654897742934 2163.4799322060885061\n 380 416.70757 -1026.1012 -1015.8132 4342.3766 2163.4799 \n390 409.72420781272143131 -1025.88134765625 -1015.765794648480437 -3450.7249787115588333 2163.4799322060885061\n 390 409.72421 -1025.8813 -1015.7658 -3450.725 2163.4799 \n400 394.80920947988295211 -1025.70263671875 -1015.95531544679136 2652.5861336972902791 2163.4799322060885061\n 400 394.80921 -1025.7026 -1015.9553 2652.5861 2163.4799 \n410 422.82324586378160802 -1026.1741943359375 -1015.7352432686203656 -225.36224076115135517 2163.4799322060885061\n 410 422.82325 -1026.1742 -1015.7352 -225.36224 2163.4799 \n420 413.89894493054578106 -1026.1680908203125 -1015.9494690316322476 2078.2117382508563423 2163.4799322060885061\n 420 413.89894 -1026.1681 -1015.9495 2078.2117 2163.4799 \n430 395.27518527021993577 -1025.7569580078125 -1015.9981324050927469 1347.8967052914140368 2163.4799322060885061\n 430 395.27519 -1025.757 -1015.9981 1347.8967 2163.4799 \n440 380.74592536404071552 -1025.70556640625 -1016.3054491637934689 -2874.8196658917681816 2163.4799322060885061\n 440 380.74593 -1025.7056 -1016.3054 -2874.8197 2163.4799 \n450 400.66887351650512983 -1026.021240234375 -1016.1292515470184981 581.92806061408475671 2163.4799322060885061\n 450 400.66887 -1026.0212 -1016.1293 581.92806 2163.4799 \n460 398.14875522088902926 -1025.8626708984375 -1016.0329006246359995 -1075.0429855684494669 2163.4799322060885061\n 460 398.14876 -1025.8627 -1016.0329 -1075.043 2163.4799 \n470 380.37486801224810051 -1025.5836181640625 -1016.1926618406812395 3332.0170868604695897 2163.4799322060885061\n 470 380.37487 -1025.5836 -1016.1927 3332.0171 2163.4799 \n480 422.64425955235878973 -1026.5401611328125 -1016.1056290026398301 650.47644334875144523 2163.4799322060885061\n 480 422.64426 -1026.5402 -1016.1056 650.47644 2163.4799 \n490 411.69368051031727873 -1026.0535888671875 -1015.8894121630631844 -1347.8853738152106416 2163.4799322060885061\n 490 411.69368 -1026.0536 -1015.8894 -1347.8854 2163.4799 \n500 409.15463300468798025 -1025.697998046875 -1015.5965070936599659 4266.4235048339542118 2163.4799322060885061\n 500 409.15463 -1025.698 -1015.5965 4266.4235 2163.4799 \nLoop time of 94.1532 on 1 procs for 500 steps with 192 atoms\n\nPerformance: 0.229 ns/day, 104.615 hours/ns, 5.310 timesteps/s, 1.020 katom-step/s\n88.7% CPU use with 1 MPI tasks x 1 OpenMP threads\n\nMPI task timing breakdown:\nSection | min time | avg time | max time |%varavg| %total\n---------------------------------------------------------------\nPair | 93.192 | 93.192 | 93.192 | 0.0 | 98.98\nNeigh | 0.91859 | 0.91859 | 0.91859 | 0.0 | 0.98\nComm | 0.023645 | 0.023645 | 0.023645 | 0.0 | 0.03\nOutput | 0.0064293 | 0.0064293 | 0.0064293 | 0.0 | 0.01\nModify | 0.0095891 | 0.0095891 | 0.0095891 | 0.0 | 0.01\nOther | | 0.003215 | | | 0.00\n\nNlocal: 192 ave 192 max 192 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\nNghost: 9037 ave 9037 max 9037 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\nNeighs: 0 ave 0 max 0 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\nFullNghs: 349944 ave 349944 max 349944 min\nHistogram: 1 0 0 0 0 0 0 0 0 0\n\nTotal # of neighbors = 349944\nAve neighs/atom = 1822.625\nNeighbor list builds = 8\nDangerous builds = 0\nTotal wall time: 0:01:35\n")
We claimed that the two species mix and hydrogen-bond to each other; we can count those bonds explicitly. Using the standard geometric definition (an O-H…O motif with the two oxygens within 3.5 Å and an O-H…O angle above 150°) we classify each hydrogen bond as water-water or water-ethanol. (A hydroxyl H is identified as the H whose nearest heavy neighbor is an oxygen; an ethanol O is one bonded to a carbon.)
