Johannes HojapersName, Leonardo Medrano SandonaspersName, Brian G. ErnstpersName, Alvaro Vazquez-MayagoitiapersName, Robert A. DiStasiopersName, Alexandre TkatchenkopersName (2021date). “QM7-X, a comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules.” Scientific Datatitle·j.
Object of study — QM7-Xterm, a quantum-mechanical dataset of equilibrium and non-equilibrium structuresterm and local and global physicochemical propertiesterm
Research question — how to systematically sample a broad small-molecule chemical compound spaceterm and compute tightly converged properties suitable for machine learning
Contribution — a reusable dataset of about 4.2 million structures with 42 PBE0+MBD-level properties, exhaustive isomer coverage, controlled non-equilibrium sampling, validation, and optional duplicate handling
phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | the structure–property and property–property variation of small organic molecules across equilibrium, distorted, constitutional, stereochemical, and conformational space — “Over 40 different physicochemical properties were computed to describe the structure–property and property–property relationships in QM7-X.” | |
| claim-type | existence — “The approximately 4.2 M equilibrium and non-equilibrium structures generated using these procedures form the QM7-X dataset (see Table 1 ).” | |
| method — evidence | — “This was followed by the generation of 100 non-equilibrium structures ( via DFTB normal-mode displacements of each equilibrium structure) for a total of ≈4.2 M molecular structures. For each of these equilibrium and non-equilibrium molecular structures, QM7-X also includes an extensive number of QM-obtained physicochemical properties, most of which were computed using non-empirical hybrid density-functional theory (DFT) with a many-body treatment of vdW dispersion interactions ( i.e ., PBE0+MBD) in conjunction with tightly-converged numeric atom-centered orbitals 30 .” | |
| object of study — evidence | — “We introduce QM7-X, a comprehensive dataset of 42 physicochemical properties for ≈4.2 million equilibrium and non-equilibrium structures of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms.” | |
| research question — evidence | — “In order to convincingly address these four challenges in this work, we present QM7-X, which aims to provide a systematic, extensive, and tightly converged dataset of QM-based physical and chemical properties for a fundamentally important region of CCS covering small organic molecules (see Fig. 1 ).” | |
| contribution — evidence | — “In total, QM7-X contains 42 molecular (global) and atom-in-a-molecule (local) properties, which range from ground state quantities (such as total and atomization energies, atomic forces, HOMO-LUMO gaps, dipole/quadrupole moments, Hirshfeld quantities, etc.) to response quantities (such as polarizability tensors and dispersion coefficients)—all of which could be utilized for the construction of next-generation intra- and inter-molecular force fields.” | |
| mechanism | systematic isomer enumeration Open Babel, MMFF94, and Confab generate three-dimensional and conformational variants from canonical structures. — “Based on these SMILES strings, initial 3D structures were obtained using the MMFF94 force field 31 – 35 via the gen3d option in Open Babel 36 . For each of these structures, we also generated a set of sufficiently different (meta-)stable conformational isomers, i.e ., isomers which can be interconverted by rotations around single bonds. To do this, we performed a conformational isomer search with the Confab tool 37 in conjunction with the MMFF94 force field.” | mechanisms[0] |
| mechanism | conformer filtering MMFF94 candidates are retained within a 50-kcal/mol window and a 0.5-Å RMSD difference, then DFTB3+MBD conformers require more than 1.0 Å separation. — “At the MMFF94 level, we retained the set of conformers that were within 50 kcal/mol of the most stable structure and differed by a root-mean-square deviation (RMSD) of 0.5 Å.” | mechanisms[1] |
| mechanism | normal-mode displacement sampling Each equilibrium structure supplies 100 non-equilibrium geometries obtained from linear combinations of DFTB3+MBD normal modes. — “In order to sample some of the non-equilibrium sectors of CCS, we generated 100 non-equilibrium structures for each of the (meta-)stable equilibrium structures described above. This was achieved by displacing each molecular structure along a linear combination of normal mode coordinates computed at the DFTB3+MBD level within the harmonic approximation (for consistency with the level of theory used to optimize the corresponding molecular structures).” | mechanisms[2] |
| mechanism | explicit Boltzmann acceptance Candidate energies are recomputed and only structures that fit the required Boltzmann energy distribution are accepted, limiting harmonic-approximation errors. — “Although a similar approach was utilized during the construction of the ANI-1 dataset 24 , we have eliminated all issues related to the inaccuracy of the harmonic approximation by recomputing the energy of every candidate structure and only accepting those structures with a Boltzmann energy distribution (see Methods).” | mechanisms[3] |
| mechanism | two-level quantum workflow DFTB3+MBD generates structures, while robust PBE0+MBD single-point calculations supply energies, forces, and other properties. — “In this work, the structure generation process was performed using DFTB3+MBD, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBD level of theory.” | mechanisms[4] |
| mechanism | a posteriori duplicate detection Potential duplicate equilibrium structures are identified using six PBE0/MBD energy, gap, polarizability, and dipole properties with a 10−3-unit similarity threshold. — “Therefore, approximately 4.6% of the equilibrium structures constitute duplicates (see file DupMols.dat in the ZENODO repository 50 ), which were identified by an additional a posteriori approach that considered similarities between potential duplicate structures in the following six physicochemical properties: PBE0 energy, MBD energy, HOMO-LUMO gap, HOMO energy, molecular polarizability, and total dipole moment. The threshold used to check for similarity was set to 10 −3 × the corresponding unit for each property.” | mechanisms[5] |
| mechanism | non-equilibrium property exploration Structural distortions create property fluctuations around equilibrium values and thereby expand coverage of molecular property space. — “Generally speaking, structural distortions produce significant fluctuations around the values of each property for the equilibrium structures, and therefore improve the exploration and description of molecular property space.” | mechanisms[6] |
| mechanism | structured HDF5 access Each structure is a labeled Python dictionary in HDF5 whose keys expose atomic numbers, coordinates, and properties. — “The information for each molecular structure is stored in a Python dictionary (dict) type containing all relevant properties and recorded in groups in HDF5 file format. HDF5 keys to access the atomic numbers, atomic positions (coordinates), and physicochemical properties in each dictionary are provided in Table 2 .” | mechanisms[7] |
| builds-on | QM7 and QM9 single-structure benchmark datasets — “The QM7 and QM9 datasets have been widely used for benchmarking ML approaches and exploring molecular structure–property correlations 3 .” | claim_relations[0] |
| builds-on | ANI-1 and ANI-1x equilibrium/non-equilibrium datasets — “A more substantial coverage of CCS for small organic molecules was provided by Smith et al . 24 , 25 with the generation of the ANI-1 dataset, which consists of more than 20 M equilibrium and non-equilibrium conformations of molecules containing up to eight heavy (C, N, O) atoms from GDB-11 26 , 27 . More recently, the ANI-1x dataset 28 was introduced, which also contains 20 physicochemical properties for about 5 M structures computed using the semi-empirical ω B97X 29 density functional.” | claim_relations[1] |
| contrasts-with | prior datasets with narrower isomer, property, or theory coverage — “While many of the considered molecules do overlap with those in the ANI-1 dataset 24 , QM7-X also contains a more extensive sampling of equilibrium stereoisomers and a significantly different sampling of non-equilibrium structures ( vide infra ). Moreover, the number of reported physicochemical properties and the employed level of electronic structure theory in QM7-X is substantially more advanced compared to prior work.” | claim_relations[2] |
| sense | QM7-X as a comprehensive quantum-property dataset — “We introduce QM7-X, a comprehensive dataset of 42 physicochemical properties for ≈4.2 million equilibrium and non-equilibrium structures of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms.” | senses[0] |
| sense | chemical compound space as all feasible molecular compositions and conformations — “A crucial aspect of drug discovery 1 and molecular materials design 2 is an extensive exploration and understanding of chemical compound space (CCS)—the extremely high-dimensional space containing all feasible molecular compositions and conformations.” | senses[1] |
| sense | QM7-X coverage as stable structures plus 100 non-equilibrium variations — “as well as 100 non-equilibrium structural variations thereof to reach a total of ≈4.2 million molecular structures.” | senses[2] |
| sense | PBE0+MBD as the high-accuracy property level — “In this work, the structure generation process was performed using DFTB3+MBD, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBD level of theory.” | senses[3] |
| sense | DFTB3+MBD as the structure-generation level — “In this work, the structure generation process was performed using DFTB3+MBD, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBD level of theory.” | senses[4] |
| sense | non-equilibrium sampling as Boltzmann-filtered normal-mode displacement — “Although a similar approach was utilized during the construction of the ANI-1 dataset 24 , we have eliminated all issues related to the inaccuracy of the harmonic approximation by recomputing the energy of every candidate structure and only accepting those structures with a Boltzmann energy distribution (see Methods).” | senses[5] |
| sense | physicochemical-property scope as local/global and ground-state/response — “To provide an example of the significant information that can be obtained from QM7-X, we have plotted the distribution of several physicochemical properties in Fig. 4 according to the classification scheme defined in Table 2 , i.e ., division into global (molecular) and local (atom-in-a-molecule) properties, as well as ground-state and response properties.” | senses[6] |
| note | QM7 and QM9 single-structure benchmark datasets — QM7-X extends established GDB-derived quantum benchmarks. — “The QM7 and QM9 datasets have been widely used for benchmarking ML approaches and exploring molecular structure–property correlations 3 .” | claim_relations[0] |
| weight | QM7 and QM9 single-structure benchmark datasets — 0.95 — “The QM7 and QM9 datasets have been widely used for benchmarking ML approaches and exploring molecular structure–property correlations 3 .” | claim_relations[0] |
| note | ANI-1 and ANI-1x equilibrium/non-equilibrium datasets — The paper presents QM7-X after and against these larger prior resources. — “A more substantial coverage of CCS for small organic molecules was provided by Smith et al . 24 , 25 with the generation of the ANI-1 dataset, which consists of more than 20 M equilibrium and non-equilibrium conformations of molecules containing up to eight heavy (C, N, O) atoms from GDB-11 26 , 27 . More recently, the ANI-1x dataset 28 was introduced, which also contains 20 physicochemical properties for about 5 M structures computed using the semi-empirical ω B97X 29 density functional.” | claim_relations[1] |
