# QM7 Dataset

## Description

This dataset is a subset of GDB-13 (a database of nearly 1 billion stable and synthetically accessible organic molecules) composed of all molecules of up to 23 atoms (including 7 heavy atoms C, N, O, and S), totalling 7165 molecules. We provide the Coulomb matrix representation of these molecules and their atomization energies computed similarly to the FHI-AIMS implementation of the Perdew-Burke-Ernzerhof hybrid functional (PBE0). This dataset features a large variety of molecular structures such as double and triple bonds, cycles, carboxy, cyanide, amide, alcohol and epoxy. The Coulomb matrix is defined as

\begin{align*} C_{ii} &= \frac{1}{2}Z_i^{2.4} \\ C_{ij} &= \frac{Z_iZ_j}{|R_i - R_j|} \end{align*}

where $$Z_i$$ is the nuclear charge of atom $$i$$ and $$R_i$$ is its position. The Coulomb matrix has built-in invariance to translation and rotation of the molecule. The atomization energies are given in kcal/mol and are ranging from -800 to -2000 kcal/mol).

The dataset is composed of three multidimensional arrays X (7165 x 23 x 23), T (7165) and P (5 x 1433) representing the inputs (Coulomb matrices), the labels (atomization energies) and the splits for cross-validation, respectively. The dataset also contain two additional multidimensional arrays Z (7165) and R (7165 x 3) representing the atomic charge and the cartesian coordinate of each atom in the molecules.

## Benchmark results

Average cross-validation error using the five splits of the dataset and using mean absolute error (MAE) are reported below.

Rupp et al. PRL, 2012 | Kernel ridge regression with Gaussian Kernel on Coulomb matrix sorted eigenspectrum | 9.9 kcal/mol Montavon et al. NIPS, 2012 | Multilayer perceptron with binarized random Coulomb matrices | 3.5 kcal/mol

## Code

• code/nn-qm7.tar.gz: Simple multilayer perceptron trained on the QM7 dataset with error backpropagation and yielding errors in the range of 3-4 kcal/mol. Train the network by running $python nntrain.py [split] where [split] is a number between 0 and 4. The training takes place in background (warning, training can take up to two days depending on the machine). To test current performance, open another terminal and run $ python nntest.py [split] where [split] has the same value as for training. The command returns the training and test error at current time in terms of MAE and RMSE.

## How to cite

When using this dataset, please make sure to cite the following two papers:

# QM7b Dataset

## Description

This dataset is an extension of the QM7 dataset for multitask learning where 13 additional properties (e.g. polarizability, HOMO and LUMO eigenvalues, excitation energies) have to be predicted at different levels of theory (ZINDO, SCS, PBE0, GW). Additional molecules comprising chlorine atoms are also included, totalling 7211 molecules.

The dataset is composed of two multidimensional arrays X (7211 x 23 x 23) and T (7211 x 14) representing the inputs (Coulomb matrices) and the labels (molecular properties) and one array names of size 14 listing the names of the different properties.

## Benchmark results

We report test error with 5000 training samples drawn randomly from the dataset and remaining 2211 test samples. For conciseness, we report only MAE values for Polarizability-PBE0, HOMO-GW and IP-ZINDO as a vector of numbers (measured in A3 and eV).

Montavon et al., New J. Phys. 15 095003, 2013 | Multitask MLP with binarized random Coulomb matrices and binarized outputs | 0.11, 0.16, 0.17

## How to cite

When using this dataset, please make sure to cite the following two papers:

# QM9 Dataset

## Abstract

Computational de novo design of new drugs and materials requires rigorous and unbiased exploration of chemical compound space. However, large uncharted territories persist due to its size scaling combinatorially with molecular size. We report computed geometric, energetic, electronic, and thermodynamic properties for 134k stable small organic molecules made up of CHONF. These molecules correspond to the subset of all 133,885 species with up to nine heavy atoms (CONF) out of the GDB-17 chemical universe of 166 billion organic molecules. We report geometries minimal in energy, corresponding harmonic frequencies, dipole moments, polarizabilities, along with energies, enthalpies, and free energies of atomization. All properties were calculated at the B3LYP/6-31G(2df,p) level of quantum chemistry. Furthermore, for the predominant stoichiometry, C7H10O2, there are 6,095 constitutional isomers among the 134k molecules. We report energies, enthalpies, and free energies of atomization at the more accurate G4MP2 level of theory for all of them. As such, this data set provides quantum chemical properties for a relevant, consistent, and comprehensive chemical space of small organic molecules. This database may serve the benchmarking of existing methods, development of new methods, such as hybrid quantum mechanics/machine learning, and systematic identification of structure-property relationships.

