Justin S. SmithpersName, Olexandr IsayevpersName, Adrian E. RoitbergpersName (2017date). “ANI-1, A data set of 20 million calculated off-equilibrium conformations for organic molecules.” Scientific Datatitle·j.
Object of study — the ANI-1term dataset of off-equilibrium molecular conformationsterm·var, DFTterm energiesterm, and associated molecular descriptors
Research question — how to construct and validate a large reference dataset spanning chemical and conformational spaceterm for trainingterm transferable machine-learned atomistic potentials
Contribution — a reusable HDF5term dataset of roughly 20 million off-equilibrium conformations for 57,462 organic molecules, generated with normal-mode sampling and DFTterm calculations and accompanied by a reader library
phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | coverage of off-equilibrium molecular energy landscapes across both chemical composition and molecular conformation — “The primary concept of including non-equilibrium data is to sample regions of chemical space that would be sparsely covered in equilibrium only data sets.” | |
| claim-type | existence — “Therefore, we expect it will become a new standard benchmark of comparison for current and future methods in the machine learned potential community. More importantly, it is a sound foundation for the development of future general-purpose machine learned potentials, providing an exhaustive head start on data generation, which can be augmented with future data sets covering relevant regions of chemical space.” | |
| method — evidence | — “The ANI-1 data set presented here is built from an exhaustive sampling of a subset of the GDB-11 database containing molecules with between 1 and 8 heavy atoms and limiting the atomic species to C, N, and O. This leaves a subset of 57,947 starting molecules. All molecules are neutral and with a singlet electronic ground state. The conformation generation process is carried out in five steps starting with these 57,947 molecules.” | |
| object of study — evidence | — “In this data descriptor, we report a large dataset of non-equilibrium DFT total energy calculations for organic molecules.” | |
| research question — evidence | — “We address this need by providing access to a large computational DFT database, which consists of more than 20 M off equilibrium conformations for 57,462 small organic molecules.” | |
| contribution — evidence | — “In total, we provide access to the total energies of ~20 M molecular conformations for 57,462 molecules from the GDB database 26 , 27 , which samples both chemical and conformational degrees of freedom at the same time.” | |
| mechanism | normal mode displacement Random signed displacements scale normal-mode coordinates, whose superposition produces a new molecular conformation for a single-point energy calculation. — “The sign of R i is determined randomly from a Bernoulli distribution where P =0.5 to ensure that both sides of the harmonic potential are sampled equally. Each R i is used to scale the normalized normal mode coordinates by q i R = R i q i . Next, a new conformation of the molecule is generated by displacing the structurally optimized coordinates by Q R , the superposition of all q i R . Finally, a single point energy at the desired level of theory is calculated using the newly displaced coordinates as input.” | mechanisms[0] |
| mechanism | joint chemical and conformational sampling The data combine many molecular compositions with non-equilibrium conformations so chemical and conformational degrees of freedom are sampled together. — “In total, we provide access to the total energies of ~20 M molecular conformations for 57,462 molecules from the GDB database 26 , 27 , which samples both chemical and conformational degrees of freedom at the same time.” | mechanisms[1] |
| mechanism | three-dimensional structure preparation RDKit generates hydrogen-saturated neutral singlet structures from SMILES and MMFF94 pre-optimizes them to a stationary point. — “Smiles strings from the GDB-11 subset described above are used to generate 3D conformations using RDKit. Also with RDKit, all structures are saturated with hydrogens such that each has charge 0 and multiplicity 1. The 3D structures are then pre-optimized to a stationary point using the MMFF94 force field 38 as implemented in RDKit.” | mechanisms[2] |
| mechanism | geometry convergence filtering Only structures whose DFT geometry optimization converges are retained for the final sampling set. — “If convergence fails, the structure is not included in the data set. At this step, 485 (0.84% of total) molecules failed to converge during the structural optimization. The final data set is built from these 57,462 equilibrium geometries.” | mechanisms[3] |
| mechanism | single-point convergence filtering Conformations whose self-consistent-field energy calculation fails to converge are omitted. — “For this reason, if a structure’s single point energy calculation failed to converge, then this data is not included in the data set.” | mechanisms[4] |
| mechanism | high-energy partitioning A 275 kcal/mol relative-energy cutoff separates the lower-energy ANI-1 training subset while the complete high-energy data remain available. — “For this reason, energies greater than 275 kcal×mol −1 higher than the lowest energy conformer were not included into the training set of the ANI-1 potential. This removed 2,630,435 (10.7% of the original total) structures yielding 22,057,374 structures. Regions this high in energy are generally not considered in bio-chemical research. However, this data might be useful for some purposes. Therefore, we include both the high-energy and the low energy datasets as described in the data description section.” | mechanisms[5] |
| mechanism | per-molecule HDF5 organization Each molecule is exposed as a Python dictionary whose coordinates, energies, and species keys access conformer-level containers. — “Data is stored per molecule as described in Fig. 2 . Data for each X molecule is stored in a python dict type containing all conformer data. The keys shown in Fig. 2 : coordinates, energies, and species give access to containers of the type shown, and containing data described by the key.” | mechanisms[6] |
| mechanism | reader-library access A Python reader library supplies an interface and examples for extracting ANI-1 data. — “To ensure that all readers have easy access to the ANI-1 data set, we have developed a python library with an easy to use interface for extracting the data. Examples uses of this library are included in the ‘readers’ folder.” | mechanisms[7] |
| builds-on | QM7 and QM9 equilibrium quantum-chemistry benchmark datasets — “A common feature of all QMx datasets is that they only explore chemical degrees of freedom by providing information about energy minimized (equilibrium) molecular configurations. In these molecules, the forces of all atoms are equal to zero. Therefore, considerable efforts were undertaken to produce off-equilibrium datasets using ab initio molecular dynamics (AIMD) simulations.” | claim_relations[0] |
| builds-on | the previously introduced ANI-1 neural-network potential — “We recently introduced a neural network potential (NNP) called ANI-1, the first NNP for organic molecules shown to transfer to molecular systems well outside of its training set. As presented, the ANI-1 potential was trained on a data set, which spans both conformational and configurational space, built from small organic molecules of up to 8-heavy atoms.” | claim_relations[1] |
| contrasts-with | equilibrium-only molecular benchmark datasets — “The primary concept of including non-equilibrium data is to sample regions of chemical space that would be sparsely covered in equilibrium only data sets.” | claim_relations[2] |
| sense | ANI-1 as an off-equilibrium DFT reference dataset — “In this data descriptor, we report a large dataset of non-equilibrium DFT total energy calculations for organic molecules.” | senses[0] |
| sense | ANI-1 as a benchmark foundation for machine-learned potentials — “Therefore, we expect it will become a new standard benchmark of comparison for current and future methods in the machine learned potential community. More importantly, it is a sound foundation for the development of future general-purpose machine learned potentials, providing an exhaustive head start on data generation, which can be augmented with future data sets covering relevant regions of chemical space.” | senses[1] |
| sense | chemical-space coverage as molecular-composition diversity — “A common feature of all QMx datasets is that they only explore chemical degrees of freedom by providing information about energy minimized (equilibrium) molecular configurations.” | senses[2] |
| sense | conformational-space coverage as variation away from energy-minimized geometry — “As expected, the normal mode sampling method used to generate non-equilibrium conformations visits areas of conformational space not covered by equilibrium only data.” | senses[3] |
| sense | normal mode sampling as randomized displacement of optimized geometries — “The sign of R i is determined randomly from a Bernoulli distribution where P =0.5 to ensure that both sides of the harmonic potential are sampled equally. Each R i is used to scale the normalized normal mode coordinates by q i R = R i q i . Next, a new conformation of the molecule is generated by displacing the structurally optimized coordinates by Q R , the superposition of all q i R .” | senses[4] |