| weight | ANI-1 and ANI-1x equilibrium/non-equilibrium datasets — 0.95 — “A more substantial coverage of CCS for small organic molecules was provided by Smith et al . 24 , 25 with the generation of the ANI-1 dataset, which consists of more than 20 M equilibrium and non-equilibrium conformations of molecules containing up to eight heavy (C, N, O) atoms from GDB-11 26 , 27 . More recently, the ANI-1x dataset 28 was introduced, which also contains 20 physicochemical properties for about 5 M structures computed using the semi-empirical ω B97X 29 density functional.” | claim_relations[1] |
| note | prior datasets with narrower isomer, property, or theory coverage — The article explicitly contrasts sampling, property count, and theory level. — “While many of the considered molecules do overlap with those in the ANI-1 dataset 24 , QM7-X also contains a more extensive sampling of equilibrium stereoisomers and a significantly different sampling of non-equilibrium structures ( vide infra ). Moreover, the number of reported physicochemical properties and the employed level of electronic structure theory in QM7-X is substantially more advanced compared to prior work.” | claim_relations[2] |
| weight | prior datasets with narrower isomer, property, or theory coverage — 0.95 — “While many of the considered molecules do overlap with those in the ANI-1 dataset 24 , QM7-X also contains a more extensive sampling of equilibrium stereoisomers and a significantly different sampling of non-equilibrium structures ( vide infra ). Moreover, the number of reported physicochemical properties and the employed level of electronic structure theory in QM7-X is substantially more advanced compared to prior work.” | claim_relations[2] |
| note | chemical compound space —same-as→ CCS — The naming equivalence is categorical. — “A crucial aspect of drug discovery 1 and molecular materials design 2 is an extensive exploration and understanding of chemical compound space (CCS)—the extremely high-dimensional space containing all feasible molecular compositions and conformations.” | concept_edges[0] |
| relation | chemical compound space —same-as→ CCS — CCS is the parenthetical abbreviation for chemical compound space. — “A crucial aspect of drug discovery 1 and molecular materials design 2 is an extensive exploration and understanding of chemical compound space (CCS)—the extremely high-dimensional space containing all feasible molecular compositions and conformations.” | concept_edges[0] |
| note | canonical SMILES —same-as→ simplified molecular-input line-entry system — The parenthetical expansion is categorical. — “Encoded as canonical SMILES (simplified molecular-input line-entry system) strings, the GDB datasets only provide the molecular formula and chemical connectivity, and do not contain any structural or molecular property information.” | concept_edges[1] |
| relation | canonical SMILES —same-as→ simplified molecular-input line-entry system — SMILES is expanded parenthetically as simplified molecular-input line-entry system. — “Encoded as canonical SMILES (simplified molecular-input line-entry system) strings, the GDB datasets only provide the molecular formula and chemical connectivity, and do not contain any structural or molecular property information.” | concept_edges[1] |
| note | QM7-X —contrasted-with→ QM7 and QM9 — In contrast to is explicit; the weight reflects a flat comparison. — “In contrast to many other QM-based datasets like QM7 and QM9, which contain a single structure per molecule, the QM7-X dataset not only includes constitutional/structural isomers, but also stereoisomers ( e.g ., enantiomers and diastereomers, including cis-/trans- and conformational isomers) as well as non-equilibrium structural variations thereof.” | concept_edges[2] |
| relation | QM7-X —contrasted-with→ QM7 and QM9 — QM7-X is contrasted with single-structure QM7 and QM9 by its isomer and non-equilibrium coverage. — “In contrast to many other QM-based datasets like QM7 and QM9, which contain a single structure per molecule, the QM7-X dataset not only includes constitutional/structural isomers, but also stereoisomers ( e.g ., enantiomers and diastereomers, including cis-/trans- and conformational isomers) as well as non-equilibrium structural variations thereof.” | concept_edges[2] |
| weight | QM7-X —contrasted-with→ QM7 and QM9 — 0.95 — “In contrast to many other QM-based datasets like QM7 and QM9, which contain a single structure per molecule, the QM7-X dataset not only includes constitutional/structural isomers, but also stereoisomers ( e.g ., enantiomers and diastereomers, including cis-/trans- and conformational isomers) as well as non-equilibrium structural variations thereof.” | concept_edges[2] |
| note | structural distortions —causes→ significant fluctuations — Produce is an explicit causal cue; generally speaking keeps it below categorical certainty. — “Generally speaking, structural distortions produce significant fluctuations around the values of each property for the equilibrium structures, and therefore improve the exploration and description of molecular property space.” | concept_edges[3] |
| relation | structural distortions —causes→ significant fluctuations — Structural distortions produce significant fluctuations in property values. — “Generally speaking, structural distortions produce significant fluctuations around the values of each property for the equilibrium structures, and therefore improve the exploration and description of molecular property space.” | concept_edges[3] |
| weight | structural distortions —causes→ significant fluctuations — 0.95 — “Generally speaking, structural distortions produce significant fluctuations around the values of each property for the equilibrium structures, and therefore improve the exploration and description of molecular property space.” | concept_edges[3] |
| note | randomly selected training samples —contrasted-with→ more refined training sets — Compared to is explicit and task-specific. — “In this work, it was found that randomly selected training samples have a better performance compared to more refined training sets ( e.g ., consisting of equilibrium structures together with a given number ( X ) of non-equilibrium structures) when developing accurate many-body repulsive potentials for the DFTB method via deep tensor neural networks.” | concept_edges[4] |
| relation | randomly selected training samples —contrasted-with→ more refined training sets — Random selection is contrasted favorably with more refined training-set construction for the reported task. — “In this work, it was found that randomly selected training samples have a better performance compared to more refined training sets ( e.g ., consisting of equilibrium structures together with a given number ( X ) of non-equilibrium structures) when developing accurate many-body repulsive potentials for the DFTB method via deep tensor neural networks.” | concept_edges[4] |
| weight | randomly selected training samples —contrasted-with→ more refined training sets — 0.95 — “In this work, it was found that randomly selected training samples have a better performance compared to more refined training sets ( e.g ., consisting of equilibrium structures together with a given number ( X ) of non-equilibrium structures) when developing accurate many-body repulsive potentials for the DFTB method via deep tensor neural networks.” | concept_edges[4] |
| relation | extensive and comprehensive QM-based datasets → progress exploring chemical compound space — Extensive comprehensive quantum datasets are required for progress in this exploration. — “However, progress along these lines can only happen with the availability of extensive and comprehensive QM-based datasets that adequately describe the complex structure–property relationships in molecules across CCS.” | unhoused_relations[0] |
| relation | DFTB3+MBD → structure generation process — DFTB3+MBD is used to generate structures. — “In this work, the structure generation process was performed using DFTB3+MBD, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBD level of theory.” | unhoused_relations[1] |
| relation | PBE0+MBD → energy, force, and property calculations — PBE0+MBD is used for energies, forces, and properties. — “In this work, the structure generation process was performed using DFTB3+MBD, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBD level of theory.” | unhoused_relations[2] |
| relation | inclusion of non-equilibrium structures → better coverage of the conformational space — Non-equilibrium structures provide better conformational-space coverage. — “The inclusion of non-equilibrium structures for each (meta-)stable equilibrium structure also provides better coverage of the conformational space than initially provided by the equilibrium structures, as seen in the pairwise distance distribution plots shown in Fig. 2 .” | unhoused_relations[3] |
| weight | inclusion of non-equilibrium structures → better coverage of the conformational space — 0.95 — “The inclusion of non-equilibrium structures for each (meta-)stable equilibrium structure also provides better coverage of the conformational space than initially provided by the equilibrium structures, as seen in the pairwise distance distribution plots shown in Fig. 2 .” | unhoused_relations[3] |
| relation | QM7-X dataset → eight HDF5 based files — QM7-X is distributed as eight HDF5 files. — “The QM7-X dataset is provided in eight HDF5 based files in a ZENODO.ORG data repository 50 .” | unhoused_relations[4] |
| relation | QM7-X → continued development of ML approaches — QM7-X is expected to enable further machine-learning development. — “Regarding ML applications, we are confident that the data provided by QM7-X will enable continued development of ML approaches, identification of novel QM-based molecular descriptors, as well as determination of robust training sample selection methods that will improve the accuracy and reliability of molecular property predictions.” | unhoused_relations[5] |
| weight | QM7-X → continued development of ML approaches — 0.65 — “Regarding ML applications, we are confident that the data provided by QM7-X will enable continued development of ML approaches, identification of novel QM-based molecular descriptors, as well as determination of robust training sample selection methods that will improve the accuracy and reliability of molecular property predictions.” | unhoused_relations[5] |
| no type for this | extensive and comprehensive QM-based datasets → progress exploring chemical compound space — Progress in QM-plus-ML exploration depends on extensive, comprehensive datasets. — “However, progress along these lines can only happen with the availability of extensive and comprehensive QM-based datasets that adequately describe the complex structure–property relationships in molecules across CCS.” | unhoused_relations[0] |
| no type for this | DFTB3+MBD → structure generation process — DFTB3+MBD is assigned the functional role of generating structures. — “In this work, the structure generation process was performed using DFTB3+MBD, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBD level of theory.” | unhoused_relations[1] |
| no type for this | PBE0+MBD → energy, force, and property calculations — PBE0+MBD is assigned the functional role of computing properties after structure generation. — “In this work, the structure generation process was performed using DFTB3+MBD, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBD level of theory.” | unhoused_relations[2] |
