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Figure shows the XRD peak of only (111) Au NPs for two different triturations (3X and 6X). For higher trituration (i.e., 6X), we observe a higher angle shift with a line broadening as compared to 3X trituration. The shift of the XRD pattern reveals the presence of strain (~4%) in the materials. The origin of the strain is due to the mechanical grinding during trituration. Here, we have used the Debye Scherrer equation for calculating the crystalline size of the samples .
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The 3X and 6X triturated sample shows a crystalline size of ~2.6 and 2.4 nm respectively. The reduction in crystalline size is due to continuous mechanical grinding of metallic Gold in the presence of covalently bonded sugar of milk crystals. The mechanical grinding results in lattice strain, and after critical stress, the Au particles fracture and form nano sized crystalline materials.
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It is important to note that, as per previous observations, NPs are found in higher dilution medicine samples, but the origin of nanoparticle formation is not reported so far. Based on the current observation, we can clearly see that the nanocrystalline Au NPs are formed during the trituration process itself. This highlights a unique observation that the initial preparation (starting material) for the high homeopathic dilution is very much different from the other conventional medicinal preparation, which was never noticed so far, leading to erroneous conclusions.
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Figure shows a schematic diagram of a glass bottle containing the homeopathic potency. The spectra of the solution have been taken from two different portions of the glass bottle (upper and lower part), as shown in Figure . Figure shows the variation of UV-Vis absorption spectra of the top and bottom part solution with different potencies. The presence of three absorption-band is observed for all samples. To know the exact positions of the bands, we have plotted the second derivative of a spectrum as a function of wavelength (Figure ). The occurrence of absorption band at ~557 nm and ~721 nm due to the presence of anisotropic structure of different sized Au nanoparticles with localized surface plasmon resonance (LSPR). Additionally, it also shows that the shape and absorption intensity of the spectra change with potencies. At higher potency (i.e., concentration-10 6 to 10 17 times dilution), a broad absorption band has been observed, and it gradually became narrow/sharp after 24C. Similar variation has been observed for both the upper and lower part of the potencies.
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From the fitting, we have observed that three major peaks are present. The first peak, at ~456 nm, is associated with silica NPs. The peak is absent in samples processed in plastic bottles; the details are described in supporting information (Figure ). The other two peaks originate due to the localized surface plasmon resonance (SPR) of Au NPs. The narrowing of the absorption peaks in the absorption spectra (Figure C. the ratio of Au/sugar increases as an effect of homeopathic potentization.
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The succussion process was studied in detail using optical measurements. The UV-vis absorption spectra have been taken in different successions for different potencies. A representative spectrum of 200C potency after different succussions is shown in Figure ; other spectra are shown in supporting information (Figure ). Figure shows an enlarged view of the first absorption band (~210-260 nm), denoted as I. This peak is due to the presence of carbon sources (C=C, C=O groups) in the solution. The peak intensity increases with the increase of succussion. Figure (II) presents the second absorption band, as denoted II, originating from the aromatic π-system. This band also shows similar nature as the succussion number increases, peak intensity increases. During the succussion process, the carbon layers disintegrate and lead to an increase in carbonyl groups. In
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Quantitative measurement of particles present in the different potencies is performed using DLS, as shown in Figure -D. To measure particle size, we have taken the solution in two different parts of the glass bottle (top and bottom part), as described earlier. Most of the particles are in size in the upper portion of the bottle (~200-600 nm) (Figure ). However, mostly large size (~6µm) particles are found (Figure ). The distribution of particle size decreases (size range of particles present) as the potency increases. It is important to note that the bulk particle size measurement (large sample volume) using DLS clearly shows the non-uniform size distribution of particles in the solution (top and bottom part). Hence, during the potentization process, we take the solution from the top part, i.e., smaller particles. Hence, potentization results in solutions with smaller particles, which improves the effectiveness of the medicine on human health. We have measured the particle size in different successions, as shown in Figure (upper and lower parts of the bottle). Interestingly, we have seen that in the upper part of the bottle, the average size of the particles decreases with an increase of successions number. Hence, more active nanoparticles are exposed to the surface. However, in the lower part, the size of the particle increases with succession during potentization. This result indicates an increase in the air-bubble formation and a mixture of nanoparticles with bubbles.
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Zeta potential is also an essential parameter for knowing the stability of colloidal systems. It also helps to quantify the surface charge of the particle. Here, the zeta potential of all samples has been measured using the Zeta analyzer measurement system, as shown in Figure . The plot of zeta potential as a function of potency shows a change of the value from negative to positive, which means the nature of the solutions is very unstable. Such experimental values suggest the un-
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The above discussions are further supported using the TEM study, as shown in Figure . Here, two different potencies (low and high) are used to understand the morphology (size, shape etc.) and chemical composition of the particles. Figure shows the TEM and high-resolution TEM (HRTEM) images of a low potency sample with different size distribution. It is observed that Au NPs are embedded in the carbon layer. Figure shows that the Au NPs are distributed on the carbon layer. The carbon layer is formed from the sugar of milk (sucrose, glucose, fructose etc.).
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The HRTEM image of Au NPs, shown in Figure , confirms the well crystalline nature of the nanoparticles. However, in the case of higher potency, well-separated monodispersed Au nanoparticles are observed, as shown in Figure . Figure -F shows a single particle of Au coated with a carbon layer. Interestingly, here we have not observed any large carbon layer.
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confirmed the reactive edge of the Au NPs. We have schematically presented the TEM observation in Figures and. It is observed that a carbon layer of sugar milk is formed at low potency, and the Au NPs are embedded in the carbon layer. However, when diluted the solution, the carbon layer may disintegrate and form a carbon coating on every nanoparticle. Additionally, at very high potency, the surface of the particles is more active, and this active surface reacts with humans. We have taken the Raman spectra of different diluted samples to confirm our assumption, and obtained results are well-matched with the TEM results. As shown in Figure , the Raman vibrations are well-matched with previously reported data. It is found that several Raman peaks have appeared related to sucrose, lactose, and glucose, which strongly supports the TEM results.
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Here, we have mixed the gold piece with the milk of sugar for the preparation of powder. The gold plate has been mechanically grinded very well by adding milk of sugar. After mechanical grinding, we got an Au particle and sugar (lactose) combination powder. XRD measurement confirms the presence of Au (~2.6 nm crystallite size). Also, we observe a shift due to repeated mechanical grinding when we were mixing Au particles and sugar powder. After that, we mix this mixed powder with Dispensing Alcohol. We have prepared solutions in different proportions and gradually decreased the concentrations, such as 6C, 7C up to 200C. The absorption characteristics of Au NPs are getting more prominent as the ratio of sugar and Au particles is gradually decreasing.
