SIESTA Single-Element Density Dataset

Overview

This dataset contains 30,000 converged density functional theory (DFT) single-point calculations for elemental aluminium (Al), iron (Fe), and nickel (Ni), with 10,000 configurations per element. The calculations were performed using SIESTA 5.4.2 under a common numerical protocol.

Each configuration provides atomic and lattice information, the complete self-consistent field output, three-dimensional electron-density and electrostatic-potential grids, and associated metadata.

The dataset is designed as a controlled benchmark for:

• Structure-to-electron-density prediction

• Structure-to-electrostatic-potential prediction

• Density-based representation learning

• Surrogate electronic-structure methods

• Inverse structure–density problems

• Reproducible comparison of machine-learning architectures operating on periodic volumetric fields

The dataset is not intended as a survey of chemical diversity, equilibrium crystal structures, magnetic ordering, or thermodynamic phase space.

Revision note

This revised release preserves the original 30,000 calculations, structures, energies, and volumetric fields. No calculations were regenerated or replaced.

The revision corrects and expands the documentation of:

• The two-atom reference topology

• The coordinate convention used during lattice deformation

• The exact perturbation transformations

• The non-spin-polarized nature of the calculations

• The interpretation of the relative-energy distributions

• The intended uses and limitations of the dataset

Earlier documentation described the reference cell as “FCC-derived.” Direct inspection of the lattice vectors and atomic positions shows that the reference structure is a two-atom hcp topology. The legacy generator label fcc_2atom is therefore a nomenclature error and does not describe the actual structural files. The lattice vectors and atomic coordinates stored in the .fdf, .XV, and .STRUCT_OUT files are authoritative.

Dataset composition

All three elements use the same initial two-atom hcp reference topology and the same structural sampling procedure.

The Fe and Ni calculations are non-spin-polarized. They should therefore be interpreted as controlled non-magnetic reference systems, not as representations of their equilibrium magnetic phases.

Reference structure

The initial lattice-vector matrix, in ångströms, is

H0 =
[[ 2.479598,  0.000000,  0.000000],
 [-1.239799,  2.147395,  0.000000],
 [ 0.000000,  0.000000,  4.064263]]

The initial Cartesian atomic coordinates, in ångströms, are

R0 =
[[-0.000001,  1.431597,  1.016066],
 [ 1.239800,  0.715798,  3.048197]]

These positions correspond approximately to the hcp fractional coordinates

(1/3, 2/3, 1/4)
(2/3, 1/3, 3/4)

The same reference lattice and Cartesian positions were used for Al, Fe, and Ni. This common reference is a methodological starting point and is not asserted to be the equilibrium structure or equilibrium volume of each element.

Coordinate convention

All generated SIESTA input files use

AtomicCoordinatesFormat Ang

The atomic positions are therefore supplied as Cartesian coordinates in ångströms.

For lattice-only deformation classes, the lattice vectors were changed while the Cartesian atomic coordinates were retained:

R' = R0

Consequently, the corresponding fractional coordinates change when the lattice is deformed.

This convention differs from a conventional homogeneous-strain operation in which fractional atomic coordinates are held fixed. The isotropic, anisotropic, and shear subsets should therefore be interpreted as lattice deformations at fixed Cartesian atomic coordinates, not as conventional elasticity trajectories.

Perturbation classes

Each element contains the following mixture:

The short labels are retained for compatibility with the generation workflow. In this documentation, iso and aniso refer to lattice deformations at fixed Cartesian atomic coordinates.

Cartesian atomic displacement

The lattice is retained and independent Gaussian noise is added to every Cartesian coordinate:

H' = H0
R' = R0 + δR

Each component of δR is drawn from a zero-mean Gaussian distribution. The standard deviation is selected from:

σ ∈ {0.02, 0.05, 0.08} Å

Isotropic lattice deformation

All lattice vectors are scaled by the same factor:

H' = H0 × (1 + ε)
R' = R0

with

ε ~ Uniform(-0.02, 0.02)

Anisotropic lattice deformation

The Cartesian components of the lattice vectors are scaled independently:

H' = H0 × diag(1 + εx, 1 + εy, 1 + εz)
R' = R0

where εx, εy, and εz are sampled independently:

εx, εy, εz ~ Uniform(-0.02, 0.02)

Lattice shear

An upper-triangular shear matrix is applied on the right of the lattice matrix:

H' = H0 × M
R' = R0

where

M =
[[1, sxy, sxz],
 [0,   1, syz],
 [0,   0,   1]]

and the three shear components are sampled independently:

sxy, sxz, syz ~ Uniform(-0.01, 0.01)

Combined perturbation

Combined configurations contain an isotropic lattice deformation and a Cartesian atomic displacement. A lattice shear is additionally applied with probability 0.5.