| no type for this | inclusion of non-equilibrium structures → better coverage of the conformational space — Including displaced structures expands conformational coverage beyond equilibrium geometries. — “The inclusion of non-equilibrium structures for each (meta-)stable equilibrium structure also provides better coverage of the conformational space than initially provided by the equilibrium structures, as seen in the pairwise distance distribution plots shown in Fig. 2 .” | unhoused_relations[3] |
| no type for this | QM7-X dataset → eight HDF5 based files — The dataset is serialized and distributed as eight HDF5 files. — “The QM7-X dataset is provided in eight HDF5 based files in a ZENODO.ORG data repository 50 .” | unhoused_relations[4] |
| no type for this | QM7-X → continued development of ML approaches — The authors expect QM7-X to enable improved machine-learning methods, descriptors, and sample selection. — “Regarding ML applications, we are confident that the data provided by QM7-X will enable continued development of ML approaches, identification of novel QM-based molecular descriptors, as well as determination of robust training sample selection methods that will improve the accuracy and reliability of molecular property predictions.” | unhoused_relations[5] |
| limitation | Chemical-compound-space dimensionality scales exponentially with molecule size, making larger regions difficult to explore. — “In this regard, one challenge that is encountered during the generation of such datasets is the fact that their dimension scales exponentially with molecule size, thereby making it difficult to explore increasingly large swaths of CCS.” | limitations[0] |
| limitation | Tightly converged quantum-mechanical calculations impose steep computational costs. — “The second challenge is the steep computational cost of tightly converged QM calculations, which are critical for obtaining an accurate and reliable description of the structure and physicochemical properties of each molecule.” | limitations[1] |
| limitation | The source GDB datasets contain formula and connectivity but no structural or molecular-property information. — “Encoded as canonical SMILES (simplified molecular-input line-entry system) strings, the GDB datasets only provide the molecular formula and chemical connectivity, and do not contain any structural or molecular property information.” | limitations[2] |
| limitation | QM7-X excludes 261 of 7,211 GDB13 formulae because a complete energy distribution could not be obtained. — “Since we were unable to obtain a complete energy distribution (as described above) for 261 of the 7,211 molecular formulae taken from the GDB13 dataset, molecules with these molecular formulae were not included in QM7-X.” | limitations[3] |
| limitation | About 4.6% of equilibrium structures are duplicates, and the authors acknowledge that they may affect machine-learning performance. — “Therefore, approximately 4.6% of the equilibrium structures constitute duplicates (see file DupMols.dat in the ZENODO repository 50 ), which were identified by an additional a posteriori approach that considered similarities between potential duplicate structures in the following six physicochemical properties: PBE0 energy, MBD energy, HOMO-LUMO gap, HOMO energy, molecular polarizability, and total dipole moment. The threshold used to check for similarity was set to 10 −3 × the corresponding unit for each property. While the presence of some duplicate equilibrium structures in the QM7-X dataset might influence the performance of ML models developed using this data, the non-equilibrium structures associated with these duplicate equilibrium structures are not identical and probe different regions of the molecular PES.” | limitations[4] |
| limitation | Only 0.06% of QM7-X contains chlorine-bearing molecules, limiting coverage of that composition class. — “On the other hand, only 0.06% of QM7-X includes Cl-containing molecules.” | limitations[5] |
| limitation | Computational feasibility limited sampling to 100 non-equilibrium structures per stable conformer at PBE0+MBD. — “Since it was only computationally feasible to consider 100 non-equilibrium structures at the PBE0+MBD level, these structures were chosen to cover as much of the PES surrounding each (meta-)stable equilibrium structure as possible.” | limitations[6] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | QM7-X contains 42 properties for about 4.2 million equilibrium and non-equilibrium structures with up to seven heavy C/N/O/S/Cl atoms. — “We introduce QM7-X, a comprehensive dataset of 42 physicochemical properties for ≈4.2 million equilibrium and non-equilibrium structures of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms.” | content_tags.findings[0] |
| finding | The dataset adds 100 non-equilibrium structural variations for its stable equilibrium structures, reaching about 4.2 million structures. — “as well as 100 non-equilibrium structural variations thereof to reach a total of ≈4.2 million molecular structures.” | content_tags.findings[1] |
| finding | QM7-X covers 96.4% of GDB13 molecules with up to seven heavy atoms and 98.8% of their stable stereoisomers. — “As such, QM7-X covers 96.4% of all molecules containing up to seven heavy atoms from GDB13 (and 98.8% of the corresponding (meta-)stable stereoisomers), which should provide a sufficiently accurate and representative sample of the small organic molecules contained in CCS.” | content_tags.findings[2] |
| finding | About 4.6% of equilibrium structures are identified duplicates, but their associated non-equilibrium structures remain distinct. — “While the presence of some duplicate equilibrium structures in the QM7-X dataset might influence the performance of ML models developed using this data, the non-equilibrium structures associated with these duplicate equilibrium structures are not identical and probe different regions of the molecular PES.” | content_tags.findings[3] |
| finding | PBE0+MBD reoptimization of 63 geometries found only minima and an average DFTB3+MBD-to-PBE0+MBD RMSD of 0.1 Å. — “In doing so, it was found that all 63 so obtained PBE0+MBD geometries constitute local or global minima ( i.e ., with no imaginary frequencies), and the average RMSD between the DFTB3+MBD and PBE0+MBD structures amounts to only 0.1 Å.” | content_tags.findings[4] |
| finding | Seven-heavy-atom molecules dominate QM7-X with 37,438 equilibrium and 3,743,800 non-equilibrium structures. — “In QM7-X, molecules made of seven heavy atoms are the most abundant with 37,438 equilibrium structures (including conformational isomers) and 3,743,800 non-equilibrium structures, followed by molecules containing six heavy atoms (see Table 1 ).” | content_tags.findings[5] |
| finding | The dataset is compositionally rich in H/C/N, H/C/O, and H/N/O structures. — “Here, it was found that 68.0% and 65.0% of the QM7-X dataset is comprised of molecular structures which contain only [H,C,N] and [H,C,O] atoms, respectively, while structures containing [H,N,O] atoms are found in 38.7% of the dataset.” | content_tags.findings[6] |
| finding | Non-equilibrium distortions broaden conformational and molecular-property coverage relative to equilibrium structures alone. — “The inclusion of non-equilibrium structures for each (meta-)stable equilibrium structure also provides better coverage of the conformational space than initially provided by the equilibrium structures, as seen in the pairwise distance distribution plots shown in Fig. 2 .” | content_tags.findings[7] |
| finding | For one reported application, randomly selected QM7-X training samples outperformed more refined equilibrium-plus-distortion training sets. — “In this work, it was found that randomly selected training samples have a better performance compared to more refined training sets ( e.g ., consisting of equilibrium structures together with a given number ( X ) of non-equilibrium structures) when developing accurate many-body repulsive potentials for the DFTB method via deep tensor neural networks.” | content_tags.findings[8] |
| finding | QM7-X is distributed as eight HDF5 files through Zenodo with a README and optional duplicate handling. — “The QM7-X dataset is provided in eight HDF5 based files in a ZENODO.ORG data repository 50 . One can also find there a README file with technical usage details and examples of how to access the information stored in QM7-X (with and without considering duplicates, see createDB.py file).” | content_tags.findings[9] |
| quantity | 42 — physicochemical properties in QM7-X — “We introduce QM7-X, a comprehensive dataset of 42 physicochemical properties for ≈4.2 million equilibrium and non-equilibrium structures of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms.” | content_tags.quantities[0] |
| quantity | ≈4.2 million — equilibrium and non-equilibrium molecular structures in QM7-X — “We introduce QM7-X, a comprehensive dataset of 42 physicochemical properties for ≈4.2 million equilibrium and non-equilibrium structures of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms.” | content_tags.quantities[1] |
| quantity | 100 — non-equilibrium variations generated for each stable equilibrium structure — “In order to sample some of the non-equilibrium sectors of CCS, we generated 100 non-equilibrium structures for each of the (meta-)stable equilibrium structures described above.” | content_tags.quantities[2] |
| quantity | 50 kcal/mol — MMFF94 conformer energy window relative to the most stable structure — “At the MMFF94 level, we retained the set of conformers that were within 50 kcal/mol of the most stable structure and differed by a root-mean-square deviation (RMSD) of 0.5 Å.” | content_tags.quantities[3] |
| quantity | 0.5 Å — MMFF94 RMSD difference criterion for retained conformers — “At the MMFF94 level, we retained the set of conformers that were within 50 kcal/mol of the most stable structure and differed by a root-mean-square deviation (RMSD) of 0.5 Å.” | content_tags.quantities[4] |
| quantity | 261 of the 7,211 — GDB13 molecular formulae excluded for incomplete energy distributions — “Since we were unable to obtain a complete energy distribution (as described above) for 261 of the 7,211 molecular formulae taken from the GDB13 dataset, molecules with these molecular formulae were not included in QM7-X.” | content_tags.quantities[5] |
| quantity | 96.4% — coverage of GDB13 molecules with up to seven heavy atoms — “As such, QM7-X covers 96.4% of all molecules containing up to seven heavy atoms from GDB13 (and 98.8% of the corresponding (meta-)stable stereoisomers), which should provide a sufficiently accurate and representative sample of the small organic molecules contained in CCS.” | content_tags.quantities[6] |
| quantity | 98.8% — coverage of corresponding stable stereoisomers — “As such, QM7-X covers 96.4% of all molecules containing up to seven heavy atoms from GDB13 (and 98.8% of the corresponding (meta-)stable stereoisomers), which should provide a sufficiently accurate and representative sample of the small organic molecules contained in CCS.” | content_tags.quantities[7] |
| quantity | approximately 4.6% — equilibrium structures identified as duplicates — “Therefore, approximately 4.6% of the equilibrium structures constitute duplicates (see file DupMols.dat in the ZENODO repository 50 ), which were identified by an additional a posteriori approach that considered similarities between potential duplicate structures in the following six physicochemical properties: PBE0 energy, MBD energy, HOMO-LUMO gap, HOMO energy, molecular polarizability, and total dipole moment.” | content_tags.quantities[8] |