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The higher potentization removes the sugar layer and exposes Au NPs. With the repeated successions in the solution, the layer of sugar moves away from the top of the NPs, and the surface of the NPs is coming out. The more surface of these NPs comes out, the more quickly it will react with human health and increase its medicinal effect. At low dilution, there is a significant carbon sheet/layer and Au NPs embedding on it. However, in the case of high dilution, we observed that instead of this sheet/layer, each particle is wrapped in a sheet. Also, we have observed that the surface of the nanoparticle is more reactive. Therefore, this reactive surface of each particle can easily attach to the human organ and quickly cure diseases. Raman analysis shows that the D band and G band of carbon have been created, and their intensity has changed with dilution. Therefore, we can say that when we do more and more dilution, the properties of nanoparticles become more prominent and the less the dominance of lactose. Simultaneously, when we shake it repeatedly, the layer of sugar is removed from the surface of the NPs, and the NPs are exposed; thus, the nanoparticles are more capable of working in human health. Tindal effect shows the particles in the solutions, and the number of these particles increases with shaking. The reason for the increase in particle size is that we can see that more and more water bubbles are forming as we go. This is why homeopathic medicines need to be shaken repeatedly before taking them to make them more effective. We may conclude that higher potencies of Aurum Met expressing the dynamic action in the presence of Nanoparticles. In the drag-delivery system, the agglomeration and clustering of nanoparticles have a wide range of applications. In homeopathy medicine, these agglomeration and clustering have an enormous effect due to the presence of nanoparticles. In higher dilution, the nanoparticle surface energy, particle-particle interaction, ionic strength, uniform distribution etc. determine the effectiveness in several applications. Therefore, we believe that this work provided a new pathway for future applications in the drug delivery system.
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in a machine-readable database format with the Jupyter notebook example for analysis. Looking forward, we discuss the challenges associated with the rapid growth of quantum chemical data sets and databases, emphasizing the need for updatable and accessible resources to ensure the long-term utility of them. We also address the importance of data format standardization and the ongoing efforts to align with the FAIR principles to enhance data interoperability and reusability. Drawing inspiration from established materials databases, we advocate for the development of user-friendly and sustainable platforms for these data sets and databases.
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Accurate and efficient prediction of molecular properties is a cornerstone of computational chemistry. While quantum mechanical (QM) calculations provide unparalleled precision, their computational cost often limits their application to large-scale systems. To bridge this gap, machine learning (ML) potentials have emerged as promising alternatives, capable of predicting molecular properties with reasonable accuracy and remarkable efficiency.
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Central to the development of robust ML potentials is the availability of high-quality training data. Quantum chemical data sets and databases serve as the foundation for these models, providing essential information on molecular structures, energies, forces, and other properties. The breadth and depth of these data sets and databases directly influence the ability of ML models to learn complex chemical phenomena and generalize to new systems. Furthermore, accessible and well-curated data sets and databases are essential for reproducibility and benchmarking in the field.
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Given the plethora of ML potentials and their growing importance in computational chemistry, this review aims to provide an overview of the current landscape of molecular quantum chemical data sets and databases. We explore the key characteristics and functionalities of prominent resources, examining the type of information they store (e.g., molecular structures, various properties), the level of electronic structure theory employed (e.g., density functional theory (DFT), second-order Møller-Plesset perturbation theory (MP2)), the size and diversity of the chemical space they cover, and the methodologies used for data creation. While the possible selection of the data sets an databases is very broad, we mostly focus on the data collections which were specifically designed with the goal of developing and evaluating ML potentials of molecules or have a potential to be used for such applications. Data sets for both ground and excited state potentials are included and many data sets also contain properties that go beyond energies and forces. We also included data collections that provide the sets of 3D nuclear geometries and energies which are frequently used in the context of structure-property relations such as QM9 data set but in principle can be used to train ML potentials and, indeed, QM9 is sometimes used to benchmark ML potentials . Surely, there are more data sets generated in the plenitude of studies involving MLPs, which either served to highlight the particular strengths and shortcomings of a new methodology such as a new active learning protocol or were a "by-product" of investigating an interesting chemical phenomenon. Although these data collections are undoubtedly very useful, we have to exclude them to limit the scope of our current overview. Here were we aim to focus on the data sets generated wit as little as possible involvement of ML potentials to have a collection less biased to a particular ML potential. This is admittedly hard to avoid as, e.g., ANI-1x data set was generated using techniques such as normal mode sampling but the final composition was obtained via pool-based active learning with the ANI-type universal potential.
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With these limitations in mind, we introduce an updatable online resource designed to track the emerging data sets and databases, ensuring researchers have access to the latest and most relevant data (). This GitHub repository allows other researchers to make updates by creating pull requests or issues and it is less limited than the current overview because, e.g., the researchers can add data collections generated with active learning. In addition, for easier navigation through the data resources, we collect them in the JSON database format and provide Jupyter notebooks with examples to, e.g., convert it to the common spreadsheet formats or create the tables like Table in this Review.
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This review also highlights several key challenges in the field, including ensuring the long-term accessibility of data sets, maintaining updatable resources, and advancing data format standardization in line with the FAIR principles. By identifying these challenges, we aim to guide researchers toward the most effective use of available resources and best practices for future developments.
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QM9 data set is one of the widely used data sets, a collection of molecular structures and properties for 134,000 small organic molecules. QM9 targets neutral organic molecules containing up to nine non-hydrogen atoms (C, N, O, and F). This selection corresponds to the GDB-9 subset of the larger GDB-17 database. While ensuring a manageable size, it captures a significant portion of organic chemical space. Notably, the data set incorporates relevant biomolecules like amino acids (glycine, alanine) and nucleobases (cytosine, uracil, thymine), alongside pharmaceutically important building blocks (pyruvic acid, piperazine, hydroxyurea). Among the 134,000 molecules, 621 distinct chemical formulas (stoichiometries) are present, with C 7 H 10 O 2 being the most abundant, containing 6,095 constitutional isomers.
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Computational Methodology: QM9 focuses on organic molecules with selection process opting for neutral molecules and excluding cations and anions. While, zwitterions are kept due to their importance in biomolecules like amino acids, heavier halogens (sulfur, bromine, chlorine, iodine) are excluded from the selection. Initial 3D structures were generated using SMILES strings followed by geometry optimization using computational methods (pre-optimization at PM7 semi-empirical level with MOPAC software and final optimization at B3LYP/6-31G(2df,p) with the Gaussian 09 software ). Stringent convergence criteria were employed to guarantee high-quality structures. Following geometry optimization, the B3LYP/6-31G(2df,p) level was employed to calculate various properties for each molecule. Notably, for 6,095 constitutional isomers of C 7 H 10 O 2 , a more accurate method G4MP2 was employed for energetics calculations.
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The QM9-G4MP2 database is built upon the existing QM9 data set by providing highly accurate G4MP2 (Gaussian-4 theory using reduced order perturbation ) calculations for the molecular structures within QM9. The G4MP2 approach employed in this database comprises the calculations with a series of methods including DFT, Hartree-Fock (HF), Møller-Plesset perturbation theory (MP2), and coupled-cluster single and double excitations with perturbative triple correction (CCSD(T)).
