PolyMLP_Seko_2022p1_LiTi__MO_671224571016_000
| Title
A single sentence description.
|
Polynomial machine learning potential for Li-Ti developed by Seko (2022) v000 |
|---|---|
| Description
A short description of the Model describing its key features including for example: type of model (pair potential, 3-body potential, EAM, etc.), modeled species (Ac, Ag, ..., Zr), intended purpose, origin, and so on.
|
Polynomial machine learning potential (MLP) for Li-Ti system. This potential is gtinv-257 potential in Li-Ti-2022-06-12 taken from Polynomial MLP Repository. The RMS errors for energy and forces are 6.562 meV/atom and 0.1004 eV/angstrom, respectively. The estimated computational cost required for a single core calculation is 0.79 ms/atom/step. |
| Species
The supported atomic species.
| Li, Ti |
| Disclaimer
A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.
|
Several models from the PolyMLP repository are available for LiTi, all laying on a pareto front of computational speed vs. RMS accuracy. They are labeled p1, p2, p3, p4, p5 in their KIM IDs. Higher numbers mean slower models. The author-recommended model for this system is p1 (this model). |
| Content Origin | PolyMLP Repository (Kyoto University) https://cms.mtl.kyoto-u.ac.jp/seko/mlp-repository/index.html |
| Contributor |
Atsuto Seko |
| Maintainer |
Atsuto Seko |
| Developer | Atsuto Seko |
| Published on KIM | 2026 |
| How to Cite |
This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Seko A. Tutorial: Systematic development of polynomial machine learning potentials for elemental and alloy systems. J Appl Phys. 2023Jan;133(1). doi:10.1063/5.0129045 — (Primary Source) A primary source is a reference directly related to the item documenting its development, as opposed to other sources that are provided as background information. [2] Seko A. Polynomial machine learning potential for Li-Ti developed by Seko (2022) v000. OpenKIM; 2026. doi:10.25950/29b9876a [3] Seko A. Model driver for polynomial machine learning potentials (PolyMLP) ported from pypolymlp v000. OpenKIM; 2026. doi:10.25950/948ad72c [4] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [5] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a |
| Funding | Not available |
| Short KIM ID
The unique KIM identifier code.
| MO_671224571016_000 |
| Extended KIM ID
The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.
| PolyMLP_Seko_2022p1_LiTi__MO_671224571016_000 |
| DOI |
10.25950/29b9876a https://doi.org/10.25950/29b9876a https://commons.datacite.org/doi.org/10.25950/29b9876a |
| KIM Item Type
Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).
| Portable Model using Model Driver PolyMLP__MD_367995833009_000 |
| Driver | PolyMLP__MD_367995833009_000 |
| KIM API Version | 2.3 |
| Potential Type | polymlp |
| Grade | Name | Category | Brief Description | Full Results | Aux File(s) |
|---|---|---|---|---|---|
| P | vc-periodicity-support | mandatory | Periodic boundary conditions are handled correctly; see full description. |
Results | Files |
| P | vc-permutation-symmetry | mandatory | Total energy and forces are unchanged when swapping atoms of the same species; see full description. |
Results | Files |
| P | vc-objectivity | informational | Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description. |
Results | Files |
| P | vc-inversion-symmetry | informational | Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description. |
Results | Files |
| P | vc-memory-leak | informational | The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description. |
Results | Files |
| P | vc-unit-conversion | mandatory | The model is able to correctly convert its energy and/or forces to different unit sets; see full description. |
Results | Files |
| P | vc-contributing-atom-energy | informational | other |
Results | Files |
BCC Lattice Constant
This bar chart plot shows the mono-atomic body-centered cubic (bcc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
Cohesive Energy Graph
This graph shows the cohesive energy versus volume-per-atom for the current mode for four mono-atomic cubic phases (body-centered cubic (bcc), face-centered cubic (fcc), simple cubic (sc), and diamond). The curve with the lowest minimum is the ground state of the crystal if stable. (The crystal structure is enforced in these calculations, so the phase may not be stable.) Graphs are generated for each species supported by the model.
Diamond Lattice Constant
This bar chart plot shows the mono-atomic face-centered diamond lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
Dislocation Core Energies
This graph shows the dislocation core energy of a cubic crystal at zero temperature and pressure for a specific set of dislocation core cutoff radii. After obtaining the total energy of the system from conjugate gradient minimizations, non-singular, isotropic and anisotropic elasticity are applied to obtain the dislocation core energy for each of these supercells with different dipole distances. Graphs are generated for each species supported by the model.