| quantity | 63 — PBE0+MBD-reoptimized geometries in the structural-agreement validation — “In doing so, it was found that all 63 so obtained PBE0+MBD geometries constitute local or global minima ( i.e ., with no imaginary frequencies), and the average RMSD between the DFTB3+MBD and PBE0+MBD structures amounts to only 0.1 Å.” | content_tags.quantities[9] |
| quantity | 0.1 Å — average RMSD between DFTB3+MBD and PBE0+MBD validation geometries — “In doing so, it was found that all 63 so obtained PBE0+MBD geometries constitute local or global minima ( i.e ., with no imaginary frequencies), and the average RMSD between the DFTB3+MBD and PBE0+MBD structures amounts to only 0.1 Å.” | content_tags.quantities[10] |
| quantity | 0.06% — share of QM7-X containing chlorine-bearing molecules — “On the other hand, only 0.06% of QM7-X includes Cl-containing molecules.” | content_tags.quantities[11] |
| variable | molecular composition (chemical dimension enumerated across GDB13 formulae and isomers) — “A crucial aspect of drug discovery 1 and molecular materials design 2 is an extensive exploration and understanding of chemical compound space (CCS)—the extremely high-dimensional space containing all feasible molecular compositions and conformations.” | content_tags.variables[0] |
| variable | normal mode coordinates (directions combined to perturb stable structures into non-equilibrium candidates) — “This was achieved by displacing each molecular structure along a linear combination of normal mode coordinates computed at the DFTB3+MBD level within the harmonic approximation (for consistency with the level of theory used to optimize the corresponding molecular structures).” | content_tags.variables[1] |
| variable | RMSD (geometric difference criterion for conformer selection, duplicate detection, and cross-level validation) — “At the MMFF94 level, we retained the set of conformers that were within 50 kcal/mol of the most stable structure and differed by a root-mean-square deviation (RMSD) of 0.5 Å.” | content_tags.variables[2] |
| variable | PBE0+MBD energy (one property used to identify potential duplicate equilibrium structures) — “Therefore, approximately 4.6% of the equilibrium structures constitute duplicates (see file DupMols.dat in the ZENODO repository 50 ), which were identified by an additional a posteriori approach that considered similarities between potential duplicate structures in the following six physicochemical properties: PBE0 energy, MBD energy, HOMO-LUMO gap, HOMO energy, molecular polarizability, and total dipole moment.” | content_tags.variables[3] |
| variable | physicochemical properties (global and local prediction targets computed for each molecular structure) — “Over 40 different physicochemical properties were computed to describe the structure–property and property–property relationships in QM7-X.” | content_tags.variables[6] |
| variable | training sample selection (machine-learning design variable evaluated for predictive performance) — “In this work, it was found that randomly selected training samples have a better performance compared to more refined training sets ( e.g ., consisting of equilibrium structures together with a given number ( X ) of non-equilibrium structures) when developing accurate many-body repulsive potentials for the DFTB method via deep tensor neural networks.” | content_tags.variables[7] |
| definition | chemical compound space — “A crucial aspect of drug discovery 1 and molecular materials design 2 is an extensive exploration and understanding of chemical compound space (CCS)—the extremely high-dimensional space containing all feasible molecular compositions and conformations.” | content_tags.definitions[0] |
| definition | canonical SMILES — “Encoded as canonical SMILES (simplified molecular-input line-entry system) strings, the GDB datasets only provide the molecular formula and chemical connectivity, and do not contain any structural or molecular property information.” | content_tags.definitions[1] |
| definition | conformational isomers — “For each of these structures, we also generated a set of sufficiently different (meta-)stable conformational isomers, i.e ., isomers which can be interconverted by rotations around single bonds.” | content_tags.definitions[2] |
| definition | Hirshfeld ratios — “Hirshfeld ratios correspond to the Hirshfeld volumes divided by the free atom volumes.” | content_tags.definitions[4] |
| definition | exact exchange energy — “The exact exchange energy is the amount of exact (or Hartree-Fock) exchange that has been admixed into the exchange-correlation energy.” | content_tags.definitions[5] |
| concept | QM7-X — not defined in this paper's own words; the comprehensive equilibrium and non-equilibrium quantum-property dataset introduced here — “We introduce QM7-X, a comprehensive dataset of 42 physicochemical properties for ≈4.2 million equilibrium and non-equilibrium structures of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms.” | concepts[0] |
| concept | chemical compound space — not defined in this paper's own words; the high-dimensional space of feasible molecular compositions and conformations — “A crucial aspect of drug discovery 1 and molecular materials design 2 is an extensive exploration and understanding of chemical compound space (CCS)—the extremely high-dimensional space containing all feasible molecular compositions and conformations.” | concepts[1] |
| concept | CCS — not defined in this paper's own words; the abbreviation for chemical compound space — “A crucial aspect of drug discovery 1 and molecular materials design 2 is an extensive exploration and understanding of chemical compound space (CCS)—the extremely high-dimensional space containing all feasible molecular compositions and conformations.” | concepts[2] |
| concept | canonical SMILES — not defined in this paper's own words; canonical molecular composition and connectivity strings — “Encoded as canonical SMILES (simplified molecular-input line-entry system) strings, the GDB datasets only provide the molecular formula and chemical connectivity, and do not contain any structural or molecular property information.” | concepts[3] |
| concept | simplified molecular-input line-entry system — not defined in this paper's own words; the expanded name of SMILES — “Encoded as canonical SMILES (simplified molecular-input line-entry system) strings, the GDB datasets only provide the molecular formula and chemical connectivity, and do not contain any structural or molecular property information.” | concepts[4] |
| concept | GDB13 database — not defined in this paper's own words; the enumerated small-organic-molecule source for QM7-X — “As a basis for the QM7-X dataset, we considered all molecules containing up to seven heavy (non-hydrogen) atoms in the GDB13 database 10 , which provides an enumeration of the CCS spanned by small organic molecules comprised of H, C, N, O, S, and Cl atoms.” | concepts[5] |
| concept | structural/constitutional isomers — not defined in this paper's own words; molecules sharing formula but differing in connectivity — “the QM7-X dataset not only includes constitutional/structural isomers, but also stereoisomers” | concepts[6] |
| concept | stereoisomers — not defined in this paper's own words; enantiomeric and diastereomeric structures with shared connectivity — “the QM7-X dataset not only includes constitutional/structural isomers, but also stereoisomers” | concepts[7] |
| concept | conformational isomers — not defined in this paper's own words; isomers connected by rotations around single bonds — “For each of these structures, we also generated a set of sufficiently different (meta-)stable conformational isomers, i.e ., isomers which can be interconverted by rotations around single bonds.” | concepts[8] |
| concept | MMFF94 force field — not defined in this paper's own words; the force field used for initial structures and conformer search — “Based on these SMILES strings, initial 3D structures were obtained using the MMFF94 force field 31 – 35 via the gen3d option in Open Babel 36 .” | concepts[9] |
| concept | Open Babel — not defined in this paper's own words; software whose gen3d option generates initial three-dimensional structures — “Based on these SMILES strings, initial 3D structures were obtained using the MMFF94 force field 31 – 35 via the gen3d option in Open Babel 36 .” | concepts[10] |
| concept | Confab tool — not defined in this paper's own words; the conformational-isomer search tool — “To do this, we performed a conformational isomer search with the Confab tool 37 in conjunction with the MMFF94 force field.” | concepts[11] |
| concept | DFTB3+MBD — not defined in this paper's own words; the tight-binding plus many-body-dispersion level used for structure generation — “In this work, the structure generation process was performed using DFTB3+MBD, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBD level of theory.” | concepts[12] |
| concept | PBE0+MBD — not defined in this paper's own words; the hybrid-DFT plus many-body-dispersion level used for properties — “In this work, the structure generation process was performed using DFTB3+MBD, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBD level of theory.” | concepts[13] |
| concept | normal mode coordinates — not defined in this paper's own words; vibrational directions linearly combined for molecular displacement — “This was achieved by displacing each molecular structure along a linear combination of normal mode coordinates computed at the DFTB3+MBD level within the harmonic approximation (for consistency with the level of theory used to optimize the corresponding molecular structures).” | concepts[14] |
| concept | Boltzmann energy distribution — not defined in this paper's own words; the energy distribution enforced for accepted non-equilibrium candidates — “Although a similar approach was utilized during the construction of the ANI-1 dataset 24 , we have eliminated all issues related to the inaccuracy of the harmonic approximation by recomputing the energy of every candidate structure and only accepting those structures with a Boltzmann energy distribution (see Methods).” | concepts[15] |
| concept | potential energy surface — not defined in this paper's own words; the molecular energy landscape sampled around stable structures — “Another important target of the QM7-X dataset is efficient PES sampling for a large number of small organic molecules.” | concepts[16] |
| concept | PES — not defined in this paper's own words; the abbreviation for potential energy surface — “Another important target of the QM7-X dataset is efficient PES sampling for a large number of small organic molecules.” | concepts[17] |
| concept | equilibrium structures — not defined in this paper's own words; optimized stable or metastable molecular geometries — “The approximately 4.2 M equilibrium and non-equilibrium structures generated using these procedures form the QM7-X dataset (see Table 1 ).” | concepts[18] |
| concept | non-equilibrium structures — not defined in this paper's own words; normal-mode-displaced geometries away from optimized structures — “The approximately 4.2 M equilibrium and non-equilibrium structures generated using these procedures form the QM7-X dataset (see Table 1 ).” | concepts[19] |
| concept | physicochemical properties — not defined in this paper's own words; computed local and global ground-state and response quantities — “Over 40 different physicochemical properties were computed to describe the structure–property and property–property relationships in QM7-X.” | concepts[20] |