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Computational Methodology: To generate the QM9-G4MP2 data set, the geometries of all QM9 molecules underwent reoptimization using the B3LYP/6-31G(2df,p) level theory, followed by single-point energy calculations employing CCSD(T,FC)/6-31G(d), MP2(FC)/G3MP2largeXP, RHF/modaug-cc-pVTZ, and RHF/mod-aug-cc-pVQZ methods. These calculations were executed using the Gaussian 16 package (version A.03) utilized in the original QM9. Additionally, to derive accurate atomization energies, G4MP2 calculations were performed for individual atoms of H, C, N, O, and F, maintaining identical charge and spin multiplicity as those within the QM9 molecules. Note that these calculations were conducted in varying computational environments and with Gaussian 16 instead of Gaussian 09 employed in QM9.
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The MultiXC-QM9 data set significantly expands upon the well-established QM9 data set for studying small molecules. While QM9 focuses on a single functional (B3LYP) and basis set, MultiXC-QM9 offers a richer resource, encompassing 76 different DFT functionals alongside three basis sets and a complementary semi-empirical method (GFN2-xTB). Beyond molecular energies, MultiXC-QM9 provides energies for all possible monomolecular interconversions (A↔B type) within the QM9 data set, calculated using the same methodology as the molecular energies. Additionally, the data set includes information on bond changes associated with these 162 million reactions.
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This multifaceted nature makes MultiXC-QM9 useful for delta learning, transfer learning and multitask learning. The presence of data from both high and low fidelity methods enables models to learn the relationships between these methods and improve prediction accuracy. Computational Methodology: The MultiXC-QM9 data set was constructed using xyz molecular geometries obtained from the QM9-G4MP2 data set . Molecular energies were computed using the ADF package, which implements various post-self-consistent field (SCF) methods for different functionals. Specifically, the PBE functional was employed for generalized gradient approximation (GGA) level energy calculations, with SZ, DZP, and TZP basis sets; these calculations were performed for 133k molecules. Additionally, single-point energies were computed using the GFN2-xTB semi-empirical method.
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In the calculation of reaction energies, all possible "A↔B type" isodesmic reactions were identified among the QM9 molecules, and their corresponding indices were saved in a separate CSV file named "reactions.csv". Subsequently, the energy changes associated with each reaction were computed using the same level of theory as for the energy calculations of individual molecules and stored in additional CSV files.
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Data Accessibility: The MultiXC-QM9 data set is available on Figshare platform at and provides information on both molecules and reactions in separate files. Energy calculations for molecules are provided in CSV and SQLite formats. CSV format contains energies from various DFT and semi-empirical methods, SMILES strings derived from xyz files, and chemical formulas for each molecule. The SQLite format stores xyz coordinates, energies, and other relevant properties derived automatically by atomistic simulation environment. Reaction data is provided in CSV format which includes reaction energies, indices of reactants and products, and SMILES strings for both reactants and products.
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Computational Methodology: The data set is the revision of the QM9 data set with the properties of ca. 130k equilibrium geometries (with up to 9 nonhydrogen atoms) calculated at a more accurate aPBE0 level with the cc-pVTZ basis set. PySCF 2.4.0 was used to perform simulations, while the adaptive parameters were supplied to it by a machine learning model trained on so that aPBE targets the CCSD(T)/cc-pVTZ atomization energies. The code to make predictions with aPBE0 is available on GitHub. The properties calculated at aPBE/cc-pVTZ include total and atomization energies, orbital energies, dipole moments, and density matrices.
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Computational Methodology: Initial 44k structures (CHNO only) are extracted from QM9 with up to 9 atoms and single-point calculations are performed at B3LYP/6-31G(2df,p) level of theory with Gaussian 16. Atomic properties are generated using AIMAll package. Data Accessibility: The dataset is publicly available at Zenodo . More than 30 atomic properties including energy, dipole moment, quadrupole moment and population are provided as well as molecular properties stored in Gaussian output files. 3.6 QM7-X QM7-X is a comprehensive data set of 4.2 million structures of small organic molecules containing up to seven non-hydrogen atoms (C, N, O, S, C). It includes a systematic sampling of all stable equilibrium structures (constitutional/structural isomers and stereoisomers) and explores 100 non-equilibrium structures for each molecule. Each structure in QM7-X is accompanied by a rich set of 42 properties, meticulously calculated using PBE0+MBD level theory. These properties range from fundamental aspects like atomization energies and dipole moments to response characteristics like polarizability and dispersion coefficients.
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Computational Methodology: To generate QM7-X data set, researchers first used the GDB13 database to identify all possible structures (constitutional/structural isomers and stereoisomers) for molecules with up to seven non-hydrogen atoms. Using SMILES strings, initial 3D structures were obtained using MMFF94 force field followed by conformational isomer search using Confab to generate various conformers for each molecule. All structures were re-optimized at DFTB3+MBD level theory. The lowestenergy structure was selected as the first conformer, and additional structures with RMSD (root mean square deviation) larger than 1.0 Å from existing conformers were included.
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In the case of non-equilibrium structures, 100 non-equilibrium structures were created for each equilibrium structure. It was accomplished by displacing the equilibrium structures along linear combinations of normal mode coordinates computed at the DFTB3+MBD level within the harmonic approximation. It was ensured that the generated structures follow a Boltzmann distribution with a specific average energy difference from the corresponding equilibrium structure.
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This process resulted in about 4.2 million equilibrium and non-equilibrium structures forming the QM7-X data set. Physicochemical properties were calculated on the generated structures using PBE0+MBD level of theory with the FHI-aims code. Tight settings were used for basis functions and integration grids. Various properties were calculated including energies, forces, atomic charges, dipole moments, polarizabilities, and more.
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Curated from the much larger GDB-13 database containing nearly 1 billion molecules, QM7 focuses on a subset of 7,165 small organic molecules. These molecules contain up to 23 atoms, with a maximum of 7 being "heavy atoms" -C, N, O, and S. The remaining positions are filled with hydrogen atoms. The data set provides Coulumb matrices, atomization energies, atomic charge and the Cartesian coordinate of each atom in the molecules.
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Computational Methodology: The researchers selected a subset of 7,165 molecules from GDB-13 with atomization energies ranging from -800 to -2000 kcal/mol. This subset encompasses molecules with features like double and triple bonds, cycles, and various functional groups including carboxy, cyanide, amide, alcohol, and epoxy groups. In addition, only constitutional isomers (molecules with different chemical bond arrangements) were included and conformational isomers were excluded. For calculations, researchers first used Open Babel software to generate 3D structures for each molecule from the subset. Next, they employed DFT calculations with PBE functional/tier2 basis set implemented in the FHI-aims code to calculate the atomization energy for each molecule with high accuracy.