| sense | low-energy ANI-1 as the under-275-kcal/mol partition — “Figure 3b,c show the distribution of total energies minus the sum of all individual atomic energies (tabulated in Supplementary Information Table 1 ) for the full and ‘low energy’ (less than 275 kcal×mol −1 from the minimum energy) data sets, respectively.” | senses[5] |
| sense | Species as the ordered atomic-symbol list aligned to coordinates — “Species is a python list of strings containing the atomic symbol of each atom and its order corresponds correctly to dimension 1 of the coordinates numpy array.” | senses[6] |
| sense | fitting as machine-learning training — “These models are heavily dependent on the quality and quantity of data used in their fitting, also called training.” | senses[7] |
| note | QM7 and QM9 equilibrium quantum-chemistry benchmark datasets — ANI-1 extends benchmark resources beyond equilibrium configurations. — “A common feature of all QMx datasets is that they only explore chemical degrees of freedom by providing information about energy minimized (equilibrium) molecular configurations. In these molecules, the forces of all atoms are equal to zero. Therefore, considerable efforts were undertaken to produce off-equilibrium datasets using ab initio molecular dynamics (AIMD) simulations.” | claim_relations[0] |
| weight | QM7 and QM9 equilibrium quantum-chemistry benchmark datasets — 0.95 — “A common feature of all QMx datasets is that they only explore chemical degrees of freedom by providing information about energy minimized (equilibrium) molecular configurations. In these molecules, the forces of all atoms are equal to zero. Therefore, considerable efforts were undertaken to produce off-equilibrium datasets using ab initio molecular dynamics (AIMD) simulations.” | claim_relations[0] |
| note | the previously introduced ANI-1 neural-network potential — This data descriptor releases and documents the training-data foundation underlying the prior potential. — “We recently introduced a neural network potential (NNP) called ANI-1, the first NNP for organic molecules shown to transfer to molecular systems well outside of its training set. As presented, the ANI-1 potential was trained on a data set, which spans both conformational and configurational space, built from small organic molecules of up to 8-heavy atoms.” | claim_relations[1] |
| weight | the previously introduced ANI-1 neural-network potential — 0.95 — “We recently introduced a neural network potential (NNP) called ANI-1, the first NNP for organic molecules shown to transfer to molecular systems well outside of its training set. As presented, the ANI-1 potential was trained on a data set, which spans both conformational and configurational space, built from small organic molecules of up to 8-heavy atoms.” | claim_relations[1] |
| note | equilibrium-only molecular benchmark datasets — The dataset's motivating contrast is explicit. — “The primary concept of including non-equilibrium data is to sample regions of chemical space that would be sparsely covered in equilibrium only data sets.” | claim_relations[2] |
| weight | equilibrium-only molecular benchmark datasets — 0.95 — “The primary concept of including non-equilibrium data is to sample regions of chemical space that would be sparsely covered in equilibrium only data sets.” | claim_relations[2] |
| note | Kohn-Sham density-functional theory —same-as→ DFT — The abbreviation equivalence is explicit and categorical. — “Kohn-Sham density-functional theory (KS-DFT or DFT for short) has become by far the most popular electronic structure method in computational physics and chemistry 1 .” | concept_edges[0] |
| relation | Kohn-Sham density-functional theory —same-as→ DFT — DFT is the stated short name for Kohn-Sham density-functional theory. — “Kohn-Sham density-functional theory (KS-DFT or DFT for short) has become by far the most popular electronic structure method in computational physics and chemistry 1 .” | concept_edges[0] |
| note | fitting —same-as→ training — The source gives a categorical naming equivalence. — “These models are heavily dependent on the quality and quantity of data used in their fitting, also called training.” | concept_edges[1] |
| relation | fitting —same-as→ training — Fitting is also called training in this modeling context. — “These models are heavily dependent on the quality and quantity of data used in their fitting, also called training.” | concept_edges[1] |
| note | ωB97x —is-a→ hybrid-meta GGA functional — The source makes the class relation explicitly. — “ωB97x is a hybrid-meta GGA functional 30 , which has been shown to be chemically accurate compared to high-level CCSD(T) calculations 33–37 .” | concept_edges[2] |
| relation | ωB97x —is-a→ hybrid-meta GGA functional — ωB97x is a hybrid-meta GGA functional. — “ωB97x is a hybrid-meta GGA functional 30 , which has been shown to be chemically accurate compared to high-level CCSD(T) calculations 33–37 .” | concept_edges[2] |
| note | Species —is-a→ python list of strings — This is an explicit categorical representation statement. — “Species is a python list of strings containing the atomic symbol of each atom and its order corresponds correctly to dimension 1 of the coordinates numpy array.” | concept_edges[3] |
| relation | Species —is-a→ python list of strings — The Species value is a Python list of strings. — “Species is a python list of strings containing the atomic symbol of each atom and its order corresponds correctly to dimension 1 of the coordinates numpy array.” | concept_edges[3] |
| note | MD datasets —contrasted-with→ QMx datasets — In contrast to is an explicit contrast cue. — “In contrast to the QMx datasets, these MD datasets explore conformational space while keeping composition fixed.” | concept_edges[4] |
| relation | MD datasets —contrasted-with→ QMx datasets — MD datasets are contrasted with QMx datasets by varying conformation while holding composition fixed. — “In contrast to the QMx datasets, these MD datasets explore conformational space while keeping composition fixed.” | concept_edges[4] |
| weight | MD datasets —contrasted-with→ QMx datasets — 0.95 — “In contrast to the QMx datasets, these MD datasets explore conformational space while keeping composition fixed.” | concept_edges[4] |
| note | ANI-1 data set —contrasted-with→ equilibrium data sets — Far more than is a direct gradable comparison. — “The blue background density plot shows that the ANI-1 data set covers far more angular space than the equilibrium data sets (red and orange).” | concept_edges[5] |
| relation | ANI-1 data set —contrasted-with→ equilibrium data sets — ANI-1 is contrasted with equilibrium datasets by its much broader angular-space coverage. — “The blue background density plot shows that the ANI-1 data set covers far more angular space than the equilibrium data sets (red and orange).” | concept_edges[5] |
| weight | ANI-1 data set —contrasted-with→ equilibrium data sets — 0.95 — “The blue background density plot shows that the ANI-1 data set covers far more angular space than the equilibrium data sets (red and orange).” | concept_edges[5] |
| note | atomic clashes —causes→ high-energy conformers — Caused by is an explicit positive causal cue; the nonexclusive alternative keeps weight below one. — “Since normal mode sampling is used to generate the non-equilibrium structures, high-energy conformers exist in the data set. These high energy conformations occur where the harmonic approximation of normal modes fail in anharmonic regions of a potential, and are caused by atomic clashes or other highly unfavorable molecular conformations.” | concept_edges[6] |
| relation | atomic clashes —causes→ high-energy conformers — Atomic clashes cause high-energy sampled conformations. — “Since normal mode sampling is used to generate the non-equilibrium structures, high-energy conformers exist in the data set. These high energy conformations occur where the harmonic approximation of normal modes fail in anharmonic regions of a potential, and are caused by atomic clashes or other highly unfavorable molecular conformations.” — “These high energy conformations occur where the harmonic approximation of normal modes fail in anharmonic regions of a potential, and are caused by atomic clashes or other highly unfavorable molecular conformations.” | concept_edges[6] |
| weight | atomic clashes —causes→ high-energy conformers — 0.95 — “Since normal mode sampling is used to generate the non-equilibrium structures, high-energy conformers exist in the data set. These high energy conformations occur where the harmonic approximation of normal modes fail in anharmonic regions of a potential, and are caused by atomic clashes or other highly unfavorable molecular conformations.” | concept_edges[6] |
| relation | quality and quantity of data → fitted machine-learning models — The models depend heavily on training-data quality and quantity. — “However, these models are heavily dependent on the quality and quantity of data used in their fitting.” | unhoused_relations[0] |
| weight | quality and quantity of data → fitted machine-learning models — 0.95 — “However, these models are heavily dependent on the quality and quantity of data used in their fitting.” | unhoused_relations[0] |