| concept | global properties — not defined in this paper's own words; properties defined at the molecular level — “To provide an example of the significant information that can be obtained from QM7-X, we have plotted the distribution of several physicochemical properties in Fig. 4 according to the classification scheme defined in Table 2 , i.e ., division into global (molecular) and local (atom-in-a-molecule) properties, as well as ground-state and response properties.” | concepts[21] |
| concept | local (atom-in-a-molecule) properties — not defined in this paper's own words; properties defined for atoms in molecules — “To provide an example of the significant information that can be obtained from QM7-X, we have plotted the distribution of several physicochemical properties in Fig. 4 according to the classification scheme defined in Table 2 , i.e ., division into global (molecular) and local (atom-in-a-molecule) properties, as well as ground-state and response properties.” | concepts[22] |
| concept | ground state quantities — not defined in this paper's own words; properties such as energies, forces, gaps, and moments — “Computed at the tightly converged quantum-mechanical PBE0+MBD level of theory, QM7-X contains global (molecular) and local (atom-in-a-molecule) properties ranging from ground state quantities (such as atomization energies and dipole moments) to response quantities (such as polarizability tensors and dispersion coefficients).” | concepts[23] |
| concept | response quantities — not defined in this paper's own words; properties such as polarizability tensors and dispersion coefficients — “Computed at the tightly converged quantum-mechanical PBE0+MBD level of theory, QM7-X contains global (molecular) and local (atom-in-a-molecule) properties ranging from ground state quantities (such as atomization energies and dipole moments) to response quantities (such as polarizability tensors and dispersion coefficients).” | concepts[24] |
| concept | root-mean-square deviation — not defined in this paper's own words; geometric dissimilarity measure used for conformer selection and validation — “At the MMFF94 level, we retained the set of conformers that were within 50 kcal/mol of the most stable structure and differed by a root-mean-square deviation (RMSD) of 0.5 Å.” | concepts[25] |
| concept | RMSD — not defined in this paper's own words; the abbreviation for root-mean-square deviation — “At the MMFF94 level, we retained the set of conformers that were within 50 kcal/mol of the most stable structure and differed by a root-mean-square deviation (RMSD) of 0.5 Å.” | concepts[26] |
| concept | duplicate equilibrium structures — not defined in this paper's own words; equilibrium entries identified as structurally or physically redundant — “Thus, we offer users the option to keep or exclude these duplicate equilibrium structures (as well as their corresponding non-equilibrium structures) in the QM7-X dataset via the createDB.py script uploaded to the ZENODO repository 50 .” | concepts[27] |
| concept | Python dictionary — not defined in this paper's own words; the per-structure data container recorded in HDF5 groups — “The information for each molecular structure is stored in a Python dictionary (dict) type containing all relevant properties and recorded in groups in HDF5 file format.” | concepts[28] |
| concept | HDF5 — not defined in this paper's own words; the grouped file format used to distribute QM7-X — “The QM7-X dataset is provided in eight HDF5 based files in a ZENODO.ORG data repository 50 .” | concepts[29] |
| concept | ZENODO.ORG data repository — not defined in this paper's own words; the repository hosting QM7-X files and usage metadata — “The QM7-X dataset is provided in eight HDF5 based files in a ZENODO.ORG data repository 50 .” | concepts[30] |
| concept | structural distortions — not defined in this paper's own words; departures from equilibrium that perturb computed property values — “Generally speaking, structural distortions produce significant fluctuations around the values of each property for the equilibrium structures, and therefore improve the exploration and description of molecular property space.” | concepts[31] |
| concept | significant fluctuations — not defined in this paper's own words; property variation produced around equilibrium values — “Generally speaking, structural distortions produce significant fluctuations around the values of each property for the equilibrium structures, and therefore improve the exploration and description of molecular property space.” | concepts[32] |
| concept | randomly selected training samples — not defined in this paper's own words; random QM7-X samples used to define predictive training sets — “In this work, it was found that randomly selected training samples have a better performance compared to more refined training sets ( e.g ., consisting of equilibrium structures together with a given number ( X ) of non-equilibrium structures) when developing accurate many-body repulsive potentials for the DFTB method via deep tensor neural networks.” | concepts[33] |
| concept | more refined training sets — not defined in this paper's own words; structured mixtures of equilibrium and selected non-equilibrium examples — “In this work, it was found that randomly selected training samples have a better performance compared to more refined training sets ( e.g ., consisting of equilibrium structures together with a given number ( X ) of non-equilibrium structures) when developing accurate many-body repulsive potentials for the DFTB method via deep tensor neural networks.” | concepts[34] |
| concept | QM7 and QM9 — not defined in this paper's own words; prior single-structure quantum-chemistry datasets used as comparators — “In contrast to many other QM-based datasets like QM7 and QM9, which contain a single structure per molecule, the QM7-X dataset not only includes constitutional/structural isomers, but also stereoisomers ( e.g ., enantiomers and diastereomers, including cis-/trans- and conformational isomers) as well as non-equilibrium structural variations thereof.” | concepts[35] |
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QM7-Xterm, a comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules Abstract We introduce QM7-Xterm, a comprehensive dataset of 42 physicochemical propertiesterm for ≈4.2 million equilibrium and non-equilibrium structuresterm of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms. To span this fundamentally important region of chemical compound spaceterm (CCSterm), QM7-Xterm includes an exhaustive sampling of (meta-)stable equilibrium structuresterm—comprised of constitutional/structural isomers and stereoisomersterm, e.g., enantiomers and diastereomers (including cis- / trans - and conformational isomersterm)—as well as 100 non-equilibrium structural variations thereof to reach a total of ≈4.2 million molecular structures. Computed at the tightly converged quantum-mechanical PBE0+MBDterm level of theory, QM7-Xterm contains global (molecular) and local (atom-in-a-molecule) propertiesterm ranging from ground state quantitiesterm (such as atomization energies and dipole moments) to response quantitiesterm (such as polarizability tensors and dispersion coefficients). By providing a systematic, extensive, and tightly-converged dataset of quantum-mechanically computed physicochemical propertiesterm, we expect that QM7-Xterm will play a critical role in the development of next-generation machine-learning based models for exploring greater swaths of CCSterm and performing in silico design of molecules with targeted properties.
Background & Summary A crucial aspect of drug discovery 1 and molecular materials design 2 is an extensive exploration and understanding of chemical compound spaceterm (CCSterm)—the extremely high-dimensional space containing all feasible molecular compositionsterm·var and conformations. Recently, the combination of quantum mechanical (QM) calculations with machine learning (ML) has led to considerable insight into CCSterm 3 – 9 . However, progress along these lines can only happen with the availability of extensive and comprehensive QM-based datasets that adequately describe the complex structure–property relationships in molecules across CCSterm. In this regard, one challenge that is encountered during the generation of such datasets is the fact that their dimension scales exponentially with molecule size, thereby making it difficult to explore increasingly large swaths of CCSterm. The second challenge is the steep computational cost of tightly converged QM calculations, which are critical for obtaining an accurate and reliable description of the structure and physicochemical propertiesterm of each molecule.
To begin such an extensive exploration of CCSterm, the GDB datasets 1 , 10 , 11 have enumerated up to 166 B organic molecules containing up to 17 heavy (non-hydrogen) atoms. Encoded as canonical SMILESterm (simplified molecular-input line-entry systemterm) strings, the GDB datasets only provide the molecular formula and chemical connectivity, and do not contain any structural or molecular property information. As such, QM calculations on small subsets of the GDB datasets have subsequently been used to generate meta-stable conformations for each molecular compositionterm·var. This has led to seminal QM-based datasets like QM7 10 , 12 , 13 and QM9 11 , 14 , which are comprised of a single meta-stable molecular structure per SMILES string with up to seven and nine heavy (non-hydrogen) atoms, respectively. The QM7 and QM9term datasets have been widely used for benchmarking ML approaches and exploring molecular structure–property correlations 3 . In addition, molecular dynamics (MD) based datasets have become available for a few selected molecules and solids, and contain both equilibrium and non-equilibrium structuresterm 15 – 21 ; such datasets are becoming increasingly more useful for constructing advanced interatomic potentials 16 , 22 , 23 .
A more substantial coverage of CCSterm for small organic molecules was provided by Smith et al . 24 , 25 with the generation of the ANI-1 dataset, which consists of more than 20 M equilibrium and non-equilibrium conformations of molecules containing up to eight heavy (C, N, O) atoms from GDB-11 26 , 27 . More recently, the ANI-1x dataset 28 was introduced, which also contains 20 physicochemical propertiesterm for about 5 M structures computed using the semi-empirical ω B97X 29 density functional. In addition, Smith et al . 28 also provided local CCSD(T) energies for a smaller subset of 0.5 M structures. To date, the ANI-1 datasets contain the largest available collection of GDB-based QM calculations of molecular structures and properties. However, four challenges still remain to enable a systematic exploration of CCSterm for small organic molecules: (i) providing a systematic sampling of CCSterm in terms of constitutional/structural isomers and stereoisomersterm ( e.g ., enantiomers and diastereomers, including cis-/trans- and meta-stable conformational isomersterm), (ii) assessing the accuracy and reliability of QM structures and properties with respect to the employed density-functional approximation (especially for non-equilibrium conformations), (iii) offering a large set of local (atom-in-a-molecule) and global (molecular) physicochemical propertiesterm that would enable a comprehensive exploration of structure–property relationships throughout CCSterm, and (iv) providing accurate and reliable QM data that will enable the construction of models for describing covalent and non-covalent van der Waals (vdW) interactions.