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The QM7b data set is a collection of information on over 7211 small organic molecules containing up to seven different elements: C, Cl, H, N, O, and S. It serves as an extension of the QM7 data set specifically designed for multitask learning applications in chemistry. Each molecule is described by 14 properties, including atomization energy, static polarizability, frontier orbital eigenvalues (HOMO and LUMO) and excitation energies.
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Computational Methodology: The creation of QM7b data set starts from the selection of 7211 small organic molecules from GDB-13 database. Initial molecular geometries were generated from SMILES strings using the Universal Force Field (UFF) within the Open Babel software. Subsequent geometry optimization was performed using the PBE approximation to Kohn-Sham DFT within the FHI-aims code. For molecular electronic properties, the PBE0 DFT was employed to calculate atomization energies and frontier orbital eigenvalues for each molecule. The ZINDO approach was used to determine properties like electron affinity, ionization potential, excitation energies, and maximal absorption intensity. The GW approximation was utilized to evaluate the frontier orbital eigenvalues. For static polarizability calculations, both self-consistent screening (SCS) and PBE0 were used. Software-wise, FHIaims was used for SCS, PBE0, and GW calculations, while ORCA code handled ZINDO/s calculations.
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The QM8 data set, introduced by Ramakrishnan et al. , comprises electronic spectra data for approximately 21,786 small organic molecules. It is a carefully curated subset derived from the larger QM9 data set, which includes 134,000 molecules. QM8 offers information on electronic spectra, specifically at the level of time-dependent DFT(TD-DFT) and second-order approximate Coupled Cluster (CC2), presenting the lowest two singlet transition energies and their corresponding oscillator strengths.
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Computational Methodology: QM8 originates from the QM9 data set, containing 134,000 molecules with up to nine heavy atoms. Initially, molecules with high steric strain in their initial geometries, computed using the B3LYP/6-31G(2df,p) method, were eliminated. Subsequently, the data set was narrowed down to molecules containing a maximum of eight heavy atoms (carbon, nitrogen, oxygen, and sulfur), resulting in approximately 21,800 molecules. The geometries for these molecules were assumed to be relaxed, as per the original QM9 data set. Single-point calculations were performed with the TURBO-MOLE program to determine ground (S 0 ) and the lowest two singlet excited states (S 1 and S 2 ). The used methods include long-range corrected TD-DFT (LR-TDDFT) with PBE0 and CAM-B3LYP functionals, and different basis sets (def2-SVP and def2-TZVP), as well as the resolutionof-identity approximate coupled cluster with singles and doubles substitution (RI-CC2) method with the def2-TZVP basis set. A total of 14 "exotic" molecules were excluded due to convergence issues (7 molecules) or negative lowest transition energy, potentially attributed to orbital relaxation.
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To ensure the reliability of molecular geometries, a structured three-stage optimization process was employed. Initial geometries were generated from SMILES strings using the MMFF94 force field, followed by HF optimization with the STO-3G basis set. The final relaxation step utilized B3LYP/6-31G(2df,p) to achieve accurate equilibrium geometries. Additional methods, such as meta-Lowdin population analysis, were employed to compute atomic charges, ensuring the transferability of these values across different molecular environments.
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Data Accessibility: The Alchemy data set is available at . 3.11 QM1B QM1B, introduced by Mathiasen et al. , is a colossal data set comprising one billion training examples tailored for ML applications in quantum chemistry. It encompasses molecules featuring 9-11 heavy atoms and includes properties such as energy and HOMO-LUMO gap.
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Computational Methodology: The creation of the QM1B data set commenced with 1.09 million SMILES strings sourced from the GDB-11 database, focusing on molecules with 9-11 heavy atoms. Subsequently, hydrogen atoms were added to these molecules using RDKit. Each molecule underwent the generation of up to 1000 conformers employing the ETKDG algorithm within RDKit. This process yielded a total of 305.8 million, 568.7 million, and 205.4 million conformers for molecules with 9, 10, and 11 heavy atoms, respectively. Utilizing PySCF IPU , HOMO-LUMO energies were computed for the resulting one billion conformers. Notably, a trade-off was made between data set size and data quality (DFT accuracy) to achieve the extensive data set size. Consequently, the DFT calculations (B3LYP/STO-3G) employed in QM1B may exhibit less accuracy compared to other data sets such as QM9 and PC9.
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Data Accessibility: The QM1B data set is accessible on the GitHub platform at . However, it is important to highlight that QM1B is released solely for research purposes, and caution is advised for applications necessitating high accuracy. The creators encourage further exploration into the implications of reduced DFT accuracy in downstream tasks.
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The SPICE data set , an acronym for Small-molecule/Protein Interaction Chemical Energies, focuses on the energetic interplay between drug-like small molecules and proteins. It is an essential resource for training models that can accurately predict forces and energies across a diverse array of molecules and conformations commonly encountered in drug discovery simulations.
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The initial version of SPICE featured over 1.1 million molecular conformations, covering a wide chemical space that included drug molecules, dipeptides, and solvated amino acids. It encompassed 15 different elements, spanned both charged and uncharged states, and included a range of high and low energy conformations, capturing a broad spectrum of covalent and non-covalent interactions.
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The updated version enhances this data set by adding over 20,000 new molecules, improving the sampling of non-covalent interactions, and including a new subset of PubChem molecules containing boron and silicon, which were not present in the initial version. Additionally, several calculations from version 1 have been corrected and incorporated into this latest release. Computational Methodology: In the computation of energies and gradients (forces) for each conformation within the SPICE data set, Psi4 serves as the primary tool. The calculations employ DFT with the ωB97M-D3(BJ) functional and the def2-TZVPPD basis set . Beyond forces and energies, SPICE also encompasses additional properties such as dipole and quadrupole moments, atomic charges, and bond orders.
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The PubChemQC database is a valuable asset for computational chemistry research, especially in material development, drug design, and ML applications. It contains electronic structures for a vast number of molecules, including approximately 3 million molecules optimized using DFT at the B3LYP/6-31G* level in ground states and over 2 million molecules with low-lying excited states calculated via TD-DFT at B3LYP/6-31+G*.
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Computational Methodology: The construction of the PubChemQC database involved several essential steps. Firstly, data acquisition was carried out by downloading public structure data files (SDFs) from the PubChem Project FTP site,[102] each containing information like InChI, SMILES representations, and molecular weight for around 25,000 molecules. Data preprocessing followed, retaining only relevant data (CID, InChI, and weight) for the database and excluding molecules with missing CIDs, unsuitable structures (molecules with η 5 bonds, ionic salts, water mixtures etc.) or isotopic variations. All molecules were considered neutral.
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The next phase involved geometry optimization. Initial 3D structures were generated from InChI data using Open Babel and underwent a series of optimizations. This included an initial optimization with the PM3 method, further optimization with the HF method (STO-6G basis set), and final optimization with the B3LYP functional (VWN3) and 6-31G* basis set. Subsequently, excited state calculations were performed using optimized geometries and Time-Dependent DFT (TDDFT) with the B3LYP functional and 6-31+G* basis set.