The implemented order is:

H1 = H0 × (1 + ε)
R' = R0 + δR

with probability 0.5:
    H' = H1 × M
otherwise:
    H' = H1

The isotropic parameter, displacement standard deviation, Gaussian displacements, and optional shear components follow the distributions described above.

Random-number generation

The dataset was generated using:

Global NumPy random seed: 0
Element generation order: Ni, Fe, Al

A single continuous random-number stream was used across the three elements. For each element, the requested perturbation labels were assembled using the class counts above and randomly shuffled before configuration identifiers were assigned.

Reproduction therefore requires the same generator version, global seed, element order, perturbation counts, and sequence of random-number operations.

DFT settings

All calculations were performed with the following common protocol:

The PSML pseudopotential files are not redistributed in this dataset. 

Deposited files

The Zenodo release contains:

siesta-single-elements-30k-public-core.7z
SHA256SUMS.txt

The compressed archive is approximately 7.94 GB and occupies approximately 36 GB after extraction.

The archive can be extracted using software that supports the 7z format:

7z x siesta-single-elements-30k-public-core.7z

Archive structure

public_core/
├── data/
│   ├── Al/
│   │   ├── cfg_0000/
│   │   │   ├── Al.fdf
│   │   │   ├── Al.out
│   │   │   ├── Al.XV
│   │   │   ├── Al.STRUCT_OUT
│   │   │   ├── Rho.grid.nc
│   │   │   └── ElectrostaticPotential.grid.nc
│   │   └── ...
│   ├── Fe/
│   └── Ni/
├── index_core.jsonl
├── index_core.parquet
└── README.md

Configuration-level files

Each configuration directory contains:

The structural files are the authoritative record of each evaluated configuration.

Metadata indexes

Two equivalent machine-readable indexes are provided:

index_core.jsonl
index_core.parquet

The JSON Lines file contains one JSON object per configuration. The Parquet file provides columnar access for machine-learning and large-scale data-processing workflows.

The indexes contain fields including:

• calc_id

• element

• calc_dir

• scf_converged

• scf_iterations

• final_energy_ev

• fermi_ev

• dm_read_failed

• dm_atomic_fallback

• Relative paths to the released calculation files

The dm_read_failed and dm_atomic_fallback fields describe density-matrix initialization. They do not indicate failed calculations. In these single-point calculations, the absence of a continuation density matrix causes SIESTA to initialize the density matrix from atomic data.

Example:

import pandas as pd

df = pd.read_parquet("public_core/index_core.parquet")

print(df.shape)
print(df["element"].value_counts())
print(
    df[
        [
            "element",
            "calc_dir",
            "final_energy_ev",
            "fermi_ev",
            "scf_iterations",
            "scf_converged",
        ]
    ].head()
)

Reading the volumetric fields

The NetCDF files contain variables including:

• gridfunc: volumetric scalar-field values

• cell: lattice-vector information

Example:

from netCDF4 import Dataset
import numpy as np

path = "public_core/data/Al/cfg_0000/Rho.grid.nc"

with Dataset(path) as ds:
    print(ds.variables.keys())
    print(ds.variables["gridfunc"].dimensions)
    print(ds.variables["gridfunc"].shape)

    rho = np.asarray(ds.variables["gridfunc"][:]).squeeze()
    cell = np.asarray(ds.variables["cell"][:])

print("Density shape:", rho.shape)
print("Cell:")
print(cell)

Users should inspect the NetCDF variable dimensions rather than assuming an axis order. The grid files are native SIESTA 5.4.2 outputs and were not resampled, normalized, or converted after calculation. The .fdf, .out, and structural files provide the corresponding calculation and geometry provenance.

