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Computational Methodology: For COMPAS-1, the initial polycyclic molecules are constructed with CaGe up to 11 rings. All the geometries were optimized at GFN2-xTB level and molecules containing up to 10 rings were further optimized at B3LYP-D3(BJ)/def2-SVP with ORCA 4.2.0. COMPAS-2 starts from various building blocks different in size and elements contained with the final geometries optimized using GFN1-xTB and CAM-B3LYP-D3BJ/def2-SVP. COMPAS-3 follows the same protocol as COMPAS-1 and perform calculation on the obtained molecules at GFN2-xTB and CAM-B3LYP-D3BJ/aug-cc-pVDZ//CAM-B3LYP-D3BJ/def2-SVP level of theory.
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Data Accessibility: COMPAS datasets are publicly available at where molecules and their corresponding QM properties including electronic energies, HOMO/LUMO energies and gap, ZPE, etc., are hosted. An online website is developed for easier structure search and download at . 3.33 CREMP CREMP (Conformer-Rotamer Ensembles of Macrocyclic Peptides) data set aims to explore macrocyclic peptides which is lacking in MLP field, providing 36k representative 4-, 5-, and 6-mer homodetic cyclic peptides with up to 31.3 million unique conformers with properties calculated at semiempirical level. CREMP-CycPeptMPDB data set is also provided which is built based on the established CycPeptMPDB database featuring passive membrane permeability with 8.7 million newly-generated conformers from 3k 6-, 7-, and 10-mer cyclic peptides.
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| 89 |
Computational Methodology: To generate the CREMP data set, we utilized the CREST tool to explore diverse conformational ensembles of macrocyclic peptides. We began with a set of 36,198 unique homodetic macrocyclic peptides, sampled based on key parameters such as side chains, stereochemistry, and N-methylation. Using RDKit, each peptide was converted to canonical SMILES, and initial conformers were generated via the ETKDGv3 method, followed by energy optimization using the MMFF94 force field. The 1,000 lowest-energy conformers were further optimized using GFN2-xTB in chloroform solvent. These optimized structures were then used as inputs for CREST simulations, where 14 metadynamics runs were performed in parallel. The final ensembles were filtered to ensure chemical graph consistency across all conformers.
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| 90 |
The GEOM ( Geometric Ensemble Of Molecules) data set is a comprehensive resource containing high-quality conformers for 451,186 organic molecules. This includes 317,928 drug-like species with experimental data and 133,258 molecules from the QM9 data set. The dataset encompasses 304,466 molecules sourced from AICures (), a machine learning challenge focused on drug repurposing for COVID-19 and related illnesses, as well as 16,865 molecules from the MoleculeNet benchmark, annotated with experimental properties relevant to physical chemistry, biophysics, and physiology.
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| 91 |
Computational Methodology: The data generation process for the GEOM data set involved several key steps. It began with SMILES pre-processing, where SMILES strings were converted to their canonical forms using RDKit to ensure consistency across the dataset. For drug molecules found in clusters (e.g., with counter-ions or salts), de-salting procedures were applied to isolate the main compound and adjust its ionization state. This step ensured uniform molecular representation across multiple sources.
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In the initial structure generation phase, RDKit was used to generate molecular conformers, which were optimized using the MMFF force field. The ten lowest energy conformers were further optimized with GFN2-xTB, and the lowest energy conformer was selected as the starting structure for the CREST simulations. For the QM9 dataset, molecules were re-optimized with xTB before undergoing CREST, despite already being optimized with DFT.
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| 93 |
The next step involved graph re-identification, which was crucial for handling changes in stereochemistry and reactivity during CREST simulations. RDKit was used to assign graph features to each conformer, ensuring accuracy in molecular structures. For 534 molecules from the BACE dataset, CENSO simulations were performed to further refine conformers with DFT geometry optimizations.
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Finally, with ORCA version 5.0.2, single-point DFT calculations (with r2scan-3c functional, mTZVPP basis, C-PCM model of water, and default grid 2) were carried out on all CREST conformers from the BACE dataset to provide high-accuracy energies. Additionally, Hessian calculations were performed using xTB to obtain vibrational frequencies, providing valuable thermodynamic information.
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| 95 |
The tmQM data set explores transition metal-organic compound space including Werner, bioinorganic and organometallic complexes with their respective QM properties based on Cambridge structural database, enabling wide coverage of organometallic space. There are in total 86,665 complexes with 3d, 4d, and 5d transition metals from groups 3 to 12. Lately, 60k graph data set (tmQMg) and a 30k ligand library (tmQMg-L) are constructed with NBO analysis on tmQM dataset. tmQM offers Cartesian coordinates optimized at the GFN2-xTB level, along with quantum properties computed at the DFT (TPSSh-D3BJ/def2-SVP) level. These properties include electronic and dispersion energies, metal center natural charge, HOMO/LUMO energies and gaps, dipole moments, and polarizabilities calculated at the GFN2-xTB level.
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| 96 |
Computational Methodology: The tmQM data set was generated by extracting structures from the 2020 release of the Cambridge Structural Database (CSD) using seven filters: 1) inclusion of only mononuclear transition metal (TM) compounds, 2) containing at least one carbon and one hydrogen, 3) excluding non-metal components, 4) omitting polymeric structures, 5) ensuring 3D coordinates, 6) excluding disordered atoms, and 7) removing highly charged species (charge outside -1 to +1). From the filtered CSD data, 116,332 structures were selected. After geometry optimization using the GFN2-xTB method, additional filters for convergence, geometry quality, and electron count reduced the dataset to 86,699 structures. Ultimately, quantum mechanical properties were computed using DFT with the hybrid meta-GGA TPSSh functional and the def2-SVP basis set through Gaussian 16.
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| 97 |
The OFF-ON (organic fragments from organocatalysts that are non-modular) database is developed to train machine learning models aimed at predicting the behavior of structurally and conformationally diverse functional organic molecules, particularly photoswitchable organocatalysts. This dataset contains 7,869 equilibrium geometries and 67,457 non-equilibrium geometries of organic compounds and dimers, providing a broad foundation for exploring flexible molecular structures and their free energy surfaces.
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| 98 |
Computational Methodology: The data generation process for the OFF-ON database involved two key stages. The first stage concentrated on creating a set of molecules that represent diverse chemical environments pertinent to functional organic molecules. This set included catalytic moieties, photochromic units, substituted aromatic rings, and representations of non-covalent interactions. To compile this diverse set, existing molecular databases such as OSCAR, CSD, and PubChem[102] were utilized, alongside additional generation protocols detailed in the supplementary materials. As a result, a final collection of 7,869 unique entries was established, encompassing 3,533 catalytic moieties, 538 photochromic units, 3,165 substituted rings, and 633 dimers representing non-covalent interactions.