Available via figshare.

## How to cite

When using this dataset, please make sure to cite the following two papers:

# QM8 Dataset

## Abstract

Due to its favorable computational efficiency, time-dependent (TD) density functional theory(DFT) enables the prediction of electronic spectra in a high-throughput manner across chemical space. Its predictions, however, can be quite inaccurate. We resolve this issue with machine learning models trained on deviations of reference second-order approximate coupled-cluster (CC2) singles and doubles spectra from TDDFT counterparts, or even from DFT gap. We applied this approach to low-lying singlet-singlet vertical electronic spectra of over 20 000 synthetically feasible small organic molecules with up to eight CONF atoms. The prediction errors decay monotonously as a function of training set size. For a training set of 10 000 molecules, CC2 excitation energies can be reproduced to within ±0.1 eV for the remaining molecules. Analysis of our spectral database via chromophore counting suggests that even higher accuracies can be achieved. Based on the evidence collected, we discuss open challenges associated with data-driven modeling of high-lying spectra and transition intensities.

Available via EPAPS (FTP).

## How to cite

When using this dataset, please make sure to cite the following two papers:

# MD Trajectories of small molecules

## Description

The molecular dynamics (MD) datasets in this package range in size from 150k to nearly 1M conformational geometries. All trajectories are calculated at a temperature of 500 K and a resolution of 0.5 fs. The molecules have different sizes and the molecular PESs exhibit different levels of complexity. The energy range across all data points within a set spans from 20 to 48 kcal/mol. Force components range from 266 to 570 kcal/mol/A. The total energy and force labels for each dataset were computed using the PBE+vdW-TS electronic structure method. All geometries are in Angstrom, energies and forces are given in kcal/mol and kcal/mol/A respectively.

The data is provided in xyz format with one file per conformation. The energy and force labels for each geometry are included in the comment line. This way the files remain valid xyz files. Positions are given in Angstroms, energies are given in kcal/mol.

## Benchmarks

### Energies

Mean absolute errors (in meV) for energy prediction based on training sets of size N with different methods for each dataset.

Benzene Uracil Napthalene Aspirin Saliylic acid Malonaldehyde Ethanol Toluene
DTNN (N=50k) 1.7 n/a n/a n/a 21.7 8.2 n/a 7.8
GDML (N=1k) 3.0 4.8 5.2 11.7 5.2 6.9 6.5 5.2
GDML (N=50k) 3.2 4.6 5.1 5.6 4.8 3.3 2.3 4.1
sGDML (N=1k) 4.3 4.8 5.2 8.2 5.2 4.3 3.0 4.3

### Forces

Mean absolute errors (in meV) for each force component based on training sets of size N for each dataset.

Benzene Uracil Napthalene Aspirin Saliylic acid Malonaldehyde Ethanol Toluene
GDML (N=1k) 10.0 10.4 10.0 42.9 12.1 34.7 34.3 18.6
GDML (N=50k) 10.2 1.2 1.3 1.0 1.5 3.3 4.0 2.1
sGDML (N=1k) 2.6 10.4 4.8 29.5 12.1 17.8 14.3 6.1

## How to cite

When using this dataset, please make sure to cite the following papers:

# MD Trajectories of C7O2H10

## Description

This data set consists of molecular dynamics trajectories of 113 randomly selected C7O2H10 isomers calculated at a temperature of 500 K and resolution of 1fs using density functional theory with the PBE exchange-correlation potential.

C7O2H10 is the largest set of isomer of QM9. Identifiers used in this data set agree with those used in the QM9 isomer subset.

Each trajectory is stored in a xyz-file named id.xyz with corresponding energies in id.energy.dat. Additionally, consistent energy calculations of all isomers in equilibrium (according to QM9) are provided in c7o2h10_equilibrium.dat.

## Benchmark

Mean abs. errors for energy prediction using the equilibrium energies as well as 50% of each trajectory as reference calculations for training (in eV).