| relation | O (N 3 ) complexity → capabilities to study larger systems and longer time scales — Cubic complexity limits the tractable system size and time scale. — “This O (N 3 ) complexity has become a critical bottleneck which limits capabilities to study larger realistic physical systems, as well as longer time scales relevant to actual experiment.” | unhoused_relations[1] |
| weight | O (N 3 ) complexity → capabilities to study larger systems and longer time scales — 0.95 — “This O (N 3 ) complexity has become a critical bottleneck which limits capabilities to study larger realistic physical systems, as well as longer time scales relevant to actual experiment.” | unhoused_relations[1] |
| relation | GDB molecules → SMILES strings — GDB molecules are serialized as SMILES strings. — “GDB molecules are stored as SMILES [ www.opensmiles.org ] strings representing the composition and connectivity of a molecule.” | unhoused_relations[2] |
| relation | normal mode sampling → areas of conformational space not covered by equilibrium only data — Normal-mode sampling reaches conformational regions not covered by equilibrium-only data. — “As expected, the normal mode sampling method used to generate non-equilibrium conformations visits areas of conformational space not covered by equilibrium only data.” | unhoused_relations[3] |
| weight | normal mode sampling → areas of conformational space not covered by equilibrium only data — 0.95 — “As expected, the normal mode sampling method used to generate non-equilibrium conformations visits areas of conformational space not covered by equilibrium only data.” | unhoused_relations[3] |
| relation | failed structural optimization → inclusion in the data set — Failed convergence excludes the structure from the dataset. — “If convergence fails, the structure is not included in the data set.” | unhoused_relations[4] |
| relation | single point energy calculation failed to converge → inclusion in the data set — Failed single-point convergence excludes the data from the dataset. — “For this reason, if a structure’s single point energy calculation failed to converge, then this data is not included in the data set.” | unhoused_relations[5] |
| relation | HDF5 based file → Figshare data repository — The HDF5 file is distributed through Figshare. — “The data set is provided in an HDF5 based file in a Figshare data repository (Data Citation 1).” | unhoused_relations[6] |
| relation | QM7 dataset → benchmark datasets — QM7 is one of the first benchmark datasets for atomistic ML potentials. — “The GDB databases were fundamental in creating the QM7 dataset 18 , one of the first benchmark datasets for training atomistic ML potentials.” | unhoused_relations[7] |
| no type for this | quality and quantity of data → fitted machine-learning models — Fitted models depend heavily on the quality and quantity of their training data. — “However, these models are heavily dependent on the quality and quantity of data used in their fitting.” | unhoused_relations[0] |
| no type for this | O (N 3 ) complexity → capabilities to study larger systems and longer time scales — Cubic computational complexity limits study of larger systems and longer relevant time scales. — “This O (N 3 ) complexity has become a critical bottleneck which limits capabilities to study larger realistic physical systems, as well as longer time scales relevant to actual experiment.” | unhoused_relations[1] |
| no type for this | GDB molecules → SMILES strings — GDB molecules are stored as SMILES strings representing composition and connectivity. — “GDB molecules are stored as SMILES [ www.opensmiles.org ] strings representing the composition and connectivity of a molecule.” | unhoused_relations[2] |
| no type for this | normal mode sampling → areas of conformational space not covered by equilibrium only data — Normal-mode sampling visits conformational regions absent from equilibrium-only data. — “As expected, the normal mode sampling method used to generate non-equilibrium conformations visits areas of conformational space not covered by equilibrium only data.” | unhoused_relations[3] |
| no type for this | failed structural optimization → inclusion in the data set — A structure is excluded when its geometry optimization does not converge. — “If convergence fails, the structure is not included in the data set.” | unhoused_relations[4] |
| no type for this | single point energy calculation failed to converge → inclusion in the data set — A conformation is excluded when its single-point energy does not converge. — “For this reason, if a structure’s single point energy calculation failed to converge, then this data is not included in the data set.” | unhoused_relations[5] |
| no type for this | HDF5 based file → Figshare data repository — The released HDF5 dataset file is hosted in Figshare. — “The data set is provided in an HDF5 based file in a Figshare data repository (Data Citation 1).” | unhoused_relations[6] |
| no type for this | QM7 dataset → benchmark datasets — QM7 is described as one of the first benchmark datasets for training atomistic machine-learning potentials. — “The GDB databases were fundamental in creating the QM7 dataset 18 , one of the first benchmark datasets for training atomistic ML potentials.” | unhoused_relations[7] |
| limitation | Cubic arithmetic complexity is a bottleneck for conventional electronic-structure calculations on larger systems and longer experimental time scales. — “This O (N 3 ) complexity has become a critical bottleneck which limits capabilities to study larger realistic physical systems, as well as longer time scales relevant to actual experiment.” | limitations[0] |
| limitation | Flexible machine-learning potentials require a vast amount of high-quality reference data. — “These models are heavily dependent on the quality and quantity of data used in their fitting, also called training. Neural networks are highly efficient and effective at modeling reference training data, due to their flexible functional form. However, this flexibility comes at a cost: a vast amount of reference data is required to properly train these models.” | limitations[1] |
| limitation | Earlier QMx benchmark datasets cover equilibrium molecular configurations and therefore do not span off-equilibrium conformational degrees of freedom. — “A common feature of all QMx datasets is that they only explore chemical degrees of freedom by providing information about energy minimized (equilibrium) molecular configurations. In these molecules, the forces of all atoms are equal to zero.” | limitations[2] |
| limitation | The structural-optimization stage does not distinguish local minima from saddle points. — “During the structural optimization phase, we do not distinguish between optimized structures that might land at a saddle point in the potential surface and those that land at some structural minima.” | limitations[3] |
| limitation | The 485 starting molecules whose structural optimization failed were excluded because their configurations could not immediately be validated. — “However, if the optimization fails to converge to a stationary point, as 485 molecules did, then these structures were not included in the training set, as the validity of their configuration could not immediately be confirmed.” | limitations[4] |
| limitation | Some highly elongated bonds cause self-consistent-field optimization failure, so those single-point energies are absent. — “For certain highly elongated bonds the molecular orbital optimization process, the self-consistent field procedure used in obtaining the total energy of the conformation, can fail to converge to a solution when two orbitals are too close in energy. For this reason, if a structure’s single point energy calculation failed to converge, then this data is not included in the data set.” | limitations[5] |
| limitation | Normal-mode sampling produces very high-energy conformers where the harmonic approximation fails in anharmonic regions. — “Since normal mode sampling is used to generate the non-equilibrium structures, high-energy conformers exist in the data set. These high energy conformations occur where the harmonic approximation of normal modes fail in anharmonic regions of a potential, and are caused by atomic clashes or other highly unfavorable molecular conformations.” | limitations[6] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | ANI-1 provides more than 20 million off-equilibrium conformations for 57,462 small organic molecules. — “We address this need by providing access to a large computational DFT database, which consists of more than 20 M off equilibrium conformations for 57,462 small organic molecules.” | content_tags.findings[0] |
| finding | ANI-1 samples chemical and conformational degrees of freedom simultaneously. — “In total, we provide access to the total energies of ~20 M molecular conformations for 57,462 molecules from the GDB database 26 , 27 , which samples both chemical and conformational degrees of freedom at the same time.” | content_tags.findings[1] |
| finding | ANI-1 contains roughly one hundred times as much data as QM9 and presents a harder learning task. — “As the accuracy of modern ML methods for molecules in equilibrium on the QM9 benchmark achieved 1 kcal×mol −1 , ANI-1 provides 100x more data and a much more challenging task to learn.” | content_tags.findings[2] |