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| 99 |
The second stage focused on generating a range of molecular conformations to capture out-of-equilibrium effects. This was achieved through molecular dynamics (MD) simulations, where for each of the 7,869 structures, 5 ps MD trajectories were initiated from geometries optimized using DFTB. These simulations resulted in over 2 million new geometries. The dataset was subsequently refined using the farthest point sampling (FPS) algorithm, which selected the most diverse conformations from the MD trajectories. This process led to the inclusion of 67,457 unique out-of-equilibrium structures in the database.
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In total, the OFF-ON database comprises 75,326 structures, combining both equilibrium and non-equilibrium states. The computational details of the dataset include electronic structure computations and machine learning potential modeling. The baseline energy calculations were performed at the DFTB3 level with the 3ob parameters and D3 dispersion correction, implemented in the DFTB+ software. These results were normalized using multilinear regression models. The reference energy was computed at the PBE0-D3/def2-SVP level using the TeraChem software, and the difference between DFTB and PBE0 energies was used as a correction.
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In addition to the data sets and databases described above, this subsection introduces six more data sets and databases: C7O2H10-17,[10] ISO17, , VQM24, , QCDGE, QM-22, CheMFi , QM9S and the Ten-sorMol ChemSpider data set. Among them, the C7O2H10-17 data set comprises MD trajectories for 113 randomly selected isomers of C7O2H10. These trajectories were calculated at a temperature of 500 K with a high temporal resolution of 0.5 fs, using DFT with the PBE exchange-correlation potential. Notably, C7O2H10 represents the largest set of isomers within the QM9 data set. The identifiers used in this data set are consistent with those used in the QM9 isomer subset, ensuring compatibility and ease of reference.
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| 102 |
The ISO17 data set extends the C7O2H10-17 data set, consisting of 129 isomers with the chemical formula C7O2H10. Each isomer includes 5,000 conformational geometries, energies, and forces, sampled at a resolution of 1 femtosecond in the MD trajectories. These simulations were conducted using the FHI-aims software, employing DFT with the PBE functional and the Tkatchenko-Scheffler (TS) van der Waals correction method.
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| 103 |
The VQM24 data set is a comprehensive data set containing QM properties of small organic and inorganic molecules. It encompasses 258,242 unique constitutional isomers and 577,705 conformers of varying stoichiometries, focusing on molecules composed of up to five heavy atoms from C, N, O, F, Si, P, S, Cl, Br. For each molecule, the data set provides optimized structures, thermal properties (vibrational modes, frequencies), electronic properties, wavefunctions, and, for a subset of 10,793 conformers, diffusion quantum monte carlo (DMC) energies. Calculations were performed at the ωB97X-D3/cc-pVDZ level of theory, with conformers initially generated using GFN2-xTB and subsequently relaxed using DFT. Calculations were performed with the following computational programs: Surge, RDKit, Crest, Psi4 and QMCPACK. The QCDGE database offers an extensive collection of ground and excitedstate properties for 443,106 organic molecules, each containing up to ten heavy atoms, including carbon, nitrogen, oxygen, and fluorine. These molecules are sourced from well-known databases such as QM9, PubChemQC, and GDB-11. The database provides 27 molecular properties, including ground-state energies, thermal properties, and transition electric dipole moments, among others. Ground-state geometry optimizations and frequency calculations for all compounds were carried out using the B3LYP/6-31G* level of theory with BJD3 dispersion correction, while excited-state single-point calculations were performed at the ωB97X-D/6-31G* level. All computational work was conducted using Gaussian 16.
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The QM-22 database is a compilation of molecular data sets specifically curated for DMC calculations of the zero-point state. Each data set within QM22 employs unique methodologies tailored to the specific molecules involved. Detailed computational methods for each data set can be found in their corresponding publications. The CheMFi data set is a multifidelity compilation of quantum chemical properties derived from a subset of the WS22 database, featuring 135,000 geometries sampled from nine distinct molecules. CheMFi encompasses five different levels of fidelity, each corresponding to a specific basis set size (STO-3G, 3-21G, 6-31G, def2-SVP, def2-TZVP). The data set was generated using TD-DFT calculations with the CAM-B3LYP functional, performed via the ORCA software package. It includes comprehensive data on properties such as vertical excitation energies, oscillator strengths, molecular dipole moments, and ground state energies. Moreover, computational times for each fidelity level are provided to facilitate benchmarking of multifidelity models.
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| 105 |
The QM9S dataset, used for training and testing the DetaNet deep learning model, consists of 133,885 organic molecules derived from the QM9 dataset. The molecular geometries were re-optimized using the Gaussian 16 software at the B3LYP/def-TZVP level of theory. A wide range of molecular properties were then calculated at the same level, including scalar values (e.g., energy, partial charges), vectors (e.g., electric dipole), second-order tensors (e.g., Hessian matrix, quadrupole moment, polarizability), and third-order tensors (e.g., octupole moment, first hyperpolarizability). Additionally, frequency analysis and time-dependent DFT were performed to obtain the IR, Raman, and UV-Vis spectra.
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| 106 |
The TensorMol ChemSpider data set contains potential energies and forces for 3 million conformations from 15,000 different molecules composed of carbon, hydrogen, nitrogen, and oxygen. These molecules were sourced from the ChemSpider database. The training geometries were sampled using metadynamics, and their energies were calculated using the QChem program with the ωB97X-D exchange-correlation functional and a 6-311G** basis set. Data Accessibility: The C7O2H10-17 and ISO17 data sets are available at , while the VQM24 data set can be accessed on Zenodo at . The QCDGE database is hosted at , and the QM22 database can be downloaded from . The CheMFi data set is available at . The QM9S data set is hosted at Figsharehttps. Although the TensorMol ChemSpider data set was once accessible via , as mentioned in the supplementary information, it is no longer available.
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The exploration of quantum chemical databases and data sets for ML potentials has revealed a rich landscape of resources offering valuable data for training and validating these powerful tools. We have identified a diverse range of data sets and databases, each with its own strengths in terms of information content, level of theory, molecular coverage, and creation procedures.
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As the number of quantum chemical data sets continues to grow rapidly, the importance of maintaining an up-to-date overview becomes critical. To this end, we provide an updatable resource (accessible at ), which aims to track and categorize emerging databases and data sets as they become available, ensuring researchers have access to the latest information. This resource also comes with the machine-readable representation of the overview of the data sets, which allows to easier sort and filter the data sets when required. The corresponding Jupyter notebook is also provided.
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However, the field faces significant challenges in ensuring the long-term accessibility of these data sets. Instances like the disappearance of the Tensor-Mol database highlight the fragility of data availability over time. Platforms such as Figshare and Zenodo offer solutions to some extent, with Zenodo providing free hosting for large data sets, while Figshare's service comes with a fee for larger storage needs. Ensuring the longevity and accessibility of data sets will require continued support and development of such repositories.