# Datasets including densities

## Description

These datasets contain not only molecular geometries and energies but also valence densities.

For each dataset, the energies are given in energies.txt (in kcal/mol, one line per molecular geometry). The densities are given in densities.txt (in Fourier basis coefficients, one line per molecular geometry). The structures are given in structures.xyz (with positions in Bohr).

For details on how these datasets were generated please refer to the publication.

## How to cite

When using any of these datasets, please make sure to cite the following paper:

# ISO17 - MD Trajectories of C7O2H10 with total energies and atomic forces

## Description

The molecules were randomly drawn from the largest set of isomers in the QM9 dataset [1] which consists of molecules with a fixed composition of atoms (C7O2H10) arranged in different chemically valid structures. It is an extension of the ismoer MD data used in [2].

The database was generated from molecular dynamics simulations using the Fritz-Haber Institute ab initio simulation package (FHI-aims)[3]. The simulations were carried out using the standard quantum chemistry computational method density functional theory (DFT) in the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional[4] and the Tkatchenko-Scheffler (TS) van der Waals correction method [5].

The database consist of 129 molecules each containing 5,000 conformational geometries, energies and forces with a resolution of 1 femtosecond in the molecular dynamics trajectories.

## Format

The data is stored in ASE sqlite format with the total energy in eV under the key total energy and the atomic_forces under the key atomic_forces in eV/Ang.

The following Python snippet iterates over the first 10 entries of the dataset located at path_to_db:

from ase.db import connect

with connect(path_to_db) as conn:
for row in conn.select(limit=10):
print(row.toatoms())
print(row['total_energy'])
print(row.data['atomic_forces'])


## Partitions

The data is partitioned as used in the SchNet paper [6]:

• reference.db - 80% of steps of 80% of MD trajectories
• reference_eq.db - equilibrium conformations of those molecules
• test_within.db - remaining 20% unseen steps of reference trajectories
• test_other.db - remaining 20% unseen MD trajectories
• test_eq.db - equilibrium conformations of test trajectories

In the paper, we split the reference data (reference.db) into 400k training examples and 4k validation examples. The indices are given in the files train_ids.txt and validation_idx.txt, respectively.

## Benchmarks

Model Energy (within) [eV] Force (within) [eV/A] Energy (other) [eV] Force (other) [eV/A]
SchNet [6] 0.016 0.043 0.104 0.095

## How to cite

When using this dataset, please make sure to cite the following papers:

• K.T. Schütt, P.-J. Kindermans, H.E. Sauceda, S. Chmiela, A. Tkatchenko, K.-R. Müller. SchNet: A continuous-filter convolutional neural network for modeling quantum interactions. Advances in Neural Information Processing System. 2017.
• K.T. Schütt, F. Arbabzadah, S. Chmiela, K.R. Müller, A. Tkatchenko. Quantum-chemical insights from deep tensor neural networks. Nature Communications, 8, 13890. 2017.
• R. Ramakrishnan, P. O. Dral, M. Rupp, and O. A. von Lilienfeld. Quantum chemistry structures and properties of 134 kilo molecules. Scientific Data, 1, 2014.

## References

[1] R. Ramakrishnan, P. O. Dral, M. Rupp, and O. A. von Lilienfeld. Quantum chemistry structures
and properties of 134 kilo molecules. Scientific Data, 1, 2014.
[2] Schütt, K. T., Arbabzadah, F., Chmiela, S., Müller, K. R., & Tkatchenko, A. (2017). Quantum-chemical insights from deep tensor neural networks. Nature Communications, 8, 13890.
[3] Blum, V.; Gehrke, R.; Hanke, F.; Havu, P.; Havu, V.; Ren, X.; Reuter, K.; Scheffler, M. Ab Initio Molecular Simulations with Numeric Atom-Centered Orbitals. Comput. Phys. Commun. 2009, 180 (11), 2175–2196.
[4] Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865–3868.
[5] Tkatchenko, A.; Scheffler, M. Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data. Phys. Rev. Lett. 2009, 102 (7), 73005.
[6] Schütt, K. T., Kindermans, P. J., Sauceda, H. E., Chmiela, S., Tkatchenko, A., & Müller, K. R. SchNet: A continuous-filter convolutional neural network for modeling quantum interactions. Advances in Neural Information Processing System (accepted). 2017.