TAE-PTComp: Total Atomization Energy Periodic Table Compass

TAE-PTComp is an element-resolved total atomization energy benchmark designed to probe the transferability of quantum chemical methods across a broad region of the periodic table.

The dataset contains 2097 closed-shell, single-reference molecular systems organized into 67 element-centered subsets. It covers molecules with up to 50 atoms, including neutral, cationic, and anionic species, and provides high-level coupled cluster reference data for total atomization energies (TAEs).

TAE-PTComp is intended for benchmarking, validation, and development of approximate electronic structure methods, including density functional approximations, semi-empirical quantum mechanical methods, and machine-learning interatomic or molecular energy models.

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Data set at a glance

Quantity	Description
Target property	Total atomization energy (TAE)
Reference level	PNO-LCCSD(T*)-F12/TIGHT/aVQZ' coupled cluster reference energies
Systems	2097 molecules
Element-centered subsets	67
Average subset size	31 structures per element
Molecular size	Up to 50 atoms
Charge states	Neutral, cationic, and anionic systems (0, +1, -1)
Chemical space	Covalent and coordinative compounds, noncovalently bound clusters, crystal cut-outs, atomic clusters, and selected “mindless” structures

The benchmark can be analyzed either in terms of the 67 element-resolved subsets or in terms of four broader periodic-table regions:

• s-block
• p-block (light)
• p-block (heavy)
• transition metals

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Repository structure

.
├── TAE-PTComp/
│   ├── <system>/
│   │   ├── coord
│   │   ├── struc.xyz
│   │   ├── .CHRG
│   │   └── .UHF
│   └── ...
├── RAW_DATA/
│   ├── RAW_DATA.xlsx
│   ├── RAW_DATA.numbers
│   └── csv/
│       ├── Atomic_energies_Hartree.csv
│       ├── Molecular_energies_Hartree.csv
│       ├── Reference_atomic_energies_Hartree.csv
│       ├── Total_atomization_energies_kcalmol.csv
│       └── MR_diagnostics.csv
├── data_post-processing/
│   ├── analyze.py
│   ├── .atom_number
│   ├── .corresponding_element
│   ├── ALL_OUT/
│   └── RESULTS/
├── doc/
│   └── PTComp_overview.svg
├── LICENSE.txt
└── README.md

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File formats

Structure files

Each system in TAE-PTComp/ is stored in its own directory and contains:

File	Description
coord	Molecular geometry in coord format
struc.xyz	Molecular geometry in XYZ format
.CHRG	Total molecular charge
.UHF	Number of unpaired electrons (relevant for atomic reference species)

The molecular geometries were optimized at r2SCAN-3c level of theory.

Raw numerical data

The directory RAW_DATA/ contains the publication reference data in spreadsheet and plain-text formats.

File	Contents
RAW_DATA.xlsx	Complete raw-data workbook
RAW_DATA.numbers	Complete raw-data workbook in Apple Numbers format
csv/Total_atomization_energies_kcalmol.csv	Reference total atomization energies in kcal mol⁻¹
csv/Molecular_energies_Hartree.csv	Molecular electronic energies in Hartree
csv/Atomic_energies_Hartree.csv	Atomic energies in Hartree
csv/Reference_atomic_energies_Hartree.csv	Atomic reference energies used for the atomization reactions
csv/MR_diagnostics.csv	Multi-reference diagnostic data used during dataset curation

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Reference energies and atomization reactions

The target quantity is the electronic total atomization energy. For a neutral molecule,

$$ \mathrm{A}_a\mathrm{B}_b\mathrm{C}_c \rightarrow a,\mathrm{A} + b,\mathrm{B} + c,\mathrm{C} $$

For charged systems, ionic atomization reactions are defined explicitly so that the molecular charge is assigned to an atomic fragment according to the reaction protocol described in the associated paper. The provided atomic reference energies and reaction definitions should be used consistently when benchmarking new methods.

For statistical analyses, we recommend using the scaled atomization energy,

$$ \mathrm{sTAE}_i = \frac{\mathrm{TAE}_i}{N_{\mathrm{atoms},i}} $$

and the corresponding scaled error statistics. This avoids global error measures being dominated by the largest molecules in the benchmark.

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Post-processing and error analysis

The data_post-processing/ directory contains a small Python script for computing element-resolved and block-resolved scaled error statistics from method output files.

Requirements

python >= 3.8
numpy

Example usage

Analyze one method-output file:

cd data_post-processing
python analyze.py ALL_OUT/wB97M-V.out

Analyze all method-output files stored in ALL_OUT/:

cd data_post-processing
python analyze.py all

The script writes results to

data_post-processing/RESULTS/element_resolved/
data_post-processing/RESULTS/block_resolved/

and include:

Statistic	Meaning
sMSE	scaled mean signed error
sMAE	scaled mean absolute error
sRMSE	scaled root mean square error
STD	standard deviation of signed scaled errors

The ALL_OUT/ directory contains example output files for several methods, including PBE-D4, r2SCAN-D4, M06-2X, PBE0-D4, B3LYP-D4, wB97M-V, UMA, and gxTB.

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Citation

If you use TAE-PTComp, please cite the associated paper. The final journal reference and DOI should be inserted once available.

@article{Dahl_TAE_PTComp,
  title   = {An element-resolved coupled cluster atomization energy data set ranging across the periodic table},
  author  = {Dahl, Robin and M{\"u}ller, Marcel and Kniebes, Vanessa and Werner, Hans-Joachim and Grimme, Stefan and Hansen, Andreas},
  journal = {submitted},
  year    = {2026},
  note    = {TAE-PTComp: Total Atomization Energy Periodic Table Compass}
}

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License

This repository is distributed under the terms of the MIT License.

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Contact

For questions about the dataset, reference calculations, or benchmark usage, please open an issue in this repository or contact the authors of the associated paper.