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The PubChemQC PM6 data sets, stands as one of the most extensive compilations in its domain, encompassing PM6 data for a staggering 221 million molecules. These data sets are based on PubChem Compounds database,[102] and provide optimized geometries, electronic structures, and other pivotal molecular properties. The data sets incorporate not only neutral states of molecules but also consider cationic, anionic, and spin-flipped states.
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Computational Methodology: The construction of the PubChemQC PM6 data sets commenced with the comprehensive retrieval and parsing of the entire PubChem Compound database. Subsequently, key molecule attributes such as weight, InChI, SMILES, and formula were extracted, with exclusion criteria set for molecules exceeding 1000 g/mol in weight. Leveraging Open Babel, initial 3D structures were generated from SMILES encodings. Gaussian 09 software facilitated PM6 geometry optimization for each molecule, with subsequent calculations extending to cationic, anionic, and spin-flipped states. Rigorous validation ensured the fidelity of optimized InChI compared to the original counterparts.
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The PubChemQC B3LYP/6-31G*//PM6 data set is a massive resource for researchers in chemistry, materials science, and drug discovery. It offers electronic properties for an astonishing 85,938,443 molecules (nearly 86 million), encompassing a broad spectrum of essential compounds and biomolecules with molecular weights up to 1000. This data set represents a significant portion (94%) of the PubChem Compound catalog as of August 29, 2016. For researchers with specific needs, the data is further divided into five subcollections. These subsets focus on molecules containing particular elements (like CHON) and have molecular weight limitations (under 300 or 500).
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Computational Methodology: As a first step in the workflow of data generation, molecules were extracted from the PubChemQC PM6 database, ensuring a diverse set of known molecules. Open Babel software was used to generate input files compatible with the GAMESS quantum chemistry program for the target molecules. For most elements, electronic properties were computed using B3LYP functional with the 6-31G* basis set. For heavier elements, specific basis sets were employed, and effective core potentials were applied for certain metals. These calculations yielded various properties, including orbital energies, dipole moments, and more.
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Data Accessibility: The PubChemQC B3LYP/6-31G*//PM6 data set is freely available for download at under a Creative Commons license. Researchers can access the data in three formats: GAMESS program input/output files, selected JSON output files and PostgreSQL database. This diverse range of formats allows researchers to choose the option that best suits their specific needs and computational tools.
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Computational Methodology: To ensure compatibility with QM9, PC9 is restricted to molecules containing a maximum of 9 "heavy atoms" (excluding H) from the elements H, C, N, O, and F. After imposing the heavy atom limit, PC9 undergoes a process to eliminate duplicates stemming from factors like enantiomers, tautomers, isotopes, and potential artifacts within the PubChem database, which could result in identical-looking molecules. Consequently, PC9 ends up with 99,234 distinct molecules. This subset is divided into two groups: one consisting of molecules shared with QM9 (18,357 compounds) and the other comprising molecules unique to PubChemQC (80,877 compounds). Unlike QM9, which is confined to closed-shell neutral compounds, PC9 includes molecules with multiplicities exceeding 1. Furthermore, due to variations in calculation methods, PC9 only provides the total energies without zero-point vibrational energies, unlike QM9 which provides much broader coverage of different energies.
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The bigQM7ω data set is a valuable resource for researchers focused on developing ML models to predict electronic spectra of molecules. This data set includes ground-state properties and electronic spectra for over 12,880 molecules, offering a broader range of structures compared to previous data sets like QM7 and QM9. Notably, bigQM7ω emphasizes electronic excitations and provides data across various theoretical levels.
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Computational Methodology: The creation of bigQM7ω involved a detailed, multi-step process. Initially, SMILES strings for all molecules were extracted from the GDB-11 data set. These SMILES strings were then converted into initial structures using the UFF. Geometry optimization was performed using a three-tier connectivity preserving geometry optimizations (ConnGO) workflow, ensuring structurally sound geometries and mitigating rearrangement issues during high-throughput calculations. Tight convergence criteria and basis sets def2-SVP and def2-TZVP were employed for ωB97X-D DFT optimizations. For excited state calculations, various methods were used: ZINDO calculations were performed at PM6 minimum energy geometries, and TDDFT calculations were carried out with 3-21G, def2-SVP, def2-TZVP, and def2-SVPD basis sets. Harmonic frequency analysis confirmed local minima for optimized geometries. Three molecules failing the ConnGO connectivity test were excluded due to a substructure prone to dissociation. All calculations were executed using the Gaussian suite of programs.
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Data Accessibility: The bigQM7ω data set offers multiple access points to facilitate exploration and utilization by researchers. The core data, encompassing structures, ground state properties, and electronic spectra, is conveniently available for download at . For deeper analysis, the NOMAD repository at provides the input and output files from the corresponding calculations. Additionally, a data-mining platform is available at .
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The QMugs (Quantum-Mechanical Properties of Drug-like Molecules) data set provides a rich resource for researchers in drug discovery and computational chemistry. This collection curates over 665,000 molecules relevant to biology and pharmacology, extracted from the ChEMBL database. Notably, QMugs incorporates QM properties computed using a combination of methods, specifically leveraging both semi-empirical and DFT approaches.
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Computational Methodology: The construction of the QMugs data set involved a multi-step process designed to capture a comprehensive picture of druglike molecules at both the structural and QM level. The first step focused on data extraction and SMILES processing where molecules were selected from ChEMBL database based on specific criteria, including having welldefined single-protein targets and associated activity information. This ensures the molecules hold potential relevance for drug discovery. Following extraction, the data underwent a series of cleaning steps. Molecules were neutralized to remove charged states, and extraneous components like salts and solvents were eliminated. Additionally, outlier removal techniques filtered out fragments, molecules with extreme atom counts (outside the range of 3-100 heavy atoms), and those with unaddressed radical species or persistent net charges.
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The second step addressed conformer generation and optimization where researchers employed a semi-empirical method called GFN2-xTB to generate three conformations for each drug-like molecule. Further refinement was achieved through minimization using a force field and meta-dynamics simulations. Finally, the conformations were clustered, and the lowest-energy structure from each cluster was chosen for further calculations. This approach ensured the inclusion of representative conformers for each molecule while maintaining computational efficiency.
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The final step involved higher-level quantum chemical calculations. The optimized geometries obtained in the previous step served as the basis for single-point electronic structure calculations. Here, the researchers employed DFT with the ωB97X-D functional and def2-SVP basis set calculating a wider range of properties compared to the semi-empirical method used for conformer generation. The calculated properties include formation energies, dipole moments, and crucially, wave functions.
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The data set is hosted on the ETH Library Collection service and can be downloaded at . The data is provided in multiple formats: (1) A summary.csv file containing computed molecular properties and annotations; (2) compressed tarball files containing molecule structures (SDFs) with embedded properties, grouped by ChEMBL identifiers and (3) separate compressed tarball files for vibrational spectra and wave function data.