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Moreover, data format standardization is another area requiring attention. The FAIR (Findable, Accessible, Interoperable, Reusable) principles provide a guiding framework, but the diversity of formats in use today makes unification challenging. Efforts to promote standard formats, such as ioChem-BD and Quantum Chemistry Schema, could help streamline data exchange and enhance interoperability across different platforms and research groups. Attempts to provide standard formats interoperable between software are naturally undertaken in the big software ecosystems gluing together different quantum chemical and/or ML codes like is done in MLatom and ASE. Another big issue with the growing number of data sets and databases is that they are often generated at different levels severely hampering their use in ML potentials as, e.g., training a ML potential on a merged data set would be very problematic if possible at all to achieve any reasonable result. One of the solutions is recalculating properties at the same level for the merged data sets but it is very computationally costly undertaking. Recently, some of us suggested a potentially simple solution to this problem by creating allin-one machine learning potentials which take in input the level of theory as an additional feature: we showed that this approach allows to train a single, accurate ML model on a heterogeneous data containing data at different levels of theory. This seems to be one of the most promising direction for the future explorations which we also pursue in our labs. Furthermore, maintaining updatable data sets and databases, particularly for "living" (i.e., updatable) methods like UAIQM, is crucial for the continued evolution of ML potentials. Ensuring these data sets and databases are regularly updated and accessible will require coordinated efforts within the research community, alongside the development of tools and standards that facilitate easy data curation and integration.
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Finally, materials databases such as ChemSpider, the Cambridge structural database, and the materials project serve as exemplary models of online accessibility, demonstrating how well-curated and easily navigable platforms can support a wide range of research activities. By drawing inspiration from these platforms, the quantum chemistry community can develop databases that are not only rich in content but also user-friendly and sustainable.
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In conclusion, by addressing these challenges-ranging from the rapid proliferation of data sets to the need for standardized formats and long-term accessibility-the future of quantum chemical databases and data sets holds immense promise. The integration of active learning, high-throughput calculations, and other advanced methodologies will further enhance the utility of these resources, enabling ML potentials to reach their full potential in computational chemistry. This synergy between data and algorithms will accelerate scientific discovery, driving progress across a wide array of fields and deepening our understanding of the molecular world.
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| 0 |
Li-ion batteries pose an integral part of todays energy economics but are expected to run into limitations of achievable energy density in the future, motivating the investigation of different technologies, e.g., solid-state batteries. In both, conventional Li-ion and solid-state batteries, the layered oxides LiNi1-xMnyCo1-x-yO2 (NCM) are the most utilized and thoroughly investigated cathode active material. Nonetheless, among other things, the relative scarcity of Co and Mn, and resulting material costs make the search for alternatives a promising endeavour. The cathode active material Li2FeS2 offers a cost-effective alternative given the large abundance of both iron and sulfur, comparable to the promised benefits of other alternative chemistries such as LiFePO4 (LFP) and Li-S. At the same time, moving from NCM to Li2FeS2 means higher mechanical compatibility, and moving from high-to lowpotential electrodes promises better alignment with the stability window of the state-ofthe-art sulfur-based solid-electrolytes. In addition to these benefits, Li2FeS2 on paper offers a two electron reaction following full delithiation from Li2FeS2 to FeS2. Considering this range, the theoretical capacity of Li2FeS2 amounts to 400 mAh•g -1 , exceeding the theoretical capacity of NCM811 that is ≈280 mAh g -1 but coming at the disadvantage of a lower potentials of operation.
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Nonetheless, Hansen and coworkers recently proposed that the reaction is limited to the chemical space between Li2FeS2 and Li0.5FeS2 relating to a theoretical capacity of interdependence of both conductivities on the volumetric ratio of the components makes optimizing cathode composite transport a challenging task. The situation is further complicated by the general goal of designing high energy density cathodes that are feasible for application. An increase of the energy density of the cathode, or its areal loading (in units of mAh•cm -2 ), can be achieved by increasing the CAM volume fraction given the simultaneous reduction of formaly electrochemically inactive SE. The increase of the CAM fraction leads to an increase in the effective electronic conductivity of the composite but has detrimental influence on the effective ionic conductivity. This leads to the system being ion transport limited, i.e., to insufficiently fast ion transport, when going to the desired high volume fractions of CAM. Underutilization of the cathode and saturation or decline of the achievable energy density follow. The saturation behavior can be understood considering that increasing the areal loading above a threshold of the CAM volume fraction leads to a significant loss in cathode utilizations and a net-zero win in achievable energy density. This trend is schematically depicted in Figure (red shading). Various examples of ionic transport limitations leading to cathode underutilziation can be found in literature, e.g., for Li6PS5Cl-Graphite anode composites, in Li-S solid-state cells, and in Li6PS5Cl-LiNi0.6Co0.2Mn0.2O2 cathodes. Nonetheless, the energy density of the cathode can be increased above this threshold by increasing the cathode thickness (schematically depicted in Figure , blue shading). But, the increase in cathode thickness can amplify and exacerbate already existing transport limitations at medium to high CAM fraction again limiting the achievable energy densities. This can be intuitively understood by the elongated conduction paths for both charge carriers, that require even faster effective transport through the electrode. In agreement with this viewpoint, Kato and coworkers reported on a decrease of the cathode utilization in LiCoO2-Li10GeP2S12 cathodes when increasing the cathode thickness and simulations on a comparable system using Li3PS4 as SE indicate that reaction fronts and state-of-charge gradients are the underlying reasons. In this work, we investigate the solid-state cathode system Li5.5PS4.5Cl1.5 (SE) -Li2FeS2 (CAM) with varying volume fractions of CAM to identify potential onsets of kinetic limitations. This is done by evaluating the effective conductivities using chronoamperometry, impedance spectroscopy, and effective medium modelling.
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Successively, the influence on cathode utilization is investigated and related to the transport characteristics of the system. The porous electrode theory developed by Newman and Tobias is revisited and a dimensionless descriptor identified to describe transport limitations of the system. This descriptor is used to qualitatively guide the understanding of our results. From this, it is shown that high volume fraction CAM cathodes can be realized that show good cathode utilization at low applied current densities even when aiming for thicker electrodes. Nonetheless, lower rate capability at higher applied current densities is a consequence of increasing the cathode loading, i.e., the cathode energy density. With that, this work shows the general capabilities of Li2FeS2 as CAM in solid-state batteries and reveals limitations in the field of solid-state batteries in general that have to be targeted by future research.