| finding | Of 57,947 starting molecules, 485 failed structural optimization and the final dataset uses 57,462 equilibrium geometries. — “At this step, 485 (0.84% of total) molecules failed to converge during the structural optimization. The final data set is built from these 57,462 equilibrium geometries.” | content_tags.findings[3] |
| finding | Applying the high-energy exclusion removed 2,630,435 structures and left 22,057,374 in the lower-energy training set. — “For this reason, energies greater than 275 kcal×mol −1 higher than the lowest energy conformer were not included into the training set of the ANI-1 potential. This removed 2,630,435 (10.7% of the original total) structures yielding 22,057,374 structures.” | content_tags.findings[4] |
| finding | The released data include both high- and low-energy partitions despite the lower-energy cutoff used for ANI-1 potential training. — “Regions this high in energy are generally not considered in bio-chemical research. However, this data might be useful for some purposes. Therefore, we include both the high-energy and the low energy datasets as described in the data description section.” | content_tags.findings[5] |
| finding | Normal-mode sampling reaches conformational regions absent from an equilibrium-only dataset of the same molecules. — “As expected, the normal mode sampling method used to generate non-equilibrium conformations visits areas of conformational space not covered by equilibrium only data.” | content_tags.findings[6] |
| finding | ANI-1 covers substantially more angular space than equilibrium datasets. — “The blue background density plot shows that the ANI-1 data set covers far more angular space than the equilibrium data sets (red and orange).” | content_tags.findings[7] |
| finding | The prior ANI-1 neural-network potential transferred to larger systems and reached relative-energy RMSE as low as 0.57 kcal/mol on a 10-heavy-atom test set under the stated energy window. — “ANI-1 shows exceptional predictive power on the 10-heavy atom test set, with RMSE versus DFT relative energies as low as 0.57 kcal×mol −1 when only considering molecular conformations that are within 30 kcal×mol −1 of the energy minimum for each molecule.” | content_tags.findings[8] |
| finding | The dataset is distributed as HDF5 through Figshare with usage documentation and examples on GitHub. — “The data set is provided in an HDF5 based file in a Figshare data repository (Data Citation 1). A GitHub repository containing a README file with technical usage details and examples of how to access the data set is supplied online ( https://github.com/isayev/ANI1_dataset ).” | content_tags.findings[9] |
| quantity | more than 20 M — off-equilibrium conformations in the computational DFT database — “We address this need by providing access to a large computational DFT database, which consists of more than 20 M off equilibrium conformations for 57,462 small organic molecules.” | content_tags.quantities[0] |
| quantity | 57,462 — small organic molecules represented in the released ANI-1 dataset — “We address this need by providing access to a large computational DFT database, which consists of more than 20 M off equilibrium conformations for 57,462 small organic molecules.” | content_tags.quantities[1] |
| quantity | O (N 2 ) — storage scaling of standard N-electron computational algorithms — “Although DFT calculations have become affordable on modern supercomputers, we face a dilemma: standard computational algorithms representing the N electrons system require O (N 2 ) storage and O (N 3 ) arithmetic operations.” | content_tags.quantities[2] |
| quantity | O (N 3 ) — arithmetic scaling of standard N-electron computational algorithms — “Although DFT calculations have become affordable on modern supercomputers, we face a dilemma: standard computational algorithms representing the N electrons system require O (N 2 ) storage and O (N 3 ) arithmetic operations.” | content_tags.quantities[3] |
| quantity | 166.4 billion — molecules reported in GDB-17 — “Their latest GDB-17 database 17 contains 166.4 billion molecules of up to 17 atoms of C, N, O, S, and halogens.” | content_tags.quantities[4] |
| quantity | 57,947 — starting molecules after selecting 1–8-heavy-atom C/N/O structures from GDB-11 — “This leaves a subset of 57,947 starting molecules.” | content_tags.quantities[5] |
| quantity | 485 (0.84% of total) — molecules failing convergence during structural optimization — “At this step, 485 (0.84% of total) molecules failed to converge during the structural optimization.” | content_tags.quantities[6] |
| quantity | P =0.5 — Bernoulli probability used to sample both signs of each normal-mode displacement — “The sign of R i is determined randomly from a Bernoulli distribution where P =0.5 to ensure that both sides of the harmonic potential are sampled equally.” | content_tags.quantities[7] |
| quantity | 275 kcal×mol −1 — relative-energy threshold for the low-energy ANI-1 training partition — “For this reason, energies greater than 275 kcal×mol −1 higher than the lowest energy conformer were not included into the training set of the ANI-1 potential.” | content_tags.quantities[8] |
| quantity | 2,630,435 (10.7% of the original total) — high-energy structures removed from the ANI-1 potential training set — “This removed 2,630,435 (10.7% of the original total) structures yielding 22,057,374 structures.” | content_tags.quantities[9] |
| quantity | 22,057,374 — structures remaining in the lower-energy training partition — “This removed 2,630,435 (10.7% of the original total) structures yielding 22,057,374 structures.” | content_tags.quantities[10] |
| quantity | 15 Ha — upper energy reported for structures in the complete sampled distribution — “The distribution shown in Fig. 3b visualizes the energies in the dataset, which contains structures with energies as high as 15 Ha.” | content_tags.quantities[11] |
| quantity | 100x more data — ANI-1 size relative to the QM9 benchmark as characterized by the authors — “As the accuracy of modern ML methods for molecules in equilibrium on the QM9 benchmark achieved 1 kcal×mol −1 , ANI-1 provides 100x more data and a much more challenging task to learn.” | content_tags.quantities[12] |
| quantity | 0.57 kcal×mol −1 — lowest reported ANI-1-potential RMSE versus DFT relative energies on the restricted 10-heavy-atom test conformations — “ANI-1 shows exceptional predictive power on the 10-heavy atom test set, with RMSE versus DFT relative energies as low as 0.57 kcal×mol −1 when only considering molecular conformations that are within 30 kcal×mol −1 of the energy minimum for each molecule.” | content_tags.quantities[13] |
| variable | molecular conformation (geometric degree of freedom varied by normal-mode displacement) — “Next, a new conformation of the molecule is generated by displacing the structurally optimized coordinates by Q R , the superposition of all q i R .” | content_tags.variables[1] |
| variable | normal mode coordinates (directions scaled and superposed to generate off-equilibrium conformations) — “Each R i is used to scale the normalized normal mode coordinates by q i R = R i q i . Next, a new conformation of the molecule is generated by displacing the structurally optimized coordinates by Q R , the superposition of all q i R .” | content_tags.variables[2] |
| variable | force constants (mode-specific quantities used with scaled thermal energy to calculate displacements) — “Finally, for each of the 57,462 structurally optimized molecules, a normal mode calculation is performed in the Gaussian 09 package to obtained normal mode coordinates and their associated force constants.” | content_tags.variables[3] |
| variable | single point energy (DFT target value calculated for each displaced conformation) — “Finally, a single point energy at the desired level of theory is calculated using the newly displaced coordinates as input.” | content_tags.variables[4] |
| variable | number of heavy atoms (input to the empirically selected S value controlling sample count) — “N is calculated by S × K where S is an empirically chosen value (See Table 1 ) based on the number of heavy atoms in each molecule and K is the number of degrees of freedom of the molecule.” | content_tags.variables[5] |
| variable | coordinates (stored Cartesian geometry for each conformer) — “The total energy, atomic symbols, and cartesian coordinates of the structure are stored as described in the Data Format section.” | content_tags.variables[6] |
| variable | energies (stored total-energy values for molecular conformers) — “The keys shown in Fig. 2 : coordinates, energies, and species give access to containers of the type shown, and containing data described by the key.” | content_tags.variables[7] |
| variable | species (stored ordered atomic-symbol list aligned with the coordinate array) — “Species is a python list of strings containing the atomic symbol of each atom and its order corresponds correctly to dimension 1 of the coordinates numpy array.” | content_tags.variables[8] |
| definition | fitting — “These models are heavily dependent on the quality and quantity of data used in their fitting, also called training.” | content_tags.definitions[0] |
| definition | GDB molecules — “GDB molecules are stored as SMILES [ www.opensmiles.org ] strings representing the composition and connectivity of a molecule.” | content_tags.definitions[1] |