(No matching species)FCC Elastic Constants
This bar chart plot shows the mono-atomic face-centered cubic (fcc) elastic constants predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
FCC Lattice Constant
This bar chart plot shows the mono-atomic face-centered cubic (fcc) lattice constant predicted by the current model (shown in red) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
FCC Stacking Fault Energies
This bar chart plot shows the intrinsic and extrinsic stacking fault energies as well as the unstable stacking and unstable twinning energies for face-centered cubic (fcc) predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
(No matching species)FCC Surface Energies
This bar chart plot shows the mono-atomic face-centered cubic (fcc) relaxed surface energies predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
(No matching species)SC Lattice Constant
This bar chart plot shows the mono-atomic simple cubic (sc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
Cubic Crystal Basic Properties Table
Species: LiSpecies: Ti
Disclaimer From Model Developer
Several models from the PolyMLP repository are available for LiTi, all laying on a pareto front of computational speed vs. RMS accuracy. They are labeled p1, p2, p3, p4, p5 in their KIM IDs. Higher numbers mean slower models. The author-recommended model for this system is p1 (this model).
Creators:
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/64cb38c5
This Test Driver uses LAMMPS to compute the cohesive energy of a given monoatomic cubic lattice (fcc, bcc, sc, or diamond) at a variety of lattice spacings. The lattice spacings range from a_min (=a_min_frac*a_0) to a_max (=a_max_frac*a_0) where a_0, a_min_frac, and a_max_frac are read from stdin (a_0 is typically approximately equal to the equilibrium lattice constant). The precise scaling and number of lattice spacings sampled between a_min and a_0 (a_0 and a_max) is specified by two additional parameters passed from stdin: N_lower and samplespacing_lower (N_upper and samplespacing_upper). Please see README.txt for further details.
| Test | Test Results | Link to Test Results page | Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI) |
|---|---|---|---|
| Cohesive energy versus lattice constant curve for bcc Li v004 | view | 151414 | |
| Cohesive energy versus lattice constant curve for diamond Li v004 | view | 154270 | |
| Cohesive energy versus lattice constant curve for diamond Ti v004 | view | 152386 | |
| Cohesive energy versus lattice constant curve for fcc Li v004 | view | 244680 | |
| Cohesive energy versus lattice constant curve for fcc Ti v004 | view | 151110 | |
| Cohesive energy versus lattice constant curve for sc Ti v004 | view | 164660 |
Creators:
Contributor: ilia
Publication Year: 2025
DOI: https://doi.org/10.25950/922d328f
Computes the elastic constants for an arbitrary crystal. A robust computational protocol is used, attempting multiple methods and step sizes to achieve an acceptably low error in numerical differentiation and deviation from material symmetry. The crystal structure is specified using the AFLOW prototype designation as part of the Crystal Genome testing framework. In addition, the distance from the obtained elasticity tensor to the nearest isotropic tensor is computed.
| Test | Test Results | Link to Test Results page | Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI) |
|---|---|---|---|
| Elastic constants for Ti in AFLOW crystal prototype A_cF4_225_a at zero temperature and pressure v001 | view | 528060 | |
| Elastic constants for Li in AFLOW crystal prototype A_cI2_229_a at zero temperature and pressure v001 | view | 634560 | |
| Elastic constants for Ti in AFLOW crystal prototype A_cI2_229_a at zero temperature and pressure v001 | view | 472287 | |
| Elastic constants for Li in AFLOW crystal prototype A_hR3_166_ac at zero temperature and pressure v001 | view | 828566 | |
| Elastic constants for Li in AFLOW crystal prototype A_oP6_51_ak at zero temperature and pressure v001 | view | 2321700 |
Creators: Junhao Li and Ellad Tadmor
Contributor: tadmor
Publication Year: 2019
DOI: https://doi.org/10.25950/5853fb8f
Computes the cubic elastic constants for some common crystal types (fcc, bcc, sc, diamond) by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.
| Test | Test Results | Link to Test Results page | Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI) |
|---|---|---|---|
| Elastic constants for bcc Li at zero temperature v006 | view | 29306 | |
| Elastic constants for diamond Li at zero temperature v001 | view | 72790 | |
| Elastic constants for diamond Ti at zero temperature v001 | view | 49440 | |
| Elastic constants for fcc Li at zero temperature v006 | view | 54684 | |
| Elastic constants for fcc Ti at zero temperature v006 | view | 21752 | |
| Elastic constants for sc Li at zero temperature v006 | view | 14704 | |
| Elastic constants for sc Ti at zero temperature v006 | view | 32628 |
Creators:
Contributor: ilia
Publication Year: 2025
DOI: https://doi.org/10.25950/866c7cfa
Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.