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Sample preparation. Cathode composites of Li2FeS2 and Li5.5PS4.5Cl1.5 were prepared using a shaker mill with a frequency of 15 Hz for five minutes. Synthesis details and quality control of the synthesized materials are given in the Supporting Information (Figure , Table and). The ZrO2 shaker mill cup (15 mL) was filled with 200 mg of a Li2FeS2 and Li5.5PS4.5Cl1.5 mixture in the targeted volumetric ratio. Composites with Li2FeS2 volume fractions of 0.32, 0.41, 0.51, 0.62 and 0.74 were prepared corresponding to weight fractions of 0.4, 0.5, 0.6, 0.7 and 0.8. Twenty 3 mm ZrO2 milling media were filled in the shaker cup for the processing. Sample handling and preparation was exclusively done under inert atmosphere in an Ar-filled glovebox.
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Partial transport characterization. Two techniques were employed to evaluate the partial conductivities of the composites. The electronic conductivity was exclusively measured by chronoamperometry in electron conducting/ion blocking conditions, created by placing the sample between stainless steel current collectors. The ionic conductivity is determined in electron-blocking but ion conducting conditions by stacking SE and In/LiIn symmetrically on both sites of the sample. The polarization experiments were performed in a range of -45 mV to 50 mV, and 1 mV to 8 mV, for the electronic and ionic conductivity, respectively. All raw data and details of the data evaluation are given in the Supporting Information. Potentiostatic impedance spectroscopy was conducted to corroborate the partial ionic conductivity of the composites. The spectra were collected in a half cell configuration of In/LiIn|Li5.5PS4.5Cl1.5|Li2FeS2/Li5.5PS4.5Cl1.5. The investigated frequency range was 7 MHz to 50 mHz, with 25 sampled frequencies per decade using an excitation amplitude of 10 mV. The response was analyzed using a Z-type transmission-line model. Simultaneous determination of the partial electronic conductivities could not be done reliably. This is, because the significantly lower resistance contributions lead to increased uncertainties during fitting. Thus, the electronic resistance where fixed to the expected value from chronoamperometry to stabilize the fitting procedure. Details of the data evaluation are given in the main text and the Supporting Information.
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Electrochemical characterization. Half-cells were constructed using 12 mg Li2FeS2/Li5.5PS4.5Cl1.5 cathode composites (≈73-85 μm), 80 mg of Li5.5PS4.5Cl1.5 separator and a In/LiIn anode (In-foil towards separator, Li-foil towards current collector) in a press cell setup (10 mm diameter) with stainless steel current collectors. The separator and composite are densified at a pressure of 370 MPa before application of the anode. The relative densities of the composite layer are in the range of 85±3% independent of composition. The anode is prepared by first placing Infoil (ChemPur, 0.1 mm, 99.999%) on the separator, followed by Li foil that has been freshly prepared from a Li rod (abcr GmbH, 99.8%). For the evaluation of thicker electrodes, the cathode mass was increased to 18 and 24 mg. All cells were cycled at a controlled temperature of 298 K with an applied pressure of 40 MPa and with a rate of 0.134 C (assuming theoretical capacity 300 mAh•g -1 ). The rate capability was characterized by cycling the cells for five cycles at step-wise increasing current densities starting from 0.134 C (≈0.24 to 0.98 mA•cm -2 ) going to a maximum applied current density of 5.1 mA•cm -2 . An overview of all applied current densities in terms of C-rate and the approximated cathode thicknesses is given in Table of the Supporting Information.
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Porous electrodes in (solid-state) batteries. Extensive work has been done in the past to theoretically describe the electrochemical behavior of electrodes that consist of a porous, electron conducting active material (matrix) infiltrated by ion conducting liquid electrolyte. The theory of porous electrodes aims to describe the spatial distribution of current densities and reaction rates throughout the electrode that depend on the electrode geometry, the effective electronic and ionic conductivity, and the polarization behavior of the active material. These distributions, if nonuniform, can be considered the underlying reason for cathode underutilization, or the creation of stateof-charge gradients over the electrode. Not considered specifically in the porous electrode theory, the approximations commonly made to the solvent-based electrolyte, e.g., no concentration gradients, neglecting electrochemical double-layer formation and dismissing convection, are fulfilled in SE. Consequently, the results of the porous electrode theory should persist to the solid-state configuration.
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Newman and Tobias 23 derived a description of reaction current distributions through the electrode in one dimension. In the one-dimensional approximation, the current densities and reaction rates are only a function of the relative position 𝑥 in the electrode located between the separator (𝑥 = 0) and the current collector (𝑥 = 𝐿) interface (schematically shown in Figure , left). The electronic current density ie in the active material and ionic current density iion in the electrolyte are described by Ohms law: 𝑖 ! = -𝜎 ! d𝜑 "# d𝑥 and 𝑖 $%& = -𝜎 $%& d𝜑 '( d𝑥 , Eq. 1
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where a represents the specific (CAM-SE) interfacial area and f(|φAM -φEl|) is any suitable function to describe the polarization at the interface as a function of the potential difference |φAM -φEl|. The function can take the general form of the Butler-Volmer equation, a linearized approximation for low overpotentials and a Tafel approximation for high overpotentials of charge transfer. Newman and Tobias showed that this set of equations can be cast into a differential equation to describe the reaction current density distribution. The differential equation can be solved numerically using appropriate boundary conditions. From this assessment, dimensionless descriptors were identified that scale with and give a measure of the uniformity of the reaction current density distribution. For Tafel polarization and considering symmetric charge transfer coefficients in the polarization equation, the uniformity of the reaction current density distribution is proportional to a dimensionless current density δ:
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where i = iion + ie is the total applied current density, ne is the number of electrons partaking in the reaction and L is the thickness of the electrode. The dimensionless current density describes the relative ratio of Ohmic potential losses in the cathode to limitations by (slow) reaction kinetics. For low values of δ ≲ 1, the reaction current density distribution is uniform and the kinetics of the reaction, i.e., the exchange current density, limit the system. This is the case for high effective conductivities and σion ≈ σe low applied current densities and in thin electrode configuration (red line in Figure ultimately leads to reaction fronts that have been experimentally shown to exist in both lithium-sulfur and NCM-based solid-state batteries. Considering that both, the thickness and the applied current density are desired to be high to improve energy density and enable fast charging, the conductivity term is the free composite design parameter for achieving low values of δ. The δ-parameter as a function of both effective conductivities is shown in Figure for an exemplary thickness of 200 μm and a current density of 5 mA•cm -2 . It shows that the δ-parameter is low, and reaction rates are uniform, when both conductivities are high and equal (diagonal in Figure ). When one effective conductivity is significantly lower than its counterpart, 𝛿 is high (lower and left boundaries in Figure ). With that, the uniformity of the reaction rate distribution, inversely proportional to δ, is limited by the lower conductivity. Exemplarily, this means that changing σe in the situation σion ≪ σe, while keeping σion constant, does not lead to significant changes in δ until the condition σion ≈ σe is reached (staying on the contour lines in Figure ). Opposed to that, changing σion in the same case has drastic influences ("moving" perpendicular to contour lines in Figure ). By changing the volume fractions of electrolyte and active material or the microstructure of the composite, both conductivities of the porous electrode change simultaneously, complicating this assessment. In this work, we consider the δ-parameter as stated by Newman and Tobias. Nonetheless, similar descriptors are derived by Wagner, Again, all spectra and fits are shown in the Supporting Information (Figure ).