def count_hbonds(
traj: list[ase.Atoms], r_oo: float = 3.5, angle: float = 150.0
) -> tuple[np.ndarray, np.ndarray]:
"""
Per-frame counts of (water-water, water-ethanol) hydrogen bonds.
A hydrogen bond is counted with the usual geometric criterion: a covalent donor O-H
pointing at an acceptor oxygen, with the two oxygens closer than ``r_oo`` and the
O-H...O angle wider than ``angle``. Each bond is then labelled water-water or
water-ethanol from the identity of its two oxygens.
:param traj: trajectory to analyze
:param r_oo: O-O distance cutoff in Å
:param angle: O-H...O angle cutoff in degrees
:return: tuple of two arrays of shape (n_frames,) with the counts of water-water and
water-ethanol H-bonds at each frame
"""
sym = np.array(traj[0].get_chemical_symbols())
L = traj[0].get_cell()[0, 0] # cubic box edge (minimum-image convention)
iO = np.where(sym == "O")[0]
iH = np.where(sym == "H")[0]
iC = np.where(sym == "C")[0]
heavy = np.concatenate([iO, iC]) # all heavy atoms, oxygens first then carbons
def mic(a, b):
# Minimum-image displacement vectors a[i] -> b[j] for a cubic box. We roll this
# by hand because it is far cheaper than ASE's general-cell minimum image for
# these small systems (we only need a few atom-pair blocks per frame).
d = a[:, None, :] - b[None, :, :]
return d - np.round(d / L) * L
# An ethanol oxygen is the one with a carbon neighbour; the bonding topology never
# changes, so we flag the ethanol oxygens once, from the first frame (one bool per
# atom in ``iO``).
p0 = traj[0].get_positions()
eth_O = (np.linalg.norm(mic(p0[iO], p0[iC]), axis=-1) < 1.7).any(axis=1)
cos_thr = np.cos(np.radians(angle)) # angle > thr <=> cos(angle) < cos(thr)
ww, we = [], []
for frame in traj:
p = frame.get_positions()
# Assign each H to its nearest heavy atom; keep it as a donor only if that
# neighbour is an oxygen within a covalent O-H bond length (1.3 Å).
dist_H = np.linalg.norm(mic(p[iH], p[heavy]), axis=-1)
nn = np.argmin(dist_H, axis=1)
is_oh = (nn < len(iO)) & (dist_H[np.arange(len(iH)), nn] < 1.3)
Hd, Od = iH[is_oh], iO[nn[is_oh]] # donor hydrogens and their donor oxygens
# For every (donor H, candidate acceptor O) pair, build the two bond vectors
# that meet at the hydrogen, plus the donor-acceptor oxygen distance.
vHD = p[Od] - p[Hd]
vHD -= np.round(vHD / L) * L # H -> donor O
vHA = -mic(p[Hd], p[iO]) # H -> every candidate acceptor O
rDA = np.linalg.norm(mic(p[Od], p[iO]), axis=-1) # donor O .. acceptor O
nHD = np.linalg.norm(vHD, axis=-1)
nHA = np.linalg.norm(vHA, axis=-1)