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The OrbNet Denali dataset is a comprehensive training collection used to develop OrbNet Denali, a ML-enhanced semiempirical method for electronic structure calculations. It includes over 2.3 million molecular geometries with corresponding energy labels calculated at the DFT and semi-empirical levels. Based on ChEMBL27 database, it covers a wide range of organic molecules, including various protonation states, tautomers, non-covalent interactions, and common salts. The dataset features key elements (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, I) essential to biological and organic systems.
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Computational Methodology: The OrbNet Denali data set is meticulously constructed to provide a broad chemical landscape relevant to both biological and organic chemistry. Initially, the ChEMBL27 database serves as a primary source, offering a wealth of chemical structures focused on SMILES strings containing elements frequently found in biomolecules (C, O, N, F, S, Cl, Br, I, P, Si, B, Na, K, Li, Ca, Mg). To maintain manageable complexity, the data set limits molecule sizes to 50 atoms. Strings corresponding to open-shell Lewis structures or those present in a separate validation set (Hutchison conformer benchmark ) are excluded, resulting in a random selection of over 116 943 unique SMILES strings for neutral molecules.
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To capture molecular flexibility, multiple conformations (up to four) are generated for each SMILES string using the ENTOS BREEZE conformer generator, with subsequent optimization at the GFN1-xTB level of theory . Beyond equilibrium geometries, the data set includes non-equilibrium configurations to represent the dynamic nature of molecules. Two techniques are employed: Normal-mode sampling , which simulates thermal fluctuations at 300 K, and ab initio molecular dynamics (AIMD) simulations, which mimic real-time dynamics at a higher temperature (500 K). Both methods utilize the GFN1-xTB approach, with the choice between them randomized for each molecule. This methodology yields a substantial collection of over 1 771 191 equilibrium and non-equilibrium geometries derived from ChEMBL conformers.
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The data set also extends beyond neutral molecules. It includes protonation states and tautomers (over 215,000 geometries) to capture various hydrogen attachment possibilities, with contributions from the QM7b data set enriching this aspect. Additionally, salt complexes (over 271,000 geometries) are generated by pairing ChEMBL molecules with common salts, and structures from other databases (JSCH2005, BioFragment Database ) are included to represent a broader range of non-covalent interactions crucial in biological systems. Furthermore, to avoid bias towards large molecules, the data set includes a diverse collection of small molecules (over 94,000 geometries) created using common chemical motifs and further diversified by substituting atoms.
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The MD17 and its later versions serve as foundational resources for researchers benchmarking the accuracy of force fields in molecular dynamics (MD) simulations. The two versions (the 1st version (MD17) and the revised version (rMD17) ) both offer a collection of MD snapshots with DFT energies and forces for ten small organic molecules, including benzene, ethanol, malonaldehyde, uracil, toluene, salicylic acid, paracetamol, naphthalene, azobenzene, and aspirin. The 3rd version of the data set contains fewer molecules computed at the coupled cluster level of theory (CCSD(T)). Computational Methodology: The original MD17 data set contains energy and force calculations derived from AIMD simulations of gas-phase molecules at room temperature. The electronic potential energies in this data set were obtained using Kohn-Sham DFT. However, the data set faced several limitations, such as significant numerical noise that compromised data reliability. Furthermore, the original publication lacked comprehensive details on the functional, basis set, spin-polarization, integration grid, and software used, impeding reproducibility and limiting its utility in specific chemical simulations.
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The coupled cluster data set was created using the same geometries as those in the DFT calculations. Energies and forces were recomputed employing all-electron CCSD(T). The Dunning's correlation-consistent basis set cc-pVTZ was utilized for ethanol, cc-pVDZ for toluene and malonaldehyde, and CCSD/cc-pVDZ for aspirin. All calculations were executed with the Psi4 software suite. Data Accessibility: All data sets are available at datasets. The rMD17 data set can also be accessible on Figshare at . In addition, all data sets are provided as a class in the PYG library.[123]
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Sampling in conventional MD data sets like MD17 and rMD17 is often biased towards a narrow region of the potential energy surface (PES), primarily focusing on equilibrium structures. This limited exploration restricts the ability of neural force fields (NFFs) to accurately model chemical reactions involving significant molecular deformations, such as bond breaking. To address these limitations, Pengmei et al. introduced the extended excited-state molecular dynamics (xxMD) data set. Similar to MD17, xxMD targets small to mediumsized gas-phase molecules but includes nonadiabatic trajectories to capture the dynamics of excited electronic states. This approach allows xxMD to encompass a broader range of nuclear configurations, including those essential for chemical reactions, such as transition states and products. Additionally, xxMD covers regions near conical intersections, which are critical for determining reaction pathways across different electronic states.
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Computational Methodology: The xxMD data set includes four photochemically active molecular systems: azobenzene, malonaldehyde, stilbene, and dithiophene. To investigate the complex electronic structures involved in these systems, particularly in the vicinity of deformed geometries and conical intersections, nonadiabatic simulations were performed using the trajectory surface hopping algorithm implemented in the SHARC code. The state-averaged complete active space self-consistent field (SA-CASSCF) level of theory was employed to accurately describe the potential energy surfaces of the multiple electronic states relevant to these systems. This subset of data, generated from SA-CASSCF calculations, is referred to as xxMD-CASSCF. The trajectories in xxMD-CASSCF exhibit energy conservation and provide potential energies and forces for the first three electronic states. All SA-CASSCF calculations were carried out using OpenMolcas 22.06. To ensure compatibility with existing data sets (MD17 and rMD17), a new subset xxMD-DFT is created which provides recomputed ground singlet electronic state potential energies and gradients using spin-polarized KS-DFT calculations with the M06 functional for the same geometries as used in SA-CASSCF calculations. All calculations are done with the Psi4 package interfaced with ASE package. It should be noted that the xxMD data set does not include nonadiabatic coupling vectors (NACs) for reasons described in their reference data descriptor.
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Computational Methodology: All calculations were performed using the FHIaims electronic structure software, in conjunction with i-PI for the MD simulations. The potential energy and atomic force labels were determined at the PBE+MBD level of theory. Two different types of basis sets were employed, referred to as "light" and "tight" within the FHI-aims framework. Trajectories were sampled at a resolution of 1 femtosecond (fs), with a thermostat used to regulate the temperature during simulations.
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WS22 is a comprehensive database focusing on ten organic molecules, varying in size and complexity, with up to 22 atoms. It includes 1.18 million geometries, encompassing both equilibrium and non-equilibrium states. These geometries are meticulously sampled from specific distributions and further augmented with interpolated structures, resulting in a highly diverse data set. For each geometry, WS22 provides various QM properties, such as potential energies, forces, dipole moments, and electronic energies.