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where σeff is the effective conductivity of the composite and σ1,2 and Φ1,2 are the conductivities and volume fractions of phase 1 and 2, respectively. Porosity is not specifically considered as third phase in this study, the effect of which is expected to be negligible given constant degrees of porosity between all composites in first approximation. The parameter k is a constant that describes the connectivity of the phases within the composite and determines the percolation threshold. Subsequently, the data have been fit by solving Eq. 5 for σeff and using k and the conductivity of the better conducting phase (σe,CAM for σe and σion,SE for σion) as fitting constants. With that, the experimental results of both conductivities can be well described (dashed lines in Figure ) allowing to approximate the effective transport between and closely surrounding the investigated compositional space of the cathode. The final fitting equation σeff(σ1, σ2, Φ1, Φ2, k), the resulting fitting constants and details of the procedure are given in the Supporting Information. Importantly, the effective medium model does not account for any interfacial effects between both phases, or grain boundary transport/resistance that can explain uncertainties deviation between fit and data.
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descriptor. Again, δ is a function of the effective conductivities, the cathode thickness and the applied current density and introduced as a descriptor for the tendency of the cathode to show nonuniform reaction rate distributions (δ ≫ 1), the buildup of reaction fronts and state-of-charge gradients. It must be considered that this descriptor, without accounting for important microstructural features like CAM-SE contact area, and kinetic parameters such as exchange current densities, can only be evaluated as qualitative, and not quantitative descriptor to predict potential transport limitations in the cathode. Nonetheless, we expect these transport limitations to scale with transportrelated performance properties of the cathode, e.g., the cathode utilization (general contacting of CAM and SE) and rate capability and these trends are reported in literature, where cathode utilization decreases because either σion or σe are insufficiently high or when the cathode thickness and applied current density are increased. The 𝛿-parameters characterizing the investigated Li2FeS2-Li5.5PS4.5Cl1.5 cathodes are
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shown in Figure . The depicted values are calculated according to Eq. 4 using the experimental (markers) and effective medium modelled effective conductivities (dashed line and shaded area) as input parameter. Moreover, the thicknesses L and current densities i of the cathodes later investigated as a function of the CAM volume fraction are utilized for the calculation. These are in the range of 85 μm to 73 μm, and 0.24 mAh•cm -2 to 0.49 mAh•cm -2 (0.134 C) for ΦCAM between 0.32 and 0.74 at constant cathode mass, respectively. An overview of the parameters is given in Table of the Supporting Information.
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For fractions of ΦCAM > 0.74, δ increases significantly as a consequence of reaching the percolation threshold of σion. With that, for pure Li2FeS2, a value of 300 is obtained indicating the onset of strong transport limitations (δ ≫ 1). Following, cathodes relating to these δ-parameters are investigated in terms of electrochemical performance and the potential of δ as a qualitative descriptor is evaluated.
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In/LiIn reference anode and Li5.5PS4.5Cl1.5 as separator. Initially, cells with constant cathode composite mass loading (15.3 mg•cm -2 ) are characterized to evaluate the influence of ΦCAM on the performance at comparable cathode thicknesses. These are, approximated by the relative density of the cathode and its mass, in the range of 73 μm to 85 μm (Table ). All composites were first cycled at a constant C-rate of 0.134 C assuming a theoretical specific capacity of 300 mAh•g -1 (corresponding to 0.1 C assuming a theoretical capacity of 400 mAh•g -1 for full delithiation). Afterwards, rate capability was tested at constant current densities instead. An overview of all 0.134 C rates in terms of current densities, and all current densities in terms of C-rates, is given in Table of the Supporting Information. In addition, scanning electron micrographs and energy dispersive X-ray spectroscopy signals are shown in Figure characterizing the composite microstructures. voltage with weakly pronounced features below 1.9 V. In this regime, delithiation is charge balanced by oxidation of Fe 2+ to Fe 3+ corresponding to the nominal compositional range of Li2FeS2 to Li1.5FeS2 and the profiles of the solid-state cathodes agree well with reports using liquid electrolyte (dashed line in Figure ). 10 At 1.9 V, a voltage plateau representing the two-phase regime of Li1.5FeS2-Li0.5FeS2 establishes.
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Furthermore, solid-state cells show significantly lower Coulomb efficiencies in the first cycle with values between 77% and 82% in the solid-state, compared to ≈90% in the liquid electrolyte based cells. Low first cycle efficiencies are common in other solidstate battery chemistries, e.g., using Li(Ni,Co,Mn)O2 as active material and generally, they are related to contact losses between the active material and the SE due to volumetric expansion as well as the formation of a SE-CAM interphase (CEI). The capacity retentions reflect the low initial efficiency in the first cycle, with gradual capacity losses afterwards (Figure ). The capacity retentions are comparable in general, but cathodes with the highest ΦCAM show a lower overall capacity retention of 73% (average Coulomb efficiency of 98.3%) compared to 85% (average Coulomb efficiency of 99.5%) for cathodes with the lowest ΦCAM after 40 cycles. Given the special role of the first charge cycle, these relative retentions and average efficiencies are referring to or count from the second charge onward. In addition to the capacity retention with ongoing cycling, the rate capability was tested for exemplary compositions of ΦCAM = 0.32, 0.51 and 0.74 (Figure ). In agreement with the constant C-rate cycling, no strong compositional trends can be observed in the rate retention upon first visual inspection of the data.
