ANI-1, A data set of 20 million calculated off-equilibrium conformations for organic molecules Justin S. Smith Olexandr Isayev Adrian E. Roitberg

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 ANI-1, A data set of 20 million calculated off-equilibrium conformations for organic molecules 2017 Scientific Data 10.1038/sdata.2017.193 smith2017-ani1-dataset-organic-molecules smith2017-ani1-dataset-organic-molecules.txt, the project's staged copy de0f142af569a22f49adc5d67ed8121923a80335 cc-by chemistry

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 126 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them the ANI-1 dataset of off-equilibrium molecular conformations, DFT energies, and associated molecular descriptors how to construct and validate a large reference dataset spanning chemical and conformational space for training transferable machine-learned atomistic potentials a reusable HDF5 dataset of roughly 20 million off-equilibrium conformations for 57,462 organic molecules, generated with normal-mode sampling and DFT calculations and accompanied by a reader library existence coverage of off-equilibrium molecular energy landscapes across both chemical composition and molecular conformation simulationsimulation Random signed displacements scale normal-mode coordinates, whose superposition produces a new molecular conformation for a single-point energy calculation.normal mode displacement The data combine many molecular compositions with non-equilibrium conformations so chemical and conformational degrees of freedom are sampled together.joint chemical and conformational sampling RDKit generates hydrogen-saturated neutral singlet structures from SMILES and MMFF94 pre-optimizes them to a stationary point.three-dimensional structure preparation Only structures whose DFT geometry optimization converges are retained for the final sampling set.geometry convergence filtering Conformations whose self-consistent-field energy calculation fails to converge are omitted.single-point convergence filtering A 275 kcal/mol relative-energy cutoff separates the lower-energy ANI-1 training subset while the complete high-energy data remain available.high-energy partitioning Each molecule is exposed as a Python dictionary whose coordinates, energies, and species keys access conformer-level containers.per-molecule HDF5 organization A Python reader library supplies an interface and examples for extracting ANI-1 data.reader-library access Cubic arithmetic complexity is a bottleneck for conventional electronic-structure calculations on larger systems and longer experimental time scales. Flexible machine-learning potentials require a vast amount of high-quality reference data. Earlier QMx benchmark datasets cover equilibrium molecular configurations and therefore do not span off-equilibrium conformational degrees of freedom. The structural-optimization stage does not distinguish local minima from saddle points. The 485 starting molecules whose structural optimization failed were excluded because their configurations could not immediately be validated. Some highly elongated bonds cause self-consistent-field optimization failure, so those single-point energies are absent. Normal-mode sampling produces very high-energy conformers where the harmonic approximation fails in anharmonic regions. ANI-1 data setANI-1 data set non-equilibrium DFT total energy calculationsnon-equilibrium DFT total energy calculations machine learningmachine learning ML potentialsML potentials neural network potentialneural network potential ANI-1ANI-1 reference datareference data ab initio methodsab initio methods Kohn-Sham density-functional theoryKohn-Sham density-functional theory DFTDFT chemical spacechemical space conformational spaceconformational space configurational spaceconfigurational space GDB-11 databaseGDB-11 database SMILESSMILES RDKitRDKit MMFF94 force fieldMMFF94 force field Gaussian 09Gaussian 09 ωB97xωB97x hybrid-meta GGA functionalhybrid-meta GGA functional 6–31 G(d) basis set6–31 G(d) basis set normal mode samplingnormal mode sampling normal mode coordinatesnormal mode coordinates force constantsforce constants Bernoulli distributionBernoulli distribution single point energysingle point energy HDF5HDF5 Figshare data repositoryFigshare data repository python dictpython dict SpeciesSpecies python list of stringspython list of strings high-energy conformershigh-energy conformers atomic clashesatomic clashes low energylow energy equilibrium data setsequilibrium data sets python librarypython library fittingfitting trainingtraining QMx datasetsQMx datasets MD datasetsMD datasets benchmark datasetsbenchmark datasets QM7 datasetQM7 dataset coordinatescoordinates energiesenergies quality and quantity of data → fitted machine-learning modelsFitted models depend heavily on the quality and quantity of their training data. — the relation stated: The models depend heavily on training-data quality and quantity. O (N 3 ) complexity → capabilities to study larger systems and longer time scalesCubic computational complexity limits study of larger systems and longer relevant time scales. — the relation stated: Cubic complexity limits the tractable system size and time scale. GDB molecules → SMILES stringsGDB molecules are stored as SMILES strings representing composition and connectivity. — the relation stated: GDB molecules are serialized as SMILES strings. normal mode sampling → areas of conformational space not covered by equilibrium only dataNormal-mode sampling visits conformational regions absent from equilibrium-only data. — the relation stated: Normal-mode sampling reaches conformational regions not covered by equilibrium-only data. failed structural optimization → inclusion in the data setA structure is excluded when its geometry optimization does not converge. — the relation stated: Failed convergence excludes the structure from the dataset. single point energy calculation failed to converge → inclusion in the data setA conformation is excluded when its single-point energy does not converge. — the relation stated: Failed single-point convergence excludes the data