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Computational Methodology: The construction of the WS22 database involves a meticulous four-step process. In the first step, researchers employed DFT to determine the equilibrium geometries for various conformations of each molecule. Calculations were conducted for both ground and excited electronic states (where applicable) to capture a broad range of configurations. All geometry optimizations were performed without symmetry constraints using the Gaussian 09 program with the hybrid density functional PBE0 and the 6-311G* basis set. For certain molecules, particularly those experiencing significant conformational changes upon excitation, first excited state (S 1 ) calculations were performed. In these cases, the linear-response time-dependent DFT approach was used for both geometry optimizations and frequency calculations at the same theoretical level, PBE0/6-311G*. Frequency calculations were then carried out to ensure that the optimized structures were true minima on the potential energy surface.
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Beyond the initial equilibrium structures, the researchers implemented two techniques to create a diverse set of geometries. The first technique, Wigner sampling, considers the zero-point energy of molecules to generate a broader range of configurations compared to classical simulations. This method uses the optimized geometries and harmonic frequencies obtained in step one to create an ensemble of non-equilibrium structures based on a Wigner probability distribution. For each molecule, 100,000 geometries were generated, ensuring a good distribution across different conformers.
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To further explore beyond the vibrational degrees of freedom covered by Wigner sampling, researchers performed geodesic interpolation between every possible combination of stable conformers. This creates a smooth transition between different conformational spaces, including regions near transition states on the potential energy surface, which are not accessible via Wigner sampling. This technique added an additional 20,000 geometries per data set in the WS22 database.
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The VIB5 database is a meticulously curated collection of high-quality ab initio quantum chemical data for five small polyatomic molecules with significant astrophysical relevance: methyl chloride (CH 3 Cl), methane (CH 4 ), silane (SiH 4 ), fluoromethane (CH 3 F), and sodium hydroxide (NaOH). The database includes over 300,000 grid points, with individual molecules featuring between 15,000 and 100,000 points. Each grid point corresponds to a specific nuclear configuration of the molecule, providing theoretical best estimates (TBEs) of potential energies and their constituent terms. Additionally, the data set offers energy and energy gradient calculations at various levels of theory, including MP2/cc-pVTZ and CCSD(T)/cc-pVQZ, as well as HF energies derived from these calculations using the corresponding basis sets.
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The VIB5 database is built on a foundation of grid points that represent various nuclear configurations of the target molecules. These grid points were collected in VIB5 from the previous studies by some of the authors. Detailed descriptions of the grid point generation process can be found in the published VIB5 data descriptor and authors' original publications.
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For each molecule, TBEs and energy corrections were sourced directly from previous studies by the authors. Each TBE is calculated as the sum of several constituent terms, such as coupled-cluster energy at the complete basis set limit, core-valence electron correlation energy correction, and diagonal Born-Oppenheimer correction. Not all constituent terms were calculated at the same level of theory across all molecules; specific details are provided in Table of the published VIB5 data descriptor. Various versions of MOLPRO and CFOUR programs were utilized for these calculations.
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The VIB5 data is stored in a JSON file named VIB5.json, which can be downloaded from . The file structure organizes the data by molecule, providing information on chemical formula, number of atoms, and more. Each grid point entry includes nuclear positions (both Cartesian and internal coordinates) and various property values. These property values include energies (TBE, constituent terms, HF, MP2, CCSD(T)) and energy gradients (MP2, CCSD(T)). Specific JSON keys allow access to different properties for each grid point, as detailed in Table of the original report.
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The ANI-1 data set provides a comprehensive collection of DFT total energy calculations of small organic molecules, encompassing approximately 20 million non-equilibrium conformations of 57,462 molecules. ANI-1 data set was used to train the general-purpose ANI-1 potential. Computational Methodology: The creation of the ANI-1 data set involved a multi-step process including molecule selection, geometry optimization, and normal mode sampling. Initially, the GDB-11 database was used as the source, containing organic molecules with up to 11 heavy atoms (C, N, O, F). A subset of 57,947 molecules with 1-8 heavy atoms limited to C, N, and O was chosen. RDKit software was employed to generate 3D conformations, ensuring neutral charge and singlet electronic ground state.
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Subsequently, normal mode coordinates and corresponding force constants were obtained for each optimized molecule. Random displacements for each mode were calculated based on temperature, and these displacements were used to generate new conformations by scaling the normalized normal mode coordinates. Single-point energy calculations were performed at the ωB97X level for these new conformations. The number of conformations generated (N) depended on the number of heavy atoms (S) and the molecule's degrees of freedom (K).
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The ANI-1x and ANI-1ccx data sets are foundational resources used to train the universal ANI-1x and ANI-1ccx ML potentials, respectively. These data sets provide an extensive collection of millions of organic molecule conformations containing the elements carbon, hydrogen, nitrogen, and oxygen (CHNO). The ANI-1x data set includes DFT calculations for approximately 5 million organic molecule conformations, obtained through an active learning algorithm. This data set features a much wider variety of molecular conformations compared to the ANI-1 random sampled data set, owing to the active learning methods employed in its construction. The ANI-1ccx data set is a carefully selected 10% subset of the ANI-1x data set, recomputed with CCSD(T)/CBS level of theory.
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Computational Methodology: The ANI-1x data set was developed using an active learning procedure to enhance the diversity and accuracy of the ANI-1x potential. Initially, an ensemble of ANI models was trained using bootstrapping on a preliminary data set. Molecules were then randomly sampled from extensive databases like GDB-11 and ChEMBL. Four sampling techniques were applied to these molecules within active learning: MD sampling, normal mode sampling, dimer sampling, and torsion sampling. Data points with high uncertainty, identified using the ensemble disagreement measure ρ, were selected for DFT calculations. These high-uncertainty points were then added to the training set, and the models were retrained. This process was iteratively repeated to create a more diverse and comprehensive data set.
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The ANI-1ccx data set leverages a higher level of theory, CCSD(T)*/CBS (special extrapolation scheme to CCSD(T)/complete basis set), for a subset of the ANI-1x data points. The selection process began with a random subset of ANI-1x data, for which CCSD(T)*/CBS reference data was generated. An ensemble of models was trained on this CCSD(T)*/CBS data, and ρ was calculated for all remaining ANI-1x data points. Data points with ρ values exceeding a predetermined threshold were then selected, and CCSD(T)*/CBS data for these points was generated and added to the training set. This iterative process continued until the final ANI-1ccx data set was established.
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Data Accessibility: The ANI-1x and ANI-1ccx data sets are available in a single HDF5 file, accessible via Figshare at . A Python script (example_loader.py) provided in a publicly accessible GitHub repository datasets can be used to access the data. The data set includes various properties such as energies (multiple types), forces, electronic multipole moments, and charges. These properties were calculated using three primary electronic structure methods: ωB97X/6-31G*, ωB97X/def2-TZVPP, and CCSD(T)*/CBS. All ωB97X/6-31G* calculations were performed using the Gaussian 09 electronic structure package, while ωB97X/def2-TZVPP and CCSD(T)*/CBS calculations were conducted using the ORCA software package. .