In order to convincingly address these four challenges in this work, we present QM7-Xterm, which aims to provide a systematic, extensive, and tightly converged dataset of QM-based physical and chemical properties for a fundamentally important region of CCSterm covering small organic molecules (see Fig. 1 ). To do so, we performed a systematic and exhaustive sampling of the (meta-)stable equilibrium structuresterm of all molecules with up to seven heavy (C, N, O, S, Cl) atoms in the GDB13 databaseterm 10 using a density-functional tight binding (DFTB) approach; this includes constitutional/structural isomers and stereoisomersterm, e.g ., enantiomers and diastereomers (including cis-/trans- and conformational isomersterm). This was followed by the generation of 100 non-equilibrium structuresterm ( via DFTB normal-mode displacements of each equilibrium structureterm) for a total of ≈4.2 M molecular structures. For each of these equilibrium and non-equilibrium molecular structures, QM7-Xterm also includes an extensive number of QM-obtained physicochemical propertiesterm, most of which were computed using non-empirical hybrid density-functional theory (DFT) with a many-body treatment of vdW dispersion interactions ( i.e ., PBE0+MBDterm) in conjunction with tightly-converged numeric atom-centered orbitals 30 . In total, QM7-Xterm contains 42 molecular (global) and atom-in-a-molecule (local) properties, which range from ground state quantitiesterm (such as total and atomization energies, atomic forces, HOMO-LUMO gaps, dipole/quadrupole moments, Hirshfeld quantities, etc.) to response quantitiesterm (such as polarizability tensors and dispersion coefficients)—all of which could be utilized for the construction of next-generation intra- and inter-molecular force fields. As such, we expect that QM7-Xterm will be useful for the development of accurate and reliable ML-based techniques that will provide new insight into the complex structure–property relationships in molecules, and ultimately allow for more extensive exploration of CCSterm and the rational design of molecules with tailored properties. Fig. 1 Schematic representation of the QM7-Xterm dataset. The “building blocks” for the QM7-Xterm dataset are the set of ≈7 k molecular formulae which contain up to seven heavy (non-hydrogen) atoms from the GDB13 databaseterm. The first step in the construction of QM7-Xterm is an extensive sampling of the structural/constitutional isomersterm and stereoisomersterm, e.g ., enantiomers and diastereomers (including cis-/trans- and conformational isomersterm) for each of the initial ≈7 k molecular formulae using the MMFF94 force fieldterm (schematically depicted above for some of the stereoisomersterm of 3-Amino-2-butanol). Each of these molecules was optimized at the DFTB3+MBDterm level of theory for a total of ≈40 k (meta-)stable equilibrium molecular structures. For each of these equilibrium structuresterm, 100 non-equilibrium structuresterm were generated by displacing the atoms according to linear combinations of the DFTB3+MBDterm normal modes for a total of ≈4.2 M molecular structures (with the range of atomic displacements (hydrogen/non-hydrogen atoms in pink/green) depicted above for a single 3-Amino-2-butanol conformer). We then performed QM calculations at the PBE0+MBDterm level to obtain 42 physicochemical propertiesterm for each of the ≈4.2 M molecular structures.
Methods Generation of equilibrium structuresterm As a basis for the QM7-Xterm dataset, we considered all molecules containing up to seven heavy (non-hydrogen) atoms in the GDB13 databaseterm 10 , which provides an enumeration of the CCSterm spanned by small organic molecules comprised of H, C, N, O, S, and Cl atoms. These molecules range in size from N = 4–23 atoms (see Fig. 1 ). For each molecular formula, the GDB13 databaseterm only includes chemical connectivity information ( i.e ., some structural/constitutional isomersterm) encoded as SMILES strings. To generate all of the corresponding structural/constitutional isomersterm and stereoisomersterm, e.g ., enantiomers and diastereomers (including cis-/trans- isomers) for each molecular formula, we created canonical SMILESterm strings for each possible molecular structure. Based on these SMILES strings, initial 3D structures were obtained using the MMFF94 force fieldterm 31 – 35 via the gen3d option in Open Babelterm 36 . For each of these structures, we also generated a set of sufficiently different (meta-)stable conformational isomersterm, i.e ., isomers which can be interconverted by rotations around single bonds. To do this, we performed a conformational isomerterm search with the Confab toolterm 37 in conjunction with the MMFF94 force fieldterm. At the MMFF94 level, we retained the set of conformers that were within 50 kcal/mol of the most stable structure and differed by a root-mean-square deviationterm (RMSDterm) of 0.5 Å.
All molecular structures were subsequently re-optimized with third-order self-consistent charge density functional tight binding (DFTB3) 38 – 40 supplemented with a treatment of many-body dispersion (MBD) interactions 41 – 44 , using the 3ob parameters 45 , 46 . All DFTB3+MBDterm calculations were performed using in-house versions of the DFTB+ code 47 and the Atomic Simulationterm·mth Environment (ASE) 48 . The lowest-energy structure obtained at the DFTB3+MBDterm level was considered the first conformer, and additional structures were accepted as separate conformers if the RMSDterm between the respective structure and the first conformer (as well as all subsequently accepted conformers) was larger than 1.0 Å. While most of these molecular structures correspond to local minima at the DFTB3+MBDterm level, we note in passing that some correspond to saddle points on the DFTB3+MBDterm potential energy surfaceterm (PESterm).
Generation of non-equilibrium structuresterm In order to sample some of the non-equilibrium sectors of CCSterm, we generated 100 non-equilibrium structuresterm for each of the (meta-)stable equilibrium structuresterm described above. This was achieved by displacing each molecular structure along a linear combination of normal mode coordinatesterm computed at the DFTB3+MBDterm level within the harmonic approximation (for consistency with the level of theory used to optimize the corresponding molecular structures). In order to generate comparable displacements for all equilibrium molecular structures (despite differing molecular sizes and relative stabilities), we generated a set of displaced structures which has an average energy difference (with respect to the corresponding (meta-)stable equilibrium structureterm) of 1 Δ E = 3 2 N k B T , in analogy to the equipartition theorem from classical statistical mechanics, in which each of the 3 N degrees of freedom in a monatomic ideal gas contributes 1 2 k B T to the internal energy (with k B being the Boltzmann constant and T the temperature). To sufficiently sample the PESterm for each (meta-)stable equilibrium structureterm, we set T = 1500 K. In addition to the <Δ E> convention defined in Eq. ( 1 ), the 100 non-equilibrium molecular structures were also required to follow the corresponding Boltzmann distribution: 2 P ( Δ E ) = e x p − Δ E k B T .
To generate a set of candidate non-equilibrium molecular structures, we randomly chose an energy difference (Δ ε ) for each of the 3 N –6 (or 3 N –5 in the case of a diatomic and/or linear polyatomic molecule) vibrational/normal modes in a given molecule. For the i -th vibrational/normal mode (with frequency v i ), the corresponding displacement amplitude was computed via A i = 2 Δ ε i ν i , and the corresponding displacement vector (along this mode) was obtained by multiplying the eigenvectors with A i and a randomized sign. A candidate non-equilibrium molecular structure was then obtained by simultaneously perturbing the equilibrium molecular structure along every displacement vector. Since the generation of candidate non-equilibrium molecular structures via a linear combination of normal-mode displacements assumes complete independence of the normal modes as well as the validity of the harmonic approximation, the actual Δ E corresponding to each candidate was explicitly calculated with DFTB3+MBDterm and the required Boltzmann distribution in Eq. ( 2 ) was strictly enforced. To do so, we pre-defined a histogram that accounts for 100 structures and covers a range of Δ E values from 0.0 to 4.5 × 3 2 N k B T , as shown in Fig. S1 of the Supplementary Information (SI). To generate a final set of 100 non-equilibrium molecular structures which meets the aforementioned criteria, the corresponding distribution of Δ E values had to fit this histogram. More specifically, we accepted candidate structures (with an RMSDterm >0.0075 N Å to all previously accepted structures) until all of the histogram bins were filled.
The approximately 4.2 M equilibrium and non-equilibrium structuresterm generated using these procedures form the QM7-Xterm dataset (see Table 1 ). Since we were unable to obtain a complete energy distribution (as described above) for 261 of the 7,211 molecular formulae taken from the GDB13 dataset, molecules with these molecular formulae were not included in QM7-Xterm. As such, QM7-Xterm covers 96.4% of all molecules containing up to seven heavy atoms from GDB13 (and 98.8% of the corresponding (meta-)stable stereoisomersterm), which should provide a sufficiently accurate and representative sample of the small organic molecules contained in CCSterm. We note in passing that some of the generated equilibrium structuresterm are not entirely unique, e.g ., some of the stereoisomersterm of molecules with multiple chiral centers were identical as well as some of the (rotational) conformational isomersterm; permutations of identical atoms were not initially considered when computing RMSDterm values utilizing the RMSDterm minimization tool available in ASE 49 . Therefore, approximately 4.6% of the equilibrium structuresterm constitute duplicates (see file DupMols.dat in the ZENODO repository 50 ), which were identified by an additional a posteriori approach that considered similarities between potential duplicate structures in the following six physicochemical propertiesterm: PBE0 energy, MBD energy, HOMO-LUMO gap, HOMO energy, molecular polarizability, and total dipole moment. The threshold used to check for similarity was set to 10 −3 × the corresponding unit for each property. While the presence of some duplicate equilibrium structuresterm in the QM7-Xterm dataset might influence the performance of ML models developed using this data, the non-equilibrium structuresterm associated with these duplicate equilibrium structuresterm are not identical and probe different regions of the molecular PESterm. As such, their inclusion in QM7-Xterm covers a larger swath of molecular property space, and can contribute to the development of more robust ML models for predicting the physicochemical propertiesterm in the QM7-Xterm dataset. Thus, we offer users the option to keep or exclude these duplicate equilibrium structuresterm (as well as their corresponding non-equilibrium structuresterm) in the QM7-Xterm dataset via the createDB.py script uploaded to the ZENODO repository 50 . Table 1 Content and size of the QM7-Xterm dataset. Heavy Atoms Molecules from GDB13 Stereoisomersterm Equilibrium Structuresterm Total Structures (Equilibrium + Non-Equilibrium) 1 1 1 1 101 2 2 2 2 202 3 10 10 10 1,010 4 42 45 58 5,858 5 149 193 351 35,451 6 901 1,400 3,677 371,377 7 5,845 11,627 37,438 3,781,238 Total 6,950 13,278 41,537 4,195,237 The number of molecules from GDB13, stereoisomersterm ( e.g ., enantiomers and cis-/trans- diastereomers), (meta-)stable equilibrium structuresterm (including conformational isomersterm), and the total number of equilibrium and non-equilibrium structuresterm are listed for different numbers of heavy atoms and the entire QM7-Xterm dataset.