from the dataset. HDF5 based file → Figshare data repositoryThe released HDF5 dataset file is hosted in Figshare. — the relation stated: The HDF5 file is distributed through Figshare. QM7 dataset → benchmark datasetsQM7 is described as one of the first benchmark datasets for training atomistic machine-learning potentials. — the relation stated: QM7 is one of the first benchmark datasets for atomistic ML potentials. ANI-1 as an off-equilibrium DFT reference dataset ANI-1 as a benchmark foundation for machine-learned potentials chemical-space coverage as molecular-composition diversity conformational-space coverage as variation away from energy-minimized geometry normal mode sampling as randomized displacement of optimized geometries low-energy ANI-1 as the under-275-kcal/mol partition Species as the ordered atomic-symbol list aligned to coordinates fitting as machine-learning training builds-on → QM7 and QM9 equilibrium quantum-chemistry benchmark datasetsnote: ANI-1 extends benchmark resources beyond equilibrium configurations. builds-on → the previously introduced ANI-1 neural-network potentialnote: This data descriptor releases and documents the training-data foundation underlying the prior potential. contrasts-with → equilibrium-only molecular benchmark datasetsnote: The dataset's motivating contrast is explicit. Kohn-Sham density-functional theory —same-as→ DFTthe relation itself is separately evidenced · strength of the relation: 1 · note: The abbreviation equivalence is explicit and categorical. · the relation stated: DFT is the stated short name for Kohn-Sham density-functional theory.Kohn-Sham density-functional theoryDFT fitting —same-as→ trainingthe relation itself is separately evidenced · strength of the relation: 1 · note: The source gives a categorical naming equivalence. · the relation stated: Fitting is also called training in this modeling context.fittingtraining ωB97x —is-a→ hybrid-meta GGA functionalthe relation itself is separately evidenced · strength of the relation: 1 · note: The source makes the class relation explicitly. · the relation stated: ωB97x is a hybrid-meta GGA functional.ωB97xhybrid-meta GGA functional Species —is-a→ python list of stringsthe relation itself is separately evidenced · strength of the relation: 1 · note: This is an explicit categorical representation statement. · the relation stated: The Species value is a Python list of strings.Speciespython list of strings MD datasets —contrasted-with→ QMx datasetsthe relation itself is separately evidenced · strength of the relation: 0.95 · note: In contrast to is an explicit contrast cue. · the relation stated: MD datasets are contrasted with QMx datasets by varying conformation while holding composition fixed.MD datasetsQMx datasets ANI-1 data set —contrasted-with→ equilibrium data setsthe relation itself is separately evidenced · strength of the relation: 0.95 · note: Far more than is a direct gradable comparison. · the relation stated: ANI-1 is contrasted with equilibrium datasets by its much broader angular-space coverage.ANI-1 data setequilibrium data sets atomic clashes —causes→ high-energy conformersthe relation itself is separately evidenced · strength of the relation: 0.95 · note: Caused by is an explicit positive causal cue; the nonexclusive alternative keeps weight below one. · the relation stated: Atomic clashes cause high-energy sampled conformations.atomic clasheshigh-energy conformers ANI-1 provides more than 20 million off-equilibrium conformations for 57,462 small organic molecules. ANI-1 samples chemical and conformational degrees of freedom simultaneously. ANI-1 contains roughly one hundred times as much data as QM9 and presents a harder learning task. Of 57,947 starting molecules, 485 failed structural optimization and the final dataset uses 57,462 equilibrium geometries. Applying the high-energy exclusion removed 2,630,435 structures and left 22,057,374 in the lower-energy training set. The released data include both high- and low-energy partitions despite the lower-energy cutoff used for ANI-1 potential training. Normal-mode sampling reaches conformational regions absent from an equilibrium-only dataset of the same molecules. ANI-1 covers substantially more angular space than equilibrium datasets. 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. The dataset is distributed as HDF5 through Figshare with usage documentation and examples on GitHub. training a model on reference datafitting enumerated molecules stored as SMILES strings representing molecular composition and connectivityGDB molecules a Python list of atomic-symbol strings ordered to match the first coordinate-array dimensionSpecies more than 20 M — off-equilibrium conformations in the computational DFT database 57,462 — small organic molecules represented in the released ANI-1 dataset O (N 2 ) — storage scaling of standard N-electron computational algorithms O (N 3 ) — arithmetic scaling of standard N-electron computational algorithms 166.4 billion — molecules reported in GDB-17 57,947 — starting molecules after selecting 1–8-heavy-atom C/N/O structures from GDB-11 485 (0.84% of total) — molecules failing convergence during structural optimization P =0.5 — Bernoulli probability used to sample both signs of each normal-mode displacement 275 kcal×mol −1 — relative-energy threshold for the low-energy ANI-1 training partition 2,630,435 (10.7% of the original total) — high-energy structures removed from the ANI-1 potential training set 22,057,374 — structures remaining in the lower-energy training partition 15 Ha — upper energy reported for structures in the complete sampled distribution 100x more data — ANI-1 size relative to the QM9 benchmark as characterized by the authors 0.57 kcal×mol −1 — lowest reported ANI-1-potential RMSE versus DFT relative energies on the restricted 10-heavy-atom test conformations molecular conformationmolecular conformation normal mode coordinatesnormal mode coordinates force constantsforce constants single point energysingle point energy number of heavy atomsnumber of heavy atoms coordinatescoordinates energiesenergies speciesspecies