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The initial cathode utilization is related to the transport given that it is a measure of the contacted and electrochemical active CAM in the composite, i.e., how accessible and at which rate active material particles are for both charge carriers. In the following, the initial cathode utilization is measured by the average capacity per gram CAM QCAM. The average includes both, the average over the first five cycles (excluding first charge) of each individual cell, and the average and standard deviation of all cells investigated with the same composition. Porous electrode theory can guide the understanding of these trends given that it aims to describes the reaction rate distribution throughout the cathode, as quantified by the δ-parameter (Eq. 4, Figure ). With that, the δ-parameter (Eq. 4, Figure ) should be This is the case for all composites in the range of ΦCAM = 0.32 to 0.74 at 0.134 C and with thicknesses between 85 μm and 73 μm (Figure , right). For these cells, the δparameter ranges between 0.3 and 2.8 (Figure ). Consequently, the δ-parameter analysis predicts high uniformity of the reaction rate distribution and gives a rational for the marginal changes in cathode utilization. Increasing the cathode thickness and, considering constant C-rates, the applied current density, increases the value of δ from 2.8 to 6.3 and 11.1, moving away from the desired condition of δ ≲ 1 and explaining the decrease of the cathode utilization going to a thick electrode configuration. For the edge case of pure Li2FeS2 as cathode, the δ-parameter significantly increases to ≈300
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driven by the orders of magnitude loss in effective ionic conductivity (Figure ). This strong increase manifests as a 90% decrease of the cathode utilization. With that, the δ-parameter captures the observed trends in the initially achieved capacities qualitatively. Moreover, a decrease of QCAM with the logarithm of δ can be observed, acknowledging the scattering in the dataset (Figure ). Not considered in this analysis is the residual porosity of the electrodes. Nonetheless, given that the relative density does not change significantly with an average of 85±3% for all investigated electrodes, the effect is assumed to be negligible in first approximation.
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This qualitative trend agrees with literature results considering the 𝛿-parameters approximated from reported values of σ, i and L. Systems that indicate first signs of transport limitations and underutilization of the electrode are characterized by values of ≈19 (LiNi0.6Co0.2Mn0.2O2-Li3PS4) , ≈22 (LiCoO2-Li10GeP2S12) and ≈31 (Graphite-Li6PS5Cl) . Moreover, Bradbury and coworkers showed that severe reaction fronts occur in Li-S cells that are characterized by a δ-parameter of ≈200 agreeing with the significant utilization loss when going to pure Li2FeS2 (δ ≈ 300).
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The relatively small variations in QCAM by 15% between all ΦCAM of comparable thickness, and by 7% when doubling the cathode thickness at constant composition, rationalized by the δ-parameter analysis, are promising outlooks for the Li2FeS2 battery chemistry. While these are significant changes to the cathode utilization, the loss in utilization is marginal compared to the areal loading increase 1.8 mAh•cm -2 to 3.7 mAh•cm -2 with increasing ΦCAM, and to 7.3 mAh•cm -2 upon increasing the cathode thickness. This increase of the areal loading by a factor of approximately five compensates the at maximum 22% loss in cathode utilization, so that the achieved areal capacities increase from 1.2 mAh•cm -2 to 4.4 mAh•cm -2 going from the lowest to the highest areal loadings (Figure ). Clearly, the higher δ -for instance in thicker electrodes -the more deviations of the attained capacity to the theoretical capacity can be expected.
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shows that Li5.5PS4.5Cl1.5-Li2FeS2 cathodes with high volume fractions of CAM can be realized successfully. Moreover, the achievable areal capacities can be increased further with the thickness of the cathode. Nonetheless, fast charging is desired for application and the rate capability of the electrodes needs to be considered. Therefore, electrodes with ΦCAM = 0.32, 0.51 and 0.74 (L ≈ 80 μm), and with L = 73, 110 and 145 μm (for ΦCAM = 0.74) have been tested for five cycles per current density step, starting with a current density corresponding to the theoretical rate of 0.134 C (respective current densities listed in Table ). Subsequently, the applied current density was stepwise changed between 0.6 mA•cm -2 and 5.1 mA•cm -2 . This routine was chosen to compare the composites at constant current densities despite changes to the cathode loading and with that the C-rates. The average capacity QCAM of the five charge cycles per current density step, and the average of triplicates as well as their standard deviation, are considered in the following discussion. The rate retention as a function of the applied current density is shown in the Supporting Information (Figure ).
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where I is the applied current (in mA) and Qexp(I) (in units of mAh) is the experimentally achieved capacity at that current. Thereby, this definition of rate differs from the definition of the C-rate by relating the current to a practical rather than a theoretical capacity. With that, the inverse of the practical rate directly represents the time in which the charge was acquired. 41 The cathode utilizations as a function of the practical rate are shown in Figure . At the highest applied current density, cathodes with ΦCAM = 0.32 and 0.74 and comparable thickness achieve similar capacities of 55 mAh•g -1 and 51 mAh•g -1 , respectively. Nonetheless, this capacity is achieved at a significantly higher practical rate of 14.9 h Applying this model, Eq. 7 describes the rate performance of the investigated cathodes (dashed lines in Figure ). Moreover, the resulting parameters τ and n confirm the initial hypothesis from visual inspection with both showing a detrimental linear increase with the areal loading of the cathode (Figure ). To understand this observation, we again consider the δ-parameter introduced in the porous electrode theory. While at a rate of 0.134 C, the δ-parameter was close to unity for most of the investigated cathodes, indicating uniform reaction rates and explaining the good cathode utilization even at high CAM volume fractions (Figure ), the average δ-parameter over the investigated current density range δavg is significantly increased. At a composition of ΦCAM = 0.32 this translates to δavg = 3, while for the highest CAM volume fraction and thickness this value is increased to δavg = 22. This significant increase of δavg with increase of ΦCAM and the cathode thickness indicates that nonuniformity of the reaction rate distribution, measured by δavg, can occur as consequence of applying higher current densities. In fact, the parameters τ and n quantifying the rate capability increase linearly as a function of δavg (Figure ) corroborating this hypothesis.
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With that, it can be assumed that the decrease of rate performance with areal loading (Figure ) can at least be partly explained by the onset of reaction rate nonuniformities at higher rates (Figure ). Nonetheless, it must be noted that QCAM cannot be unambiguously related to δ. An overview of all QCAM(ΦCAM, L, i) as a function of δ(ΦCAM, L, i) is shown in the Supporting Information (Figure ). Other factors such as poor ionic contacting of the CAM at high ΦCAM and the increased likelihood of isolated CAM regions in thick electrode configuration can contribute to the decreased cathode utilization and rate performance additionally and are not captured by the δ-parameter analysis.
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Energy density and transport balancing of the cathode. After examination of the initial capacity retention (Figure ) and the rate capability (Figure ), cathode composites are now evaluated regarding their (rate dependent) gravimetric energy density. In agreement with the discussion of the rate capability, the energy density is calculated from the average capacities of five cycles at a certain current density step, and the average and standard deviation of triplicates (with that relating to the data depicted Figure ). Furthermore, only the mass of the cathode, the In/LiIn and the separator are considered for calculation of the gravimetric energy density. The latter two are constant for all investigated cathodes.