Validation

The following checks were performed:

• All 30,000 calculations reached SCF convergence.

• No fatal runtime errors were detected.

• All required public-core files were present.

• Metadata paths were checked against the archive structure.

• Representative NetCDF files were opened and inspected for readability.

• Final energies and Fermi levels were parsed from the SIESTA outputs.

• All 30,000 total energies were independently reparsed from the raw output files during revision.

• The independently reparsed energies produced zero metadata mismatches at a tolerance of 10⁻⁶ eV.

• The relative-energy histograms were reproduced using multiple bin widths and separated by perturbation class.

For energy-distribution analyses, relative energies are defined separately for each element:

ΔE = E − Emin

Here, Emin is the minimum energy among the 10,000 sampled configurations of that element. It is not the pristine-reference energy and is not an equilibrium-energy assignment.

For Al, the independently calculated pristine reference is:

Eref − Emin = 0.589870 eV

The Al population near this value contains multiple perturbation classes and is formed primarily by Cartesian-displacement and lattice-shear configurations close to the reference geometry.

Symmetric sampling of perturbation parameters around zero does not require the resulting energy histogram to peak at zero. Energy is a nonlinear function of the atomic and lattice coordinates, the reference structure need not be an energy minimum, and the displayed distribution combines several perturbation populations.

Important usage limitations

Users should account for the following limitations:

1. Restricted chemistry: only Al, Fe, and Ni are included.

2. Common reference topology: all calculations originate from the same two-atom hcp reference rather than the equilibrium topology of each element.

3. Non-magnetic treatment: all calculations are non-spin-polarized. Fe and Ni therefore represent non-magnetic reference systems.

4. No structural relaxation: the structures are evaluated exactly as generated.

5. Limited structural regime: the dataset contains small controlled perturbations and does not represent thermodynamic trajectories, phase transitions, defects, surfaces, interfaces, or broad phase space.

6. Fixed-Cartesian lattice convention: lattice-only deformation classes retain Cartesian atomic coordinates, causing fractional coordinates to change.

7. Not an elasticity dataset: the iso, aniso, and shear classes should not be treated as conventional fixed-fractional-coordinate strain trajectories or used directly to infer equilibrium elastic constants.

8. Energy comparisons: absolute total energies should be compared within the same element. Cross-element raw total-energy differences are not directly meaningful. Relative energies must be defined using an explicitly stated element-specific reference.

9. Reference structure: the lowest sampled configuration must not be interpreted automatically as an equilibrium structure.

Archive integrity

Use the supplied checksum manifest to verify the downloaded archive:

sha256sum -c SHA256SUMS.txt

On macOS, an equivalent verification can be performed using:

shasum -a 256 -c SHA256SUMS.txt

Always use the SHA256SUMS.txt file supplied with the same Zenodo release because the checksum changes when the archive is revised.

Generation and processing code

The generation, execution, indexing, and public-core packaging code is available at:

https://github.com/ProyectoPhantoma/SIESTA_dataset_generation

Archived software release:

https://doi.org/10.5281/zenodo.20126108

Citation

If you use this dataset, please cite the specific revised version used in your work:

Arévalo, I. & Olleros, P. SIESTA Single-Element Density Dataset. Zenodo. https://doi.org/10.5281/zenodo.20378934 (2026).

The DOI representing all versions of the dataset is:

https://doi.org/10.5281/zenodo.18925342

BibTeX:

@dataset{arevalo2026dataset,
  author    = {Ar{\'e}valo, Irina and Olleros, Pablo},
  title     = {{SIESTA} Single-Element Density Dataset},
  year      = {2026},
  month     = {may},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.20378934},
  url       = {https://doi.org/10.5281/zenodo.20378934},
  note      = {Dataset}
}

License

This dataset is distributed under the Creative Commons Attribution 4.0 International license:

https://creativecommons.org/licenses/by/4.0/

The PSML pseudopotential files used to perform the calculations are not redistributed as part of the dataset.

Contact

Irina Arévalo
Universidad Politécnica de Madrid, Spain
irina.arevalo@upm.es

Pablo Olleros
CUNEF Universidad, Spain
pablo.olleros@cunef.edu