ANI-1, 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 methods without loss of accuracy. Machine learning (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 fitting. 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. 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. We believe it will become a new standard benchmark for comparison of current and future methods in the ML potential 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 simulations 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 theory (KS-DFT or DFT for short) has become by far the most popular electronic structure method in computational physics and chemistry 1 . DFT 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 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. 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 learning (ML) 8 , 9 . The low numerical complexity and high accuracy of machine learning algorithms makes them very attractive as a pragmatic substitute for ab-initio and DFT 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 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.

The Chemical Space 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 molecules are stored as SMILES [ www.opensmiles.org ] strings representing the composition and connectivity of a molecule.

The GDB databases were fundamental in creating the QM7 dataset 18 , one of the first benchmark datasets for training atomistic ML potentials. The QM7 dataset 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 energies, dipole moments, polarizability, and excitation energies 19 . The first ML model trained on QM7 used kernel ridge regression with the Coulomb matrix representation, which predicted atomization energies 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 dataset 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 energies, enthalpies, and free energies 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 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. The C7O2H10–17 dataset includes energies from AIMD trajectories of 113 isomers of C7O2H10 (5 k frames each). All simulations used the DFT/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 simulations 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 datasets, these MD datasets explore conformational space while keeping composition fixed.

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. 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-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. More recently, Gastegger et. al. 28 , showed similar results for large organic systems that were fragmented into smaller molecules and DFT data was generated on the fly for training. This was done in an active-learning fashion where the goal is to train the potential to a specific system during an MD simulation. Shortly after, Huang and Von Lilienfeld 29 used a fragmentation scheme for training an ML model to predict energies 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 calculations for organic molecules. 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. 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. 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.

Methods

QM 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. 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 .

Molecular geometry generation

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. Hydrogen atoms are added through the RDKit cheminformatics software package [ www.rdkit.org ] to make molecular structures that are charge neutral and have a singlet electronic ground state. 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. 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 database. The goal with this scheme is to generate a ‘window’ of the potential surface around each optimized equilibrium structure.

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.

At the chosen DFT or ab-initio level of theory, geometries are optimized until energy minima convergence. Optimization is carried out using Gaussian 09’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 09 package to obtained normal mode coordinates and their associated force constants. This is accomplished using the UltraFine DFT grid option with the ωB97x density functional.

Normal mode sampling (NMS)

To carry out normal mode sampling on an energy minimized molecule of N a atoms, first a set of N f normal mode coordinates, 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 constants, 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 coordinate 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 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.

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 atoms in each molecule and K is the number of degrees of freedom of the molecule. The total energy, atomic symbols, and cartesian coordinates of the structure are stored as described in the Data Format section.

List of information and parameters used to generate the ANI-1 data set.

Data Records

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 ).

File format

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. 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. Appending ‘HE’ to the end of the coordinates and energies 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 HDF5 file format. The ‘coordinates’ key gives access to a 3D array containing each conformer of the molecule in cartesian coordinates, while the ‘energies’ key gives the 1D array of energies for the conformers. The first dimension of each ‘coordinates’ and ‘energies’ array maps correctly to the corresponding structure. The ‘species’ 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 ‘coordinates’ key. Other keys in the returned dictionary are: ‘coordinatesHE’, ‘energiesHE’, and ‘smiles’ for the high energy coordinates, high energy energies and SMILES string, respectively.

Technical Validation

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. The distribution shown in Fig. 3b visualizes the energies in the dataset, which contains structures with energies as high as 15 Ha. 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. Figure 3c shows the new distribution of energies 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 energies divided by the number of electrons from normal mode sampling conducted on each sub set (04 through 08) of GDB-11. Each distribution is scaled to have equal area. ( b ) Distribution of atomization energies from the completed data set with the inset showing a long tail reaching greater than 12 Ha. ( c ) Distribution of atomization energies after truncating any energies 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 space, 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 space not covered by equilibrium molecule normal mode sampling. 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. 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 energies. 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.

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. Figure 3a provides validation of energy sampling by showing the distribution of total energies 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 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.

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 space. 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 sampling method used to generate non-equilibrium conformations visits areas of conformational space 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 space for three body interactions. 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). 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 ωB97x density functional with the 6–31 g(d) basis set. 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 set 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 space for three body interactions. The blue background density plot shows that the ANI-1 data set better covers angle space than the equilibrium data sets (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 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.

Additional information

How to cite this article: Smith, J. S. et al. ANI-1, A data set of 20 million calculated off-equilibrium conformations for organic molecules. Sci. Data 4:170193 doi: 10.1038/sdata.2017.193 (2017).

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

Footnotes

Data Citations

References

Associated Data

Data Citations

Supplementary Materials