# cos of the O-H...O angle at the hydrogen, for every donor/acceptor pair.
cos = (vHD[:, None, :] * vHA).sum(-1) / (nHD[:, None] * nHA + 1e-9)
# Keep pairs that are both close and near-linear. A donor's own oxygen pairs
# with itself at cos = 1, so it never passes the angle test.
hbond = (rDA < r_oo) & (cos < cos_thr)
# Split the surviving bonds by whether their donor / acceptor oxygen is ethanol.
donor_eth = eth_O[nn[is_oh]][:, None]
accpt_eth = eth_O[None, :]
ww.append(int((hbond & ~donor_eth & ~accpt_eth).sum())) # water-water
we.append(int((hbond & (donor_eth ^ accpt_eth)).sum())) # water-ethanol
return np.array(ww), np.array(we)
ethanol_traj = ase.io.read("ethanol_traj.lammpstrj", ":", format="lammps-dump-text")
hb_ww, hb_we = count_hbonds(ethanol_traj)
time_ps = np.arange(len(ethanol_traj)) * 0.0005 * 10
At every instant there are roughly a dozen water-ethanol hydrogen bonds and about forty water-water ones. That persistent water-ethanol count is the molecular signature of a miscible mixture: ethanol is not trapped in a pocket but stitched into the water hydrogen-bond network. Both counts are attached to the trajectory below: you can switch the map axis between the two curves.
for frame in ethanol_traj:
frame.wrap()
chemiscope.show(
structures=ethanol_traj,
properties={
"time [ps]": {"target": "structure", "values": time_ps},
"water-ethanol H-bonds": {"target": "structure", "values": hb_we},
"water-water H-bonds": {"target": "structure", "values": hb_ww},
},
mode="default",
settings=chemiscope.quick_settings(
trajectory=True,
x="time [ps]",
y="water-ethanol H-bonds",
structure_settings={"playbackDelay": 20, "unitCell": True},
map_settings={"markerOutline": False},
),
)
Extreme conditions: superionic water¶
The last system pushes far outside everyday chemistry. Deep inside the ice-giant planets (Uranus and Neptune) water is thought to exist in a superionic phase: the oxygen atoms stay locked on a crystalline lattice while the protons melt and diffuse through it like a liquid, turning the material into an ionic conductor. Reaching it requires roughly 3000 K and ~140 GPa. At these conditions common empirical water models are undefined, whereas an MLIP is reactive by construction.
We start from an ice-X-like configuration (a 4×4×4 supercell of a body-centered-cubic
oxygen lattice, 128 water molecules) and hold it at 3000 K and fixed volume. Two
settings change relative to the runs above: the temperature is much higher, and the
timestep is shortened to 0.2 fs (timestep 0.0002) because atoms move much faster
at 3000 K and the integration must stay stable.
# Superionic water NVT at 3000 K with PET-MAD-xs
# Pre-equilibrated at ~140 GPa; NVT keeps the volume fixed.
# Atom types: 1=H, 2=O
units metal
atom_style atomic
variable seed index 45678
variable t_target equal 3000.0
variable tdamp equal 100*dt
variable nsteps equal 50000 # 50000 * 0.2 fs = 10 ps
variable dump_every equal 25
read_data data/superionic_ice.data
pair_style metatomic pet-mad-xs-v1.5.1.pt device cpu
pair_coeff * * 1 8
timestep 0.0002 # 0.2 fs (shorter for high-T/P stability)
neighbor 2.0 bin
neigh_modify one 50000 page 500000
thermo_style custom step temp pe etotal press vol
thermo 10
velocity all create ${t_target} ${seed} mom yes rot yes dist gaussian
reset_timestep 0
fix nve_int all nve
fix thermostat all temp/csvr ${t_target} ${t_target} ${tdamp} ${seed}
print "step temp pe etotal press vol" file superionic_thermo.out
fix thermofile all print ${dump_every} "$(step) $(temp) $(pe) $(etotal) $(press) $(vol)" append superionic_thermo.out
dump traj all custom ${dump_every} superionic_traj.lammpstrj id type element xu yu zu
dump_modify traj element H O sort id
run ${nsteps}
lmp -in in_superionic_nvt.lmp
The clearest signature of the superionic phase is the mean-squared displacement (MSD) of each species. If the phase is truly superionic, the hydrogen MSD should grow linearly in time (Fickian diffusion, exactly as in a liquid) while the oxygen MSD stays small and flat, meaning that atoms can only rattle around fixed lattice sites.