Calculation of physicochemical propertiesterm These ≈4.2 M DFTB3+MBDterm structures were now utilized for more accurate QM single-point calculations using dispersion-inclusive hybrid DFT. Energies, forces, and several other physicochemical propertiesterm (see Table 2 ) were calculated at the PBE0+MBDterm 41 , 51 , 52 level using the FHI-aims code 53 , 54 (version 180218). For all calculations, “tight” settings were applied for basis functions and integration grids. Energies were converged to 10 −6 eV and the accuracy of the forces was set to 10 −4 eV/Å. The convergence criteria used during self-consistent field (SCF) optimizations were 10 −3 eV for the sum of eigenvalues and 10 −6 electrons/Å 3 for the charge density. Table 2 List of physicochemical propertiesterm in the QM7-Xterm dataset. # Symbol Property Unit Dimension Type Level HDF5term keys 1 Z Atomic numbers — N S — ‘atNUM’ 2 R Atomic positions (coordinates) Å 3 N S TB ‘atXYZ’ 3 Δ R RMSDterm to optimized structure Å 1 S — ‘sRMSD’ 4 I Moment of inertia tensor amu·Å 2 9 S — ‘sMIT’ 5 E tot Total PBE0+MBD energyterm·var eV 1 M,G P0M ‘ePBE0+MBD’ 6 E TB Total DFTB3+MBDterm energy eV 1 M,G TB ‘eDFTB+MBD’ 7 E at Atomization energy eV 1 M,G P0 ‘eAT’ 8 E PBE0 PBE0 energy eV 1 M,G P0 ‘ePBE0’ 9 E MBD MBD energy eV 1 M,G P0M ‘eMBD’ 10 E TS TS dispersion energy eV 1 M,G P0 ‘eTS’ 11 E nn Nuclear-nuclear repulsion energy eV 1 M,G — ‘eNN’ 12 E kin Kinetic energy eV 1 M,G P0 ‘eKIN’ 13 E ne Nuclear-electron attraction eV 1 M,G P0 ‘eNE’ 14 E coul Classical coulomb energy (el-el) eV 1 M,G P0 ‘eEE’ 15 E xc Exchange-correlation energy eV 1 M,G P0 ‘eXC’ 16 E x Exchange energy eV 1 M,G P0 ‘eX’ 17 E c Correlation energy eV 1 M,G P0 ‘eC’ 18 E xx Exact exchange energyterm·def eV 1 M,G P0 ‘eXX’ 19 E KS Sum of Kohn-Sham eigenvalues eV 1 M,G P0 ’eKSE’ 20 ε Kohn-Sham eigenvalues eV * M,G P0 ‘KSE’ 21 E HOMO HOMO energy eV 1 M,G P0 ‘eH’ 22 E LUMO LUMO energy eV 1 M,G P0 ‘eL’ 23 E gap HOMO-LUMO gap eV 1 M,G P0 ‘HLgap’ 24 D s Scalar dipole moment e· Å 1 M,G P0 ‘DIP’ 25 D Dipole moment e· Å 3 M,G P0 ‘vDIP’ 26 Q tot Total quadrupole moment e· Å 2 3 M,G P0 ‘vTQ’ 27 Q ion Ionic quadrupole moment e· Å 2 3 M,G P0 ‘vIQ’ 28 Q elec Electronic quadrupole moment e· Å 2 3 M,G P0 ‘vEQ’ 29 C 6 Molecular C 6 coefficient E h ⋅ a 0 3 1 M,R P0M ‘mC6’ 30 α s Molecular polarizability (isotropic) a 0 3 1 M,R P0M ‘mPOL’ 31 α Molecular polarizability tensor a 0 3 9 M,R P0M ‘mTPOL’ 32 F tot Total PBE0+MBDterm atomic forces eV/Å 3 N A,G P0M ‘totFOR’ 33 F PBE0 PBE0 atomic forces eV/Å 3 N A,G P0 ’pbe0FOR’ 34 F MBD MBD atomic forces eV/Å 3 N A,G P0M ‘vdwFOR’ 35 V H Hirshfeld volumes a 0 3 N A,G P0 ‘hVOL’ 36 V ratio Hirshfeld ratiosterm·def — N A,G P0 ‘hRAT’ 37 q H Hirshfeld charges e N A,G P0 ‘hCHG’ 38 D H,s Scalar Hirshfeld dipole moments e·a 0 N A,G P0 ‘hDIP’ 39 D H Hirshfeld dipole moments e·a 0 3 N A,G P0 ‘hVDIP’ 40 C ~ 6 Atomic C 6 coefficients E h ⋅ a 0 6 N A,R P0M ‘atC6’ 41 \[{\widetilde{\alpha }}_{s}\] α ~ s Atomic polarizabilities (isotropic) a 0 3 N A,R P0M ‘atPOL’ 42 R vdW vdW radii a 0 N A,R P0M ‘vdwR’ Each property is represented by a symbol (with units and dimension) and can be found in the HDF5term files using the corresponding HDF5term keys. Different property types are distinguished as follows: structural (S), molecular (M), atom-in-a-molecule (A), ground-state (G), and response (R). Different levels of theory are indicated as follows: DFTB3+MBDterm (TB), PBE0 (P0), and PBE0+MBDterm (P0M). The P0M label indicates which properties explicitly include dispersion interactions. E h and a 0 refer to the atomic units of energy (Hartree) and length (Bohr radius), respectively. *The number of Kohn-Sham eigenvalues varies for each molecule.
Here, the MBD energies, MBD atomic forces, atomic C 6 coefficients, and isotropic atomic polarizabilities were computed using the range-separated self-consistent screening (rsSCS) approach 42 , while the molecular C 6 coefficients and polarizabilities (both isotropic and tensor) were obtained via the SCS approach 41 . Hirshfeld ratiosterm·def correspond to the Hirshfeld volumes divided by the free atom volumes. The TS dispersion energy refers to the pairwise Tkatchenko-Scheffler (TS) dispersion energy in conjunction with the PBE0 functional 55 . The vdW radii were also obtained using the SCS approach via R vdW = α SCS / α TS 1 / 3 R vdW TS , where α TS and R v d W T S are the atomic polarizability and vdW radius computed according to the TS scheme, respectively. Atomization energies were obtained by subtracting the atomic PBE0 energies from the PBE0 energy of each molecular conformation (see Table S2 ). The exact exchange energyterm·def is the amount of exact (or Hartree-Fock) exchange that has been admixed into the exchange-correlation energy.
Data Records The QM7-Xterm dataset is provided in eight HDF5term based files in a ZENODO.ORG data repositoryterm 50 . One can also find there a README file with technical usage details and examples of how to access the information stored in QM7-Xterm (with and without considering duplicates, see createDB.py file).
HDF5term file format The information for each molecular structure is stored in a Python dictionaryterm (dict) type containing all relevant properties and recorded in groups in HDF5term file format. HDF5term keys to access the atomic numbers, atomic positions (coordinates), and physicochemical propertiesterm in each dictionary are provided in Table 2 . The dimension of each array depends on the number of atoms and the required property, e.g ., for a methane (CH 4 ) molecule ‘atNUM’ is a 1D array of N = 5 elements ([6, 1, 1, 1, 1]) while ‘atXYZ’ is a 2D array comprised of N = 5 rows and three columns ( x , y , z coordinates). All structures are labeled as Geom-mr-is-ct-u, where r enumerates the SMILES strings, s the stereoisomersterm (excluding conformational isomersterm), t the considered (meta-)stable conformational isomersterm, and u the optimized/displaced structures ( u = opt indicates the DFTB3+MBDterm optimized structures and u = 1, …, 100 indicates the displaced non-equilibrium structuresterm). We note in passing that the indices used in the QM7-Xterm dataset reflect the order in which a given structure was generated and do not correspond to sorted DFTB3+MBDterm (or PBE0+MBDterm) energies.
Technical Validation In contrast to many other QM-based datasets like QM7 and QM9term, which contain a single structure per molecule, the QM7-Xterm dataset not only includes constitutional/structural isomers, but also stereoisomersterm ( e.g ., enantiomers and diastereomers, including cis-/trans- and conformational isomersterm) as well as non-equilibrium structural variations thereof. While many of the considered molecules do overlap with those in the ANI-1 dataset 24 , QM7-Xterm also contains a more extensive sampling of equilibrium stereoisomersterm and a significantly different sampling of non-equilibrium structuresterm ( vide infra ). Moreover, the number of reported physicochemical propertiesterm and the employed level of electronic structure theory in QM7-Xterm is substantially more advanced compared to prior work. Therefore, the QM7-Xterm dataset contains significantly more data for flexible molecules with stereocenters than for rigid molecules without stereocenters. Since stereochemistry can play an important role in drug design, we consider that the data provided in this work will enable ML models to capture the subtle physicochemical differences existing between stereoisomersterm.