| definition | Species — “Species is a python list of strings containing the atomic symbol of each atom and its order corresponds correctly to dimension 1 of the coordinates numpy array.” | content_tags.definitions[3] |
| concept | ANI-1 data set — not defined in this paper's own words; the released off-equilibrium molecular DFT dataset — “The ANI-1 data set presented here is built from an exhaustive sampling of a subset of the GDB-11 database containing molecules with between 1 and 8 heavy atoms and limiting the atomic species to C, N, and O.” | concepts[0] |
| concept | non-equilibrium DFT total energy calculations — not defined in this paper's own words; computed energies for molecular geometries displaced away from equilibrium — “In this data descriptor, we report a large dataset of non-equilibrium DFT total energy calculations for organic molecules.” | concepts[1] |
| concept | machine learning — not defined in this paper's own words; data-driven modeling used to construct atomistic potentials — “Machine learning (ML) methods are emerging as a powerful approach to constructing various forms of transferable atomistic potentials.” | concepts[2] |
| concept | ML potentials — not defined in this paper's own words; data-fitted atomistic potential models — “Fitting highly flexible ML potentials, such as neural networks, comes at a cost: a vast amount of reference data is required to properly train these models.” | concepts[3] |
| concept | neural network potential — not defined in this paper's own words; an atomistic potential represented by a neural network — “We recently introduced a neural network potential (NNP) called ANI-1, the first NNP for organic molecules shown to transfer to molecular systems well outside of its training set.” | concepts[4] |
| concept | ANI-1 — not defined in this paper's own words; the previously introduced transferable neural-network potential — “We recently introduced a neural network potential (NNP) called ANI-1, the first NNP for organic molecules shown to transfer to molecular systems well outside of its training set.” | concepts[5] |
| concept | reference data — not defined in this paper's own words; quantum-chemical examples used to train flexible potentials — “Fitting highly flexible ML potentials, such as neural networks, comes at a cost: a vast amount of reference data is required to properly train these models.” | concepts[6] |
| concept | ab initio methods — not defined in this paper's own words; first-principles electronic-structure calculations targeted for acceleration — “One of the grand challenges in modern theoretical chemistry is designing and implementing approximations that expedite ab initio methods without loss of accuracy.” | concepts[7] |
| concept | Kohn-Sham density-functional theory — not defined in this paper's own words; the electronic-structure method abbreviated KS-DFT or DFT — “Kohn-Sham density-functional theory (KS-DFT or DFT for short) has become by far the most popular electronic structure method in computational physics and chemistry 1 .” | concepts[8] |
| concept | DFT — not defined in this paper's own words; the short name used for Kohn-Sham density-functional theory — “Kohn-Sham density-functional theory (KS-DFT or DFT for short) has become by far the most popular electronic structure method in computational physics and chemistry 1 .” | concepts[9] |
| concept | chemical space — not defined in this paper's own words; variation across molecular compositions and structures — “The primary concept of including non-equilibrium data is to sample regions of chemical space that would be sparsely covered in equilibrium only data sets.” | concepts[10] |
| concept | conformational space — not defined in this paper's own words; variation among geometries for a molecular composition — “As expected, the normal mode sampling method used to generate non-equilibrium conformations visits areas of conformational space not covered by equilibrium only data.” | concepts[11] |
| concept | configurational space — not defined in this paper's own words; variation in molecular composition spanned by the ANI-1 training data — “As presented, the ANI-1 potential was trained on a data set, which spans both conformational and configurational space, built from small organic molecules of up to 8-heavy atoms.” | concepts[12] |
| concept | GDB-11 database — not defined in this paper's own words; the enumerated molecule database from which ANI-1 starting structures are selected — “The GDB-11 database 26 , 27 provides an exhaustive search of stable and chemically viable molecules, supplied in the SMILES [ www.opensmiles.org ] string format, containing C, N, O, and F atoms with up to 11 of these ‘heavy’ atoms.” | concepts[13] |
| concept | SMILES — not defined in this paper's own words; string representation of molecular composition and connectivity — “GDB molecules are stored as SMILES [ www.opensmiles.org ] strings representing the composition and connectivity of a molecule.” | concepts[14] |
| concept | RDKit — not defined in this paper's own words; cheminformatics software used to generate and prepare three-dimensional structures — “Smiles strings from the GDB-11 subset described above are used to generate 3D conformations using RDKit.” | concepts[15] |
| concept | MMFF94 force field — not defined in this paper's own words; the force field used to pre-optimize generated structures — “The 3D structures are then pre-optimized to a stationary point using the MMFF94 force field 38 as implemented in RDKit.” | concepts[16] |
| concept | Gaussian 09 — not defined in this paper's own words; the electronic-structure package used for geometry, normal-mode, and energy calculations — “All electronic structure calculations are carried out with the ωB97x (ref. 30 ) density functional and the 6–31 G(d) basis set 31 in the Gaussian 09 (ref. 32 ) electronic structure package.” | concepts[17] |
| concept | ωB97x — not defined in this paper's own words; the hybrid-meta GGA density functional used in the dataset calculations — “ωB97x is a hybrid-meta GGA functional 30 , which has been shown to be chemically accurate compared to high-level CCSD(T) calculations 33–37 .” | concepts[18] |
| concept | hybrid-meta GGA functional — not defined in this paper's own words; the density-functional class assigned to ωB97x — “ωB97x is a hybrid-meta GGA functional 30 , which has been shown to be chemically accurate compared to high-level CCSD(T) calculations 33–37 .” | concepts[19] |
| concept | 6–31 G(d) basis set — not defined in this paper's own words; the orbital basis used for ANI-1 electronic-structure calculations — “All electronic structure calculations are carried out with the ωB97x (ref. 30 ) density functional and the 6–31 G(d) basis set 31 in the Gaussian 09 (ref. 32 ) electronic structure package.” | concepts[20] |
| concept | normal mode sampling — not defined in this paper's own words; generation of non-equilibrium conformations by random displacement along normal modes — “As expected, the normal mode sampling method used to generate non-equilibrium conformations visits areas of conformational space not covered by equilibrium only data.” | concepts[21] |
| concept | normal mode coordinates — not defined in this paper's own words; vibrational coordinate directions scaled to displace equilibrium geometries — “Each R i is used to scale the normalized normal mode coordinates by q i R = R i q i .” | concepts[22] |
| concept | force constants — not defined in this paper's own words; mode-associated stiffness values produced by the normal-mode calculation — “Finally, for each of the 57,462 structurally optimized molecules, a normal mode calculation is performed in the Gaussian 09 package to obtained normal mode coordinates and their associated force constants.” | concepts[23] |
| concept | Bernoulli distribution — not defined in this paper's own words; the random distribution determining normal-mode displacement sign — “The sign of R i is determined randomly from a Bernoulli distribution where P =0.5 to ensure that both sides of the harmonic potential are sampled equally.” | concepts[24] |
| concept | single point energy — not defined in this paper's own words; the energy computed for a displaced conformation without geometry relaxation — “Finally, a single point energy at the desired level of theory is calculated using the newly displaced coordinates as input.” | concepts[25] |
| concept | HDF5 — not defined in this paper's own words; the file container used to distribute the dataset — “The data set is provided in an HDF5 based file in a Figshare data repository (Data Citation 1).” | concepts[26] |
| concept | Figshare data repository — not defined in this paper's own words; the repository hosting the HDF5 data file — “The data set is provided in an HDF5 based file in a Figshare data repository (Data Citation 1).” | concepts[27] |
| concept | python dict — not defined in this paper's own words; the per-molecule access structure containing conformer data — “Data for each X molecule is stored in a python dict type containing all conformer data.” | concepts[28] |
| concept | Species — not defined in this paper's own words; the per-molecule ordered list of atomic symbols — “Species is a python list of strings containing the atomic symbol of each atom and its order corresponds correctly to dimension 1 of the coordinates numpy array.” | concepts[29] |