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Comparing the gravimetric energy densities for cells with ΦCAM = 0.32, 0.51 and 0.74 as a function of the practical rate (Eq. 6), it becomes evident that the gravimetric energy density can be significantly increased from 11.4 to 41.4 Wh•kg -1 by increasing ΦCAM and the cathode thickness L (Figure ) at low rates. This is, because the areal loading of the cathode is increased from 1.8 to 7.3 mAh•cm -2 , while the simultaneous cathode utilization decrease is negligible in comparison in agreement with the 𝛿-parameter analysis (Figure ). Nonetheless, this strong energy density increase is relativized going to higher rates, i.e., higher applied current densities (overview in Table ). At higher rates, and with that upon increasing 𝛿 significantly, the energy densities of all investigated cells start to converge to ≈5 Wh•kg -1 given the systematic decrease of the rate capability (Figure ) when increasing the areal loading of the cathode.
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This highlights that high energy densities can be practically achieved at low rates, but Li2FeS2/Li5.5PS4.5Cl1.5 solid-state cathodes require further improvement regarding their rate capability. This can be achieved, e.g., by improving the processing of the solid composites and by controlling the particle size distribution of its constituents. Both strategies have the ability to improve the transport properties show the best rate performance (Figure ), and in agreement with the reported rate performances by Minnmann and coworkers. In both cases, this optimum in rate performance is achieved in cathode compositions closest to the condition of σe ≈ σion (diagonal in Figure ) that minimizes the conductivity term of the δ-parameter (Eq. 4, Figure ). Moreover, this analysis shows that the investigated system is strongly limited by σion and that increasing the cell performance is intimately tied to the improvement of the ionic conductivity in the composite (to reach the condition of σe ≈ σion). The highest electrode utilization in the system LiMn2O4/Li3InCl6 44 is also reported at the composition fulfilling the condition σe ≈ σion in agreement with the δ-parameter assessment. Nonetheless, the analysis predicts that the system should suffer from transport limitations in thick electrode configurations and during fast charging (δ ≈ 160)
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In general, this assessment shows that solid-state cathode composites are limited by their ionic conductivity that is <1 mS•cm -1 , while the electronic conductivity between chemistries spreads a wide range and can be optimized more freely by introducing electron conducting additives. Consequently, the search for higher conducting solid electrolytes, and the improvement of the solid electrolyte percolation in the electrode, are of highest importance for the development of solid-state batteries in outlook on application. This need for higher conducting solid electrolyte is further emphasized by the exponential loss in ionic conductivity (Figure ) when increasing the CAM volume fraction in the cathode that is necessary to enable high areal loadings. This additionally shows that good ionically conducting active materials should be explored, as they promise a softening of the loss in effective (ionic) conductivity when going to high volume fractions of active species.
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Lastly, it has to be noted that while the δ-parameter gives an intuitive way of comparing chemistries regarding their electrode utilization, and potential challenges in rate retention, it does not include information about other important metrics such as cycle stability. In addition, the transport discussion in this study is based exclusively on asprepared cathodes, but state-of-charge dependent conductivities should be considered to provide a full understanding of transport-related effects on performance, if available.
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In conclusion, this work highlights the importance of balanced transport in composite cathodes and shows that the "transport quality" of the electrode can be qualitatively The loss in rate capability with increased areal loading motivates studies that focus on processing optimization and particle size matching as strategies to improve transport in cathodes with high areal loading. This is because improving the partial ionic conductivity will lower the δ-parameter independent on electrode thickness and applied current density. Moreover, this work highlights the importance of investigating electrodes with realistic energy densities already on the lab-scale. Thereby, the potential of new cell chemistries in outlook to application can be evaluated from the start and problems can be targeted before upscaling of the technology is attempted.
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Aqueous solutions containing amine-based molecules is a promising class of absorbents for direct air capture (DAC) of CO 2 . For CO 2 to traverse the gas/liquid boundary, it must pass through the interface. Although interfaces represent only a minor fraction of the total solvent molecules, they serve as crucial bottlenecks for controlling CO 2 transport and reactivity. A detailed molecular picture of how CO 2 moves from air into the aqueous phase and interacts with water and absorbents in the interfacial region could reveal valuable strategies to accelerate DAC. A complete understanding of the CO 2 capture mechanism requires investigating CO 2 behavior at both neat and tailored interfaces. This study aims to explore CO 2 behavior at the pure air-water interface using machine learning interatomic potentials trained based on density functional theory (DFT) calculations and contrasts them with the results from classical simulations that lack the explicit account of polarization effects.
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The air-water interface forms a unique heterogeneous environment distinctly different from the bulk phase. Characterizing CO 2 behavior at these dynamically evolving interfaces requires understanding how interfacial water structure and dynamics influence CO 2 adsorption, desorption, diffusion, and reaction rates. The nanoscale region between air and water governs the flux at which CO 2 transfers into the aqueous phase, where it subsequently interacts with absorbent molecules. The flux is indirectly affected by the anisotropy of intermolecular interactions between water and CO 2 within the instantaneous water surface, dictating the structuring and dynamics of CO 2 at this boundary. Previous studies of CO 2 at the aqueous interface have largely relied on ensemble-averaged descriptions, such as interfacial tension, width, and molecular orientation from such tech-niques as Vibrational Sum-Frequency Generation spectroscopy (VSFG), Second Harmonic Generation (SHG), or X-ray spectroscopy. However, the role of interfacial barriers and solvent effects on CO 2 transport into the aqueous phase remains poorly understood. Classical models can enable the study of long timescale behavior but often lack accuracy, while ab initio molecular dynamics (AIMD) can provide a more accurate description, but limited to short timescales due to high computational expense. To address this gap, we developed neural network potentials to describe the bulk and interfacial water in the presence of CO 2 trained on data from AIMD simulations performed using the revPBE density functional with the DFT-D3 dispersion correction. This choice of the DFT method provides a good balance between the accuracy and computational cost, given its superior performance in capturing both bulk and interfacial properties among the family of generalized gradient approximation (GGA) methods. Although more advanced ab initio methods could enhance the quality of the NNP potentials, the required timescales and system sizes to develop such potentials and accurately capture interfacial properties remain difficult to achieve, even with current computational capabilities. Using neural network potentials, we aimed to improve the accuracy of classical potentials to describe the structure and dynamics of CO 2 in the interfacial region. This work characterizes the interfacial chemical processes controlling the transport of CO 2 through the interfacial phase boundary. Understanding these processes is crucial to develop a complete understanding of the direct air capture of CO 2 at the air/water interface and explain why CO 2 reactions with amino acids are kinetically accelerated at these interfaces, as revealed by our recent study. Herein, we find that the free energy of CO 2 transport from the air to the aqueous phase is influenced by the distribution or the spread of instantaneous water molecules, creating a unique coordination environment for interfacial CO 2 . In this study, extensive AIMD simulations were carried out on 3 bulk and 4 air/water interface systems. Each system was simulated for at least 40 ps, with a total of over 280 ps of AIMD simulations. From these simulations, 280,000 snapshots were extracted and used to train the NNP models, with details provided in the SI. We then employed the trained neural network potentials in LAMMPS patched with DeepMD-kit to simulate air-water systems with two interfaces, initially placing CO 2 randomly in the simulation cell at a partial pressure of about 0.145 atm. This pressure, which is relevant for direct air capture, is sufficiently low to accurately compute interfacial properties while minimizing CO 2 clustering and bubble formation observed at higher concentrations. We performed additional simulations doubling the CO 2 concentration and observed a similar potential of mean force (PMF) for CO 2 along the z axis (Figure ). This indicates that at the studied concentrations, the PMFs remains almost unaffected, validating our system for investigating structure and dynamics under DAC conditions. However, further increases in CO 2 concentration would begin to impact interfacial properties such as interfacial tension and width. The analysis of the interfacial systems by Niblett et al. suggests that the results for certain properties such as water density distribution and orientation remain largely unaffected when explicitly modeled long-range effects are introduced. Recent studies showed that a comprehensive training on both bulk and interfacial systems can provide more accurate description of the interface, where the symmetry of the intermolecular interactions is broken and the long-range interactions are anisotropic. In this study, we followed this strategy of extensive training, ensuring that both the bulk and interfacial results are comparable. Importantly, in the systems without ions present at the interface, it is indeed possible to achieve accurate results without a significant increase in error for interfacial systems. The RMSE in energy and forces are obtained to be < 1 meV/atom and < 100 meV/Å respectively for both bulk and interface (Table ), showing similar errors for trained NNP model. In cases where ions are introduced, explicit treatment of long-range electrostatics may be required to capture the correct behavior. Additional technical details are provided in the SI.