Because the trajectory was dumped with unwrapped coordinates, the MSD is a plain average of squared displacements, with no periodic-boundary correction needed:
def compute_msd(traj: list, species: str) -> np.ndarray:
symbols = np.array(traj[0].get_chemical_symbols())
mask = symbols == species
pos = np.array([f.get_positions()[mask] for f in traj])
return np.mean(np.sum((pos - pos[0][np.newaxis]) ** 2, axis=-1), axis=-1)
sup_traj = ase.io.read("superionic_traj.lammpstrj", ":", format="lammps-dump-text")
dt_ps = 0.0002 # timestep in ps (0.2 fs)
dump_every = 25
time_ps = np.arange(len(sup_traj)) * dt_ps * dump_every
msd_H = compute_msd(sup_traj, "H")
msd_O = compute_msd(sup_traj, "O")
fig, ax = plt.subplots(figsize=(7, 4), dpi=200)
ax.plot(time_ps, msd_H, label="H")
ax.plot(time_ps, msd_O, label="O")
ax.set(
xlabel="Time (ps)",
ylabel="MSD (Ų)",
title="Superionic water (3000 K, ~140 GPa)",
)
ax.legend()
plt.show()
The two curves behave just as expected: hydrogen diffuses freely while oxygen
oscillated around lattice sites. To watch the transition itself, we ramp the
temperature from 300 K to 3000 K over a single trajectory. The input is the one above
with a single change: the thermostat target sweeps from 300 K to 3000 K instead of
being held fixed (fix temp/csvr 300 3000 ...). Run it with:
lmp -in in_superionic_ramp.lmp
While visualizing the trajectory, notice how the oxygen lattice stays ordered while the hydrogen atoms progressively diffuse and begin to flow between sites.
sup_ramp_traj = ase.io.read(
"superionic_ramp_traj.lammpstrj", ":", format="lammps-dump-text"
)
sup_ramp_thermo = np.loadtxt("superionic_ramp_thermo.out", skiprows=1)
ramp_time_ps = sup_ramp_thermo[:, 0] * 0.0002
ramp_temp_K = sup_ramp_thermo[:, 1]
chemiscope.show(
structures=sup_ramp_traj,
properties={
"time [ps]": {"target": "structure", "values": ramp_time_ps},
"temperature [K]": {"target": "structure", "values": ramp_temp_K},
},
mode="default",
settings=chemiscope.quick_settings(
trajectory=True,
x="time [ps]",
y="temperature [K]",
structure_settings={"playbackDelay": 5, "unitCell": True},
map_settings={"markerOutline": False},
),
)
Where to go next¶
Throughout this recipe we used a foundational model out of the box, changing only the system and never the potential. That is often enough for a qualitative picture, a starting structure, or a screening study. For quantitative accuracy at a specific thermodynamic state, though, one often needs fine-tuning: a small, targeted set of DFT calculations specializes the universal model to the system or conditions of interest, at a fraction of the cost of training from scratch.
To go further:
PET-MAD tutorial—how to set up and run PET-MAD yourself with ASE, i-PI and LAMMPS, for a diverse array of applications.
Fine-tuning PET-MAD—how to specialize a foundational model to a target system for production-quality accuracy.
Mendeleev’s nano-soup—the same model pushed to the limit: sampling a 102-element nanoparticle with replica-exchange MD and Monte Carlo atom swaps.
Total running time of the script: (5 minutes 8.736 seconds)