| concept | python list of strings — not defined in this paper's own words; the data structure used for the Species field — “Species is a python list of strings containing the atomic symbol of each atom and its order corresponds correctly to dimension 1 of the coordinates numpy array.” | concepts[30] |
| concept | high-energy conformers — not defined in this paper's own words; sampled geometries in anharmonic, clashing, or otherwise unfavorable regions — “Since normal mode sampling is used to generate the non-equilibrium structures, high-energy conformers exist in the data set. These high energy conformations occur where the harmonic approximation of normal modes fail in anharmonic regions of a potential, and are caused by atomic clashes or other highly unfavorable molecular conformations.” | concepts[31] |
| concept | atomic clashes — not defined in this paper's own words; one stated source of high-energy sampled conformations — “These high energy conformations occur where the harmonic approximation of normal modes fail in anharmonic regions of a potential, and are caused by atomic clashes or other highly unfavorable molecular conformations.” | concepts[32] |
| concept | low energy — not defined in this paper's own words; less than 275 kcal/mol above the conformer minimum — “Figure 3b,c show the distribution of total energies minus the sum of all individual atomic energies (tabulated in Supplementary Information Table 1 ) for the full and ‘low energy’ (less than 275 kcal×mol −1 from the minimum energy) data sets, respectively.” | concepts[33] |
| concept | equilibrium data sets — not defined in this paper's own words; comparison datasets containing energy-minimized conformations — “The blue background density plot shows that the ANI-1 data set covers far more angular space than the equilibrium data sets (red and orange).” | concepts[34] |
| concept | python library — not defined in this paper's own words; the supplied programmatic interface for extracting ANI-1 data — “To ensure that all readers have easy access to the ANI-1 data set, we have developed a python library with an easy to use interface for extracting the data.” | concepts[35] |
| concept | fitting — not defined in this paper's own words; the process also called training a machine-learning model — “These models are heavily dependent on the quality and quantity of data used in their fitting, also called training.” | concepts[36] |
| concept | training — not defined in this paper's own words; the alternate name given for model fitting — “These models are heavily dependent on the quality and quantity of data used in their fitting, also called training.” | concepts[37] |
| concept | QMx datasets — not defined in this paper's own words; equilibrium quantum-chemistry benchmark datasets discussed as prior resources — “A common feature of all QMx datasets is that they only explore chemical degrees of freedom by providing information about energy minimized (equilibrium) molecular configurations.” | concepts[38] |
| concept | MD datasets — not defined in this paper's own words; ab-initio molecular-dynamics datasets varying conformation at fixed composition — “In contrast to the QMx datasets, these MD datasets explore conformational space while keeping composition fixed.” | concepts[39] |
| concept | benchmark datasets — not defined in this paper's own words; reference collections used to train and compare atomistic ML potentials — “The GDB databases were fundamental in creating the QM7 dataset 18 , one of the first benchmark datasets for training atomistic ML potentials.” | concepts[40] |
| concept | QM7 dataset — not defined in this paper's own words; an early equilibrium benchmark derived from GDB-13 — “The GDB databases were fundamental in creating the QM7 dataset 18 , one of the first benchmark datasets for training atomistic ML potentials.” | concepts[41] |
| concept | coordinates — not defined in this paper's own words; stored Cartesian positions for conformer atoms — “The total energy, atomic symbols, and cartesian coordinates of the structure are stored as described in the Data Format section.” | concepts[42] |
| concept | energies — not defined in this paper's own words; stored DFT total energies for conformers — “The keys shown in Fig. 2 : coordinates, energies, and species give access to containers of the type shown, and containing data described by the key.” | concepts[43] |
Full text — tagged
ANI-1term, A data set of 20 million calculated off-equilibrium conformations for organic molecules Abstract One of the grand challenges in modern theoretical chemistry is designing and implementing approximations that expedite ab initio methodsterm without loss of accuracy. Machine learningterm (ML) methods are emerging as a powerful approach to constructing various forms of transferable atomistic potentials. They have been successfully applied in a variety of applications in chemistry, biology, catalysis, and solid-state physics. However, these models are heavily dependent on the quality and quantity of data used in their fittingterm. Fittingterm highly flexible ML potentialsterm, such as neural networks, comes at a cost: a vast amount of reference dataterm is required to properly train these models. We address this need by providing access to a large computational DFTterm database, which consists of more than 20 M off equilibrium conformations for 57,462 small organic molecules. We believe it will become a new standard benchmark for comparison of current and future methods in the ML potentialterm community.
Subject terms: Method development, Combinatorial libraries, Computational chemistry, Density functional theory Background & Summary Accurate descriptions of atomic and intermolecular interactions are a cornerstone of reliable computer simulationsterm·mth in biophysics, chemistry, and materials science. For the past 50 years we have seen tremendous progress in the development of theoretical methods and software tools aiming to describe more complex systems and allow for longer time scales. Kohn-Sham density-functional theoryterm (KS-DFT or DFTterm for short) has become by far the most popular electronic structure method in computational physics and chemistry 1 . DFTterm has found applications in many systems in organic chemistry 2 , 3 , biology 4 , catalysis 3 , 5 and solid state chemistry 6 , 7 . It is also frequently combined with molecular dynamics (AIMD) and classical force fields (quantum mechanics-molecular mechanics (QM-MM)) to describe chemical reactions in extended systems.
Although DFTterm calculations have become affordable on modern supercomputers, we face a dilemma: standard computational algorithms representing the N electrons system require O (N 2 ) storage and O (N 3 ) arithmetic operations. This O (N 3 ) complexity has become a critical bottleneck which limits capabilities to study larger realistic physical systems, as well as longer time scales relevant to actual experiment. Consequently, a lot of progress has been made in the development of atomistic potentials using machine learningterm (ML) 8 , 9 . The low numerical complexity and high accuracy of machine learningterm algorithms makes them very attractive as a pragmatic substitute for ab-initio and DFTterm methods. Thanks to their remarkable ability to find complex relationships among data, in many cases these ‘machine learned’ models out-perform more physically sound approximations (like force fields) and methods while also reducing the computational time required for a given application 9–15 . These models are heavily dependent on the quality and quantity of data used in their fittingterm, also called trainingterm. Neural networks are highly efficient and effective at modeling reference trainingterm data, due to their flexible functional form. However, this flexibility comes at a cost: a vast amount of reference dataterm is required to properly train these models.
The Chemical Spaceterm Project 16 computationally enumerated all possible organic molecules up to a certain size, resulting in the creation of the GDB databases. Their latest GDB-17 database 17 contains 166.4 billion molecules of up to 17 atoms of C, N, O, S, and halogens. All molecules follow the valency rules and are filtered for unstable substructures, non-synthesizable and strained topologies. GDB moleculesterm·def are stored as SMILESterm [ www.opensmiles.org ] strings representing the composition and connectivity of a molecule.
The GDB databases were fundamental in creating the QM7 datasetterm 18 , one of the first benchmark datasetsterm for trainingterm atomistic ML potentialsterm. The QM7 datasetterm consists of 7,165 energy minimized (equilibrium) molecules calculated with the PBE0 functional. All structures are a small subset of GDB-13 (older GDB database of nearly 1 billion organic molecules) composed of molecules with up to 7 heavy atoms C, N, O, and S. Later, QM7 was extended to include 13 additional properties, like frontier molecular orbital energiesterm, dipole moments, polarizability, and excitation energiesterm 19 . The first ML model trained on QM7 used kernel ridge regression with the Coulomb matrix representation, which predicted atomization energiesterm with a mean absolute error (MAE) of 9.9 kcal×mol −1 . This error was quickly reduced to 3.3 kcal×mol −1 (ref. 20 ) and eventually was under 1 kcal×mol −1 (ref. 21 ).