Another important target of the QM7-Xterm dataset is efficient PESterm sampling for a large number of small organic molecules. Since the most crucial regions of the PESterm are reasonably close to the relevant (meta-)stable equilibrium structuresterm, QM7-Xterm contains 100 distorted/non-equilibrium structuresterm for every such conformer. While most of these structures are in the vicinity of the optimized/equilibrium structuresterm, some correspond to more highly distorted structures on the PESterm. Since it was only computationally feasible to consider 100 non-equilibrium structuresterm at the PBE0+MBDterm level, these structures were chosen to cover as much of the PESterm surrounding each (meta-)stable equilibrium structureterm as possible. As such, we created these non-equilibrium structuresterm by displacing the atoms in a given molecule along linear combinations of normal modes. Although a similar approach was utilized during the construction of the ANI-1 dataset 24 , we have eliminated all issues related to the inaccuracy of the harmonic approximation by recomputing the energy of every candidate structure and only accepting those structures with a Boltzmann energy distributionterm (see Methods). In doing so, we ensure that the relevant regions of each PESterm are well-sampled and only a small (and pre-determined) number of high-energy non-equilibrium structuresterm are included in our dataset. The inclusion of non-equilibrium structuresterm for each (meta-)stable equilibrium structureterm also provides better coverage of the conformational space than initially provided by the equilibrium structuresterm, as seen in the pairwise distance distribution plots shown in Fig. 2 . Fig. 2 Distribution of atom-pairwise distances in the QM7-Xterm dataset. Corresponding atom-pair distance distributions for: ( a ) C-H, ( b ) C-C, ( c ) C-N, ( d ) C-O, ( e ) C-S, and ( f ) C-Cl in the QM7-Xterm dataset. For each distribution, we show the results corresponding to the equilibrium structuresterm only (black lines) as well as the entire QM7-Xterm dataset (blue lines). Contributions from non-equilibrium structuresterm are highlighted in grey.
In this work, the structure generation process was performed using DFTB3+MBDterm, while the subsequent energy, force, and property calculations were performed at the more robust PBE0+MBDterm level of theory. Since the focus of this work is the physicochemical propertiesterm of non-equilibrium structuresterm surrounding (meta-)stable equilibrium points on each PESterm, the use of these two methods does not introduce any significant complications and/or errors. Although the PBE0+MBDterm (relative) energies will not strictly follow the same Boltzmann distribution as that used to generate the molecular structures at the DFTB3+MBDterm level, these two distributions are often very similar and lead to virtually the same <Δ E> . An average over all histograms is depicted in Fig. S1 , where one can see some minor variations in the heights of the first few bins and only an insignificant amount of structures located slightly outside of the initially envisioned window of Δ E values. In addition, we have also quantitatively analyzed the structural agreement between conformers optimized at the DFTB3+MBDterm and PBE0+MBDterm levels. To do this, the DFTB3+MBD-optimized structures of 10 flexible molecules with at least five (meta-)stable conformers (see SI for more details) were randomly selected and re-optimized with PBE0+MBDterm, followed by a (harmonic) vibrational frequency analysis at the same level of theory. In doing so, it was found that all 63 so obtained PBE0+MBDterm geometries constitute local or global minima ( i.e ., with no imaginary frequencies), and the average RMSDterm between the DFTB3+MBDterm and PBE0+MBDterm structures amounts to only 0.1 Å. These structural differences are visualized for several conformers in Figs. S3 – S5 in the SI. Even for the conformer with the largest observed RMSDterm of 0.66 Å, we note that the PBE0+MBDterm structure did not move to any of the other considered conformers, and resulted from modifications to the backbone structure. From this analysis, we would argue that the DFTB3+MBD-optimized structures are in excellent agreement with those optimized at the PBE0+MBDterm level, and hence provide a high-fidelity representation of the critical points on the PBE0+MBDterm PESterm.
In QM7-Xterm, molecules made of seven heavy atoms are the most abundant with 37,438 equilibrium structuresterm (including conformational isomersterm) and 3,743,800 non-equilibrium structuresterm, followed by molecules containing six heavy atoms (see Table 1 ). C 5 H 11 NO turned out to be the most plentiful molecular formula with 3,200 (meta-)stable equilibrium structuresterm (see Table S1 ). To examine the molecular compositionterm·var of the QM7-Xterm dataset, we have performed a statistical analysis by counting the number of structures containing at least two or three different heavy (non-hydrogen) elements (see Fig. 3 ). Fig. 3 Statistical analysis of the molecular compositionterm·var of the QM7-Xterm dataset. Schematic illustrations representing the number of structures containing at least ( a ) two or ( b ) three different heavy (non-hydrogen) elements. Note that all molecules in QM7-Xterm contain C and H atoms. Triple combinations including C atoms are not shown in ( b ) since that information can be extracted from ( a ).
Here, it was found that 68.0% and 65.0% of the QM7-Xterm dataset is comprised of molecular structures which contain only [H,C,N] and [H,C,O] atoms, respectively, while structures containing [H,N,O] atoms are found in 38.7% of the dataset. As such, we consider that QM7-Xterm provides a representative sample of CCSterm formed by small [C,H,O,N]-based molecules. Regarding S-containing molecules, we still have a considerable number of structures with [H,C,S] (53,833), [H,N,S] (33,936), and [H,O,S] (32,017) combinations (even considering the 13,534 [H,N,O,S]-based molecules in Fig. 3(b) ) which might help to describe a wider swath of CCSterm. On the other hand, only 0.06% of QM7-Xterm includes Cl-containing molecules.
Over 40 different physicochemical propertiesterm were computed to describe the structure–property and property–property relationships in QM7-Xterm. In Table 2 , we showcase a number of properties obtained from the output of QM calculations performed at the PBE0+MBDterm level. This QM level of theory has proven to be accurate and reliable for describing intramolecular degrees of freedom in addition to intermolecular interactions in organic molecular dimers, supramolecular complexes, and molecular crystals 41 , 51 , 52 , 56 – 59 . We therefore consider that these calculations are suitable to validate the quality of future work using this dataset.
To provide an example of the significant information that can be obtained from QM7-Xterm, we have plotted the distribution of several physicochemical propertiesterm in Fig. 4 according to the classification scheme defined in Table 2 , i.e ., division into global (molecular) and local (atom-in-a-molecule) propertiesterm, as well as ground-state and response properties. For a cursory look at how some of these properties vary with molecular size, see Fig. S2 . Here, the influence of including non-equilibrium structuresterm on a given property is highlighted by comparing the property distributions corresponding to the equilibrium structuresterm only (black lines) with that of the entire QM7-Xterm dataset (blue lines). Overall, one can see many interesting trends in this data. Generally speaking, structural distortionsterm produce significant fluctuationsterm around the values of each property for the equilibrium structuresterm, and therefore improve the exploration and description of molecular property space. In the examples provided here, we find that global propertiesterm such as molecular polarizabilities ( α s ) and dispersion coefficients ( C 6 ) show similar distributions due to the strong correlation existing between them via the Casimir-Polder integral 60 (see Fig. 4(c,d) ). Whereas, their local analogs, i.e ., the atomic polarizabilities ( \[{\widetilde{\alpha }}_{{\rm{s}}}\] α ~ s ) and dispersion coefficients ( C ~ 6 ), display characteristic peaks corresponding to the specific local atomic environments found in the equilibrium and non-equilibrium molecular structures (see Fig. 4(g,h) ). We also find that intensive properties ( e.g ., HOMO-LUMO gaps and dipole moments) are more sensitive to structural distortionsterm as compared to extensive properties ( e.g ., atomization energies), see Fig. S2 . Accordingly, QM7-Xterm offers us the possibility to explore a great diversity of physicochemical propertiesterm and to search for unknown correlations among components of the CCSterm for small molecules. It also opens up a new route for rational design and precise control over the physicochemical propertiesterm of small drug-like organic molecules. Fig. 4 Distribution of physicochemical propertiesterm considered in the QM7-Xterm dataset. Global (molecular) properties are considered in the top panel, while local (atom-in-a-molecule) propertiesterm are considered in the bottom panel. For each case, we have selected two different examples ground-state and response properties: ( a ) atomization energy, ( b ) scalar dipole moment, ( c ) molecular polarizability (isotropic), ( d ) molecular C 6 coefficient, ( e ) Hirshfeld charges, ( f ) scalar Hirshfeld dipole moment, ( g ) atomic polarizability (isotropic), and ( h ) atomic C 6 coefficient. For each property, we show the results corresponding to the equilibrium structuresterm only (black lines) as well as the entire QM7-Xterm dataset (blue lines). Contributions from non-equilibrium structuresterm are highlighted in grey.
Regarding ML applications, we are confident that the data provided by QM7-Xterm will enable continued development of ML approaches, identification of novel QM-based molecular descriptors, as well as determination of robust training sample selectionterm·var methods that will improve the accuracy and reliability of molecular property predictions. For instance, Stöhr et al . 61 have recently employed different methods for selecting the molecular structures from QM7-Xterm to define training sets for the prediction of DFTB repulsive potentials. In this work, it was found that randomly selected training samplesterm have a better performance compared to more refined training setsterm ( e.g ., consisting of equilibrium structuresterm together with a given number ( X ) of non-equilibrium structuresterm) when developing accurate many-body repulsive potentials for the DFTB method via deep tensor neural networks. Hence, QM7-Xterm can be used to improve the accuracy of electronic structure methods using ML approaches such as Δ-learning. Further improvements of ML models may also be accomplished by considering physics-/chemistry-based approaches for selecting training samples ( e.g ., based on the local chemical environment surrounding each atom).
Supplementary information Supplementary Information