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The ANI-2x data set is used to train the ANI-2x ML model and contains 8.9 million nonequilibrium neutral singlet molecules with seven chemical elements (H, C, N, O, S, F, Cl) compared to its predecessor ANI-1x with compounds comprising only four elements (H, C, N, O), thus enabling wider ability on drug discovery and biomolecules. Different from previous ANI datasets, ANI-2x uses S66x8 data set to improve non-bonded interactions and a new type of sampling to improve bulk water.
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Computational Methodology: ANI-2x data set is based on GDB-11 , ChEMBL , S66x8[146] data sets, and additional randomly-generated amino acids and dipeptides to build the data sets. Similar active learning processes as previous ANI datasets are used to generate non-equilibrium geometries with refinement on torsion, non-bonded interaction, and bulk water. The obtained conformers are labeled with energies and forces at ωB97X/6-31G* level of theory using Gaussian 09.
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The Transition1x data set is a unique resource for researchers developing ML models that can handle reactive systems. Unlike existing data sets that primarily focus on near-equilibrium configurations, Transition1x incorporates crucial data from transition regions. This empowers ML models to learn features essential for accurate reaction barrier prediction. Furthermore, Tran-sition1x serves as a new benchmark for evaluating how well ML models capture reaction dynamics.
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With 9.6 million data points, each meticulously generated using DFT calculations, Transition1x encompasses the forces and energies for a staggering 10,000 organic reactions. The core data generation method is the Nudged Elastic Band (NEB) technique which efficiently explores millions of configurations within transition state regions, providing a comprehensive picture of the energetic landscape during reactions.
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Computational Methodology: The creation of Transition1x follows a meticulous workflow. First, a comprehensive database of reactant-product pairs for various organic reactions lays the foundation, providing initial geometries for reactants, products, and transition states. To ensure compatibility with the popular ANI1x data set, Transition1x utilizes the same ωB97X functional and the 6-31G(d) basis set for DFT calculations. These calculations are performed using the ORCA software. Next comes the NEB and CINEB optimization stage. NEB, along with CINEB, plays a central role. Both techniques are employed alongside the BFGS optimizer to efficiently refine the initial guess for the minimum energy pathway (MEP). The workflow involves relaxing reactant and product geometries, constructing an initial path, minimizing its energy using image dependent pair potential (IDPP) within the NEB framework, and finally using NEB and CINEB together to achieve an accurate MEP.
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Symmetry plays a pivotal role in determining various molecular characteristics, such as excitation degeneracy and transition selection rules. Despite its significance, many quantum chemistry databases often overlook this crucial aspect. Bridging this gap, the QM-sym database emerges as a valuable resource, meticulously documenting the C nh symmetry for each molecule within its vast repository. Comprising 135,000 structures featuring elements like H, B, C, N, O, F, Cl, and Br, it encompasses symmetries like C 2h , C 3h , and C 4h .
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Computational Methodology: QM-sym employs a two-step process, leveraging symmetry to streamline database generation. Initially, it constructs fundamental molecular frameworks based on standardized bond lengths and angles. Subsequently, employing a genetic algorithm, these structures undergo iterative refinement to attain stable configurations while conforming to predefined symmetrical point groups (e.g., C 2h or D 6h ).
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Following structural generation, each molecule is optimized at the B3LYP/6-31G(2df,p) level theory with Gaussian 09 software, which ensures chemical validity and stability. However, complexities may lead to convergence failures or unstable configurations. To mitigate this, a filtering mechanism akin to QM9 is enacted, setting a maximum optimization cycle limit of 200 and implementing stricter convergence criteria. Ultimately, only structures exhibiting successful optimization and positive vibrational frequencies, indicative of stability, are retained in the final QM-sym database, striking a balance between symmetry incorporation and molecular stability.
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Data Accessibility: The QM-sym database is readily accessible through platforms like GitHub and Figshare using the links and , respectively. It provides QM_sym.xyz files containing atomic coordinates and a plethora of predicted properties, encompassing point group information, enthalpies, atomization energies, zero-point energies, and energy and symmetry labels spanning from HOMO-5 to LUMO+5. Each structure is uniquely indexed by QM_sym_i.xyz, with 'i' denoting the structure's database order.
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Computational Methodology: QM-symex inherits the rigorous data generation process established in QM-sym, ensuring the stability and symmetry of its molecules. Building upon the 135,000 structures from QM-sym, an additional 38,000 molecules were meticulously generated. Maintaining symmetry preservation and stability remains a core principle. Using Gaussian 09 optimization with 100 cycles, each molecule undergoes rigorous validation to retain its original symmetry throughout the process.
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Data Accessibility: Accessible on Figshare at , QM-symex provides data in XYZ format, indexed as QM_symex_i.xyz for ease of access,where 'i' represents the order of the structure in the database. In addition to inheriting all properties from QM-sym, QM-symex enriches the data set with information on the first ten singlet and triplet transitions. This includes details such as energy, wavelength, orbital symmetry, transition distance, and other quasi-molecular properties. With the new 38k molecules, the distribution of symmetries within QM-symex is noteworthy. C 2h symmetry occupies a significant proportion of 46%, while C 3h and C 4h symmetries account for 41% and 13%, respectively.
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The ∇ 2 DFT data set provides a comprehensive collection of approximately 16 million conformers for around 2 million drug-like molecules, featuring 8 atom types (H, C, N, O, Cl, F, Br) and up to 62 atoms. It is an extension of the original ∇DFT data set , offering energies, forces, and various other properties calculated at a reasonably accurate DFT level for a wide range of molecules. Additionally, the data set includes relaxation trajectories for numerous drug-like molecules. Based on the Molecular Sets (MOSES) data set , ∇ 2 DFT contains around 1.93 million molecules with atoms C, N, S, O, F, Cl, Br, and H, 448,854 unique Bemis-Murcko scaffolds , and 58,315 unique BRICS fragments .
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To avoid redundancy, a clustering step was implemented using the Butina clustering method, which groups similar conformations based on their geometrical properties. This step effectively reduced the number of conformations while ensuring a representative set is retained. Only clusters that encompassed at least 95% of the conformations for a specific molecule were kept.
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For each conformation, electronic properties (energy, DFT Hamiltonian matrix, DFT overlap matrix, etc.) were computed using the Kohn-Sham DFT method at the ωB97X-D/def2-SVP level of theory with the Psi4 quantum chemistry software. Additionally, interatomic forces were calculated at the same level of theory for about 452,000 molecules and 2.9 million conformations.
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The COMPAS (COMputational database of Polycylic Aromatic Systems) project aims at providing structures and properties for ground-state polycyclic aromatic systems. COMPAS-1 focuses on cata-condensed polybenzenoid hydrocarbons (PBHS) with 43k molecules, COMPAS-2 provides 0.5 million cata-condensed poly(hetero)cyclic aromatic molecules and COMPAS-3 explores 40k the peri-condensed polybenzenoid hydrocarbons. All the 3 data sets contain molecules up to 11 rings with properties calculated at xTB level and molecules up to 10 rings at DFT level.
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