QM9, is perhaps the most well-known benchmark datasetterm 17 , 22 . It consists of 133,885 equilibrium organic molecules containing up to nine heavy atoms (CONF) from the GDB-17 database. In addition to energy minima it reports corresponding harmonic frequencies, dipole moments, polarizabilities, along with energiesterm, enthalpies, and free energiesterm of atomization. All properties were calculated at the B3LYP/6–31 G(2df,p) level of quantum chemistry. A subset of 6,095 constitutional isomers in QM9 corresponding to a brutto formula C7H10O2 was also calculated at the more accurate G4MP2 level of theory. Various molecular representations and ML methods were benchmarked against the QM9 dataset 20 , 21 , 23 , 24 . See also a recent survey of methods 23 . Later, a Message Passing Neural Network (MPNN) 10 achieved chemical accuracy in 11 out of 13 target properties in the QM9 dataset. Finally, the hierarchical interacting particle neural network (HIP-NN) 15 model of Lubbers et. al . achieved state-of-the-art accuracy of just 0.26 kcal×mol −1 MAE on total energy prediction.
A common feature of all QMx datasetsterm is that they only explore chemical degrees of freedom by providing information about energy minimized (equilibrium) molecular configurations. In these molecules, the forces of all atoms are equal to zero. Therefore, considerable efforts were undertaken to produce off-equilibrium datasets using ab initio molecular dynamics (AIMD) simulationsterm·mth. The C7O2H10–17 dataset includes energiesterm from AIMD trajectories of 113 isomers of C7O2H10 (5 k frames each). All simulationsterm·mth used the DFTterm/PBE level of theory and were carried out at 500 K. Very recently Schutt et al. 21 and Chmiela et al. 25 released MD17 dataset, a collection of eight AIMD/PBE+vdW-TS simulationsterm·mth for small organic molecules. Each of these consist of an MD trajectory for a single molecule extending from ~100 K to 900 K frames. In contrast to the QMx datasetsterm, these MD datasetsterm explore conformational spaceterm while keeping composition fixed.
We recently introduced a neural network potentialterm (NNP) called ANI-1term, the first NNP for organic molecules shown to transfer to molecular systems well outside of its trainingterm set. As presented, the ANI-1term potential was trained on a data set, which spans both conformational and configurational spaceterm, built from small organic molecules of up to 8-heavy atoms. We show its applicability to much larger systems, up to 50 atoms, including well known drug molecules and a random selection of molecules from the GDB-11 (refs 26 , 27 ) database with 10-heavy atoms. ANI-1term shows exceptional predictive power on the 10-heavy atom test set, with RMSE versus DFTterm relative energiesterm as low as 0.57 kcal×mol −1 when only considering molecular conformationsterm·var that are within 30 kcal×mol −1 of the energy minimum for each molecule. More recently, Gastegger et. al. 28 , showed similar results for large organic systems that were fragmented into smaller molecules and DFTterm data was generated on the fly for trainingterm. This was done in an active-learning fashion where the goal is to train the potential to a specific system during an MD simulationterm·mth. Shortly after, Huang and Von Lilienfeld 29 used a fragmentation scheme for trainingterm an ML model to predict energiesterm of large rigid drug molecules. Both studies back up the argument that information about the physics of large systems can be learned from data sets of small molecules.
In this data descriptor, we report a large dataset of non-equilibrium DFT total energy calculationsterm for organic molecules. In total, we provide access to the total energiesterm of ~20 M molecular conformationsterm·var for 57,462 molecules from the GDB database 26 , 27 , which samples both chemical and conformational degrees of freedom at the same time. As the accuracy of modern ML methods for molecules in equilibrium on the QM9 benchmark achieved 1 kcal×mol −1 , ANI-1term provides 100x more data and a much more challenging task to learn. Therefore, we expect it will become a new standard benchmark of comparison for current and future methods in the machine learned potential community. More importantly, it is a sound foundation for the development of future general-purpose machine learned potentials, providing an exhaustive head start on data generation, which can be augmented with future data sets covering relevant regions of chemical spaceterm.
Methods QM calculations All electronic structure calculations are carried out with the ωB97xterm (ref. 30 ) density functional and the 6–31 G(d) basis setterm 31 in the Gaussian 09term (ref. 32 ) electronic structure package. ωB97xterm is a hybrid-meta GGA functionalterm 30 , which has been shown to be chemically accurate compared to high-level CCSD(T) calculations 33–37 .
Molecular geometry generation The GDB-11 databaseterm 26 , 27 provides an exhaustive search of stable and chemically viable molecules, supplied in the SMILESterm [ www.opensmiles.org ] string format, containing C, N, O, and F atoms with up to 11 of these ‘heavy’ atoms. Hydrogen atoms are added through the RDKitterm cheminformatics software package [ www.rdkitterm.org ] to make molecular structures that are charge neutral and have a singlet electronic ground state. The ANI-1 data setterm presented here is built from an exhaustive sampling of a subset of the GDB-11 databaseterm containing molecules with between 1 and 8 heavy atoms and limiting the atomic speciesterm to C, N, and O. This leaves a subset of 57,947 starting molecules. All molecules are neutral and with a singlet electronic ground state. The conformation generation process is carried out in five steps starting with these 57,947 molecules. The steps are listed below and qualitatively depicted in Fig. 1 .
Schematic representation of data generation. Scheme for generating non-equilibrium conformations of 57,462 molecules from the GDB-11 databaseterm. The goal with this scheme is to generate a ‘window’ of the potential surface around each optimized equilibrium structure.
Smilesterm strings from the GDB-11 subset described above are used to generate 3D conformations using RDKitterm. Also with RDKitterm, all structures are saturated with hydrogens such that each has charge 0 and multiplicity 1. The 3D structures are then pre-optimized to a stationary point using the MMFF94 force fieldterm 38 as implemented in RDKitterm.
At the chosen DFTterm or ab-initio level of theory, geometries are optimized until energy minima convergence. Optimization is carried out using Gaussian 09term’s default method and convergence criteria. Obtained geometries correspond to the first stationary point reached on the potential surface and correspond to some local minima or in a rare case to a saddle point. If convergence fails, the structure is not included in the data set. At this step, 485 (0.84% of total) molecules failed to converge during the structural optimization. The final data set is built from these 57,462 equilibrium geometries. Finally, for each of the 57,462 structurally optimized molecules, a normal mode calculation is performed in the Gaussian 09term package to obtained normal mode coordinatesterm and their associated force constantsterm. This is accomplished using the UltraFine DFTterm grid option with the ωB97xterm density functional.
Normal mode samplingterm (NMS) To carry out normal mode samplingterm on an energy minimized molecule of N a atoms, first a set of N f normal mode coordinatesterm, Q = { q 1 , q 2 , q 3 , … q N f } , is computed at the desired ab-initio level of theory, where N f =3 N a −5 for linear molecules and N f =3 N a −6 for all others. The corresponding force constantsterm, K = { K 1 , K 2 , K 3 , ⋯ , K N f } , are obtained alongside Q . Then a set of N f uniformly distributed pseudo-random numbers, c i , are generated such that ∑ i N f c i is in the range [0,1]. Next, a displacement, R i , for each normal mode coordinateterm is computed by setting a harmonic potential equal to the c i scaled average energy of the system of particles at some temperature, T. Solving for the displacement gives, where k b is Boltzmann’s constant. The sign of R i is determined randomly from a Bernoulli distributionterm where P =0.5 to ensure that both sides of the harmonic potential are sampled equally. Each R i is used to scale the normalized normal mode coordinatesterm by q i R = R i q i . Next, a new conformation of the molecule is generated by displacing the structurally optimized coordinatesterm by Q R , the superposition of all q i R . Finally, a single point energyterm at the desired level of theory is calculated using the newly displaced coordinatesterm as input.
N data points (new conformations) are generated, representing a window of the potential surface. N is calculated by S × K where S is an empirically chosen value (See Table 1 ) based on the number of heavy atomsterm·var in each molecule and K is the number of degrees of freedom of the molecule. The total energy, atomic symbols, and cartesian coordinatesterm of the structure are stored as described in the Data Format section.