Creators:
Contributor: efuem
Publication Year: 2025
DOI: https://doi.org/10.25950/fa5ed729
This test returns reference ground state structures and energies for each element at zero temperature and applied stress. The results from this test are useful when a reference structure is required in some downstream test, such as vacancy tests (used as a reservoir). This test driver works by querying results from the EquilibriumCrystalStructure test driver using element specific reference structures following CHIPS-FF. Although the reference prototypes are independent of model, the resulting structure and energy of the prototypes are model-dependent.
| Test | Test Results | Link to Test Results page | Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI) |
|---|---|---|---|
| Reference elemental energy for Li v000 | view | 36752 |
Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/2765e3bf
Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.
| Test | Test Results | Link to Test Results page | Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI) |
|---|---|---|---|
| Equilibrium zero-temperature lattice constant for bcc Li v007 | view | 36120 | |
| Equilibrium zero-temperature lattice constant for diamond Li v007 | view | 39955 | |
| Equilibrium zero-temperature lattice constant for diamond Ti v007 | view | 40284 | |
| Equilibrium zero-temperature lattice constant for fcc Li v007 | view | 19869 | |
| Equilibrium zero-temperature lattice constant for fcc Ti v007 | view | 45400 | |
| Equilibrium zero-temperature lattice constant for sc Li v007 | view | 35231 | |
| Equilibrium zero-temperature lattice constant for sc Ti v007 | view | 32160 |
Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/c339ca32
Calculates lattice constant of hexagonal bulk structures at zero temperature and pressure by using simplex minimization to minimize the potential energy.
| Test | Test Results | Link to Test Results page | Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI) |
|---|---|---|---|
| Equilibrium lattice constants for hcp Li v005 | view | 242068 |
Creators:
Contributor: mjwen
Publication Year: 2024
DOI: https://doi.org/10.25950/9d9822ec
This Test Driver uses LAMMPS to compute the linear thermal expansion coefficient at a finite temperature under a given pressure for a cubic lattice (fcc, bcc, sc, diamond) of a single given species.
| Test | Test Results | Link to Test Results page | Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI) |
|---|---|---|---|
| Linear thermal expansion coefficient of bcc Li at 293.15 K under a pressure of 0 MPa v002 | view | 105643101 |
Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2019
DOI: https://doi.org/10.25950/6c43a4e6
Calculates the surface energy of several high symmetry surfaces and produces a broken-bond model fit. In latex form, the fit equations are given by:
E_{FCC} (\vec{n}) = p_1 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (2 ( |x+ 2y + z| + |x+2y-z| + |x-2y + z| + |x-2y-z| + |2x+y+z| + |2x+y-z| +|2x-y+z| +|2x-y-z| +|x+y+2z| +|x+y-2z| +|x-y+2z| +|x-y-2z| ) + c
E_{BCC} (\vec{n}) = p_1 (6 \left( | x+y+z| + |x+y-z| + |-x+y-z| + |x-y+z| \right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) +c.
In Python, these two fits take the following form:
def BrokenBondFCC(params, index):
import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)
return params[0]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*(abs(x+2*y+z) + abs(x+2*y-z) +abs(x-2*y+z) +abs(x-2*y-z) + abs(2*x+y+z) +abs(2*x+y-z) +abs(2*x-y+z) +abs(2*x-y-z) + abs(x+y+2*z) +abs(x+y-2*z) +abs(x-y+2*z) +abs(x-y-2*z))+params[3]
def BrokenBondBCC(params, x, y, z):
import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)
return params[0]*6*(abs(x+y+z) + abs(x-y-z) + abs(x-y+z) + abs(x+y-z)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[3]
| Test | Test Results | Link to Test Results page | Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI) |
|---|---|---|---|
| Broken-bond fit of high-symmetry surface energies in bcc Li v004 | view | 6155413 |
Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/c27ba3cd
Computes the monovacancy formation and migration energies for cubic and hcp monoatomic crystals.
| Test | Test Results | Link to Test Results page | Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI) |
|---|---|---|---|
| Vacancy formation and migration energy for bcc Li | view | 25502552 |
This Model requires a Model Driver. Click below for the Model Driver PolyMLP__MD_367995833009_000 archive.