List of information and parameters used to generate the ANI-1 data setterm.
Data Records The data set is provided in an HDF5term based file in a Figshare data repositoryterm (Data Citation 1). A GitHub repository containing a README file with technical usage details and examples of how to access the data set is supplied online ( https://github.com/isayevpersName/ANI1term_dataset ).
File format Data is stored per molecule as described in Fig. 2 . Data for each X molecule is stored in a python dictterm type containing all conformer data. The keys shown in Fig. 2 : coordinatesterm, energiesterm, and speciesterm give access to containers of the type shown, and containing data described by the key. Speciesterm is a python list of stringsterm containing the atomic symbol of each atom and its order corresponds correctly to dimension 1 of the coordinatesterm numpy array. Appending ‘HE’ to the end of the coordinatesterm and energiesterm keys will yield high energy structures as described in the technical validation section.
Data Structure. Description of the containers stored in the dictionary returned by iterating through molecules stored in the HDF5term file format. The ‘coordinatesterm’ key gives access to a 3D array containing each conformer of the molecule in cartesian coordinatesterm, while the ‘energiesterm’ key gives the 1D array of energiesterm for the conformers. The first dimension of each ‘coordinatesterm’ and ‘energiesterm’ array maps correctly to the corresponding structure. The ‘speciesterm’ key contains the atomic symbol of the atoms and is ordered to correspond to the correct atoms in the second dimension of the array returned by the ‘coordinatesterm’ key. Other keys in the returned dictionary are: ‘coordinatesHE’, ‘energiesHE’, and ‘smilesterm’ for the high energy coordinatesterm, high energy energiesterm and SMILESterm string, respectively.
Technical Validation Since normal mode samplingterm is used to generate the non-equilibrium structures, high-energy conformersterm exist in the data set. These high energy conformations occur where the harmonic approximation of normal modes fail in anharmonic regions of a potential, and are caused by atomic clashesterm or other highly unfavorable molecular conformationsterm·var. The distribution shown in Fig. 3b visualizes the energiesterm in the dataset, which contains structures with energiesterm as high as 15 Ha. For this reason, energiesterm greater than 275 kcal×mol −1 higher than the lowest energy conformer were not included into the trainingterm set of the ANI-1term potential. This removed 2,630,435 (10.7% of the original total) structures yielding 22,057,374 structures. Regions this high in energy are generally not considered in bio-chemical research. However, this data might be useful for some purposes. Therefore, we include both the high-energy and the low energyterm datasets as described in the data description section. Figure 3c shows the new distribution of energiesterm which are never larger than 0 Ha in total energy minus the sum of atomic contributions to the total energy.
Dataset energy distribution. ( a ) The distribution of total energiesterm divided by the number of electrons from normal mode samplingterm conducted on each sub set (04 through 08) of GDB-11. Each distribution is scaled to have equal area. ( b ) Distribution of atomization energiesterm from the completed data set with the inset showing a long tail reaching greater than 12 Ha. ( c ) Distribution of atomization energiesterm after truncating any energiesterm over 275 kcal×mol −1 from each molecule’s minimum energy.
During the structural optimization phase, we do not distinguish between optimized structures that might land at a saddle point in the potential surface and those that land at some structural minima. Given the goal of sampling conformational spaceterm, the fact that some structures might land at off equilibrium geometries (saddle points) could in fact help in using this data to fit potential surfaces, as it will help to cover regions of conformational spaceterm not covered by equilibrium molecule normal mode samplingterm. However, if the optimization fails to converge to a stationary point, as 485 molecules did, then these structures were not included in the trainingterm set, as the validity of their configuration could not immediately be confirmed. However, given the vast number of structures in the data set, it is likely any interaction found in these 485 molecules can be found elsewhere in the data set.
A similar process of not including information for unconverged calculations is used in the generation of the total energiesterm. For certain highly elongated bonds the molecular orbital optimization process, the self-consistent field procedure used in obtaining the total energy of the conformation, can fail to converge to a solution when two orbitals are too close in energy. For this reason, if a structure’s single point energyterm calculation failed to converge, then this data is not included in the data set.
The primary concept of including non-equilibrium data is to sample regions of chemical spaceterm that would be sparsely covered in equilibrium only data sets. Figure 3a provides validation of energy sampling by showing the distribution of total energiesterm divided by the total number of electrons for each molecule in the GDB subsets from 4 to 8-heavy atoms. Figure 3b,c show the distribution of total energiesterm minus the sum of all individual atomic energiesterm (tabulated in Supplementary Information Table 1 ) for the full and ‘low energyterm’ (less than 275 kcal×mol −1 from the minimum energy) data sets, respectively.
Further validation of the of non-equilibrium sampling is to show the data set covers a large domain of the chemical degrees of freedom in conformational spaceterm. Figure 4 contains five panels representing the distribution of atomic distances in the resulting non-equilibrium data set (blue line) compared with a data set of equilibrium only conformations (red) of the same molecule. As expected, the normal mode samplingterm method used to generate non-equilibrium conformations visits areas of conformational spaceterm not covered by equilibrium only data. A similar plot, Supplementary Information Fig. 1 shows distance distributions for the remaining atomic pairs. Figure 5 shows distributions involving the angles in the data sets, and tell a similar story in terms of coverage in conformational spaceterm for three body interactions. The blue background density plot shows that the ANI-1 data setterm covers far more angular space than the equilibrium data setsterm (red and orange). The remaining plots are included in the Supplementary Information Figs 2–4 .
Distance distribution for dataset. Distribution of atomic distances in the subset of the data set constructed from the molecules containing between 4 and 8 heavy atoms (GDB-04 to 08) of C, N, and O. The y-axis is the base 10 logarithm of the count of distances in each bin, normalized over the full domain so that the two sets can be compared. The x-axis represents the atomic distance (r) divided by the single bond equilibrium distance ( r 0 ) for the smallest possible molecule containing a single bond of the type shown, as calculated using the ωB97xterm density functional with the 6–31 g(d) basis setterm. The red histogram shows the full distribution of distances for a data set containing only equilibrium distances. The blue line shows the distribution of our non-equilibrium data set, with distances randomly sub sampled at a rate of 1%. As the figure shows, even 1% of the non-equilibrium data set covers vast areas of atomic distance space where the equilibrium data setterm fails to sample.
Angular distribution. Figure shows distributions involving the angles in the data sets, and tells a similar story in terms of coverage in conformational spaceterm for three body interactions. The blue background density plot shows that the ANI-1 data setterm better covers angle space than the equilibrium data setsterm (red and orange). The remaining figures for the angular distributions are included in the Supplementary Information .
Usage Notes To ensure that all readers have easy access to the ANI-1 data setterm, we have developed a python libraryterm with an easy to use interface for extracting the data. Examples uses of this library are included in the ‘readers’ folder.
Additional information How to cite this article: SmithpersName, J. S. et al. ANI-1term, A data set of 20 million calculated off-equilibrium conformations for organic molecules. Sci. Data 4:170193 doi: 10.1038/sdata.2017.193 (2017).
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Supplementary Material Acknowledgments J.S.S. acknowledges the University of Florida for funding through the Graduate School Fellowship (GSF). A.E.R. thanks NIH award GM110077. O.I. acknowledges support from DOD-ONR (N00014-16-1-2311) and Eshelman Institute for Innovation award. Part of this research was performed while O.I. was visiting the Institute for Pure and Applied Mathematics (IPAM), which is supported by the National Science Foundation (NSF). The authors acknowledge Extreme Science and Engineering Discovery Environment (XSEDE) award DMR110088, which is supported by National Science Foundation grant number ACI-1053575. We gratefully acknowledge the support of the U.S. Department of Energy through the LANL/LDRD Program for this work. We also acknowledge Nicholas Lubbers and Roman Zubatyuk for stimulating discussions and technical help with data organization.
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