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Herein, we first compared the radial distribution functions (RDFs) and coordination numbers between O H2O -O H2O atoms in the bulk aqueous phase, modeled using AIMD and two NNP models, with cutoff radii of 7 Å and 8 Å. Two cutoffs were tested to ensure they adequately captured the intermolecular interactions between CO 2 and water. The RDFs were compared against experimental RDF data from reference 33. Our pair-correlation results indicate only minimal deviations in the RDFs be-tween the AIMD and NNP models, with the AIMD simulations exhibiting good agreement with the water-water interactions similar to previous AIMD studies (Figure A and B). Moreover, the NNP models demonstrated excellent consistency with AIMD in terms of water coordination numbers. Recognizing that CO 2 can interact with water at two distinct sites-either the carbon atom (C CO2 ) with the oxygen atom (O H2O ) or the oxygen atom (O CO2 ) with the hydrogen atom (H H2O )-we computed the RDF and coordination numbers for both interaction types (Figure ). The overall shapes of the CO 2 -H 2 O interaction RDFs are consistent with previous studies. The smaller cutoff (7 Å), slightly overestimated coordination numbers for CO 2 -water interactions, whereas the larger cutoff of 8 Å accurately reproduced experimental structural arrangements. This highlights the importance of using larger cutoffs to accurately model structural properties of weakly bound CO 2 .
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We then characterized the distribution of CO 2 at the air-water interface in terms of the density profiles along the z-axis (Figure ). We observe that the NNP force fields showed a greater density of CO 2 within the interfacial region compared to the SPC/E and two other classical water models (TIP4P and TIP5P) (Figure ). The respective PMFs associated with CO 2 adsorption within the interfacial region show significant difference in the well depth and the barriers associated with both the desoprtion of CO 2 from the interface and the transport of CO 2 to the aqueous phase (Figure ).
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For both NNP and classical models, the desorption barrier of CO 2 from the interface to the air phase is observed to be lower than the barrier for transport into the aqueous phase. The free energy of CO 2 desorption from the classically modeled interface to the air phase is ∼ -0.7 kcal/mol lower than that from the NNP-modeled interface (Figure ). Similarly, the free energy required for CO 2 transport from the interface to the aqueous phase is ∼ -0.65 kcal/mol lower for the classical model compared to the NNP model. Other classical models showed similar PMFs compared to SPC/E (Figure ). Despite these variations, both the NNP and classical models reveal consistent differences in the thermodynamics of CO 2 adsorption and desoprtion. Collectively, these results suggest that a CO 2 molecule at the interface is more likely to move to the air phase than into the aqueous phase. To quantify how these barriers affect the rates of transport, we employed transition state theory in the harmonic approximation to obtain and compare the rate constants (k) for CO 2 desorption and transport into the aqueous phase using the equation:
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where, h is the Planck constant, T is the temperature and k B is the Boltzmann constant, ∆W represents the free energy barrier for CO 2 desorption to the air phase or transport into the aqueous phase. To obtain the relative differences in the rates between the NNP and classical model, we used
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where k NNP , ∆W NNP , k classical , and ∆W classical represent the rate constants and free energy barriers for the NNP and classical models, respectively. For the classical model, the difference in barriers results in a desorption rate that is ∼ 2.3 × faster for CO 2 desorption from the interface to the air phase than for CO 2 transport into the aqueous phase. In the case of the NNP model, CO 2 desorption is ∼ 3.0 × faster than its transport to the aqueous phase. For both systems, the desorption rate of interfacial CO 2 is faster than its transfer into the aqueous phase because, unlike air, CO 2 must penetrate the interfacial hydrogen-bonding network, moving layer by layer-such as from interfacial water layers 1 to 5 (which have intrinsic viscosity) before reaching the bulk. This process is energetically less favorable, leading to slower transport rates of CO 2 phase transfer into the aqueous phase. These results highlight that the asymmetric interactions at the air-water interface play a significant role in governing the free energies of CO 2 transport, ultimately influencing the rates of CO 2 uptake into the aqueous phase. It is important to understand the role of fixed charge distribution at the interface in stabilizing CO 2 within the interfacial region. Therefore, we computed the electrostatic potential along the z-axis for both the classical and NNP models (Figure ). The electrostatic potential, based on the interactions along the z-axis, is calculated using the equation:
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where ϵ 0 is the vacuum permittivity, ϵ r is the relative permittivity (taken as 1), and ρ c (z) represents the charge density distribution along the z-axis. Since the NNP model does not directly provide atomic charges, we applied classical atomic charges obtained from the SPC/E water model to the coordinates obtained from the NNP simulations. We found that CO 2 in the classical model would be electrostatically more strongly attracted to the interface, which exhibit a more negative electrostatic potential (∼ -0.3 V) compared to the NNP model. If these interaction are key then CO 2 molecules, FIG. : Electrostatic potential along the z-axis for both the systems modeled using the classical and neural network potentials. We used the classical charges and NNP simulation coordinates to obtain the electrostatic potential profiles.
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whether in the air or aqueous phase, would be more likely drawn to the interface in the classical model than in the NNP model. In contrast, the PMF analysis shows that CO 2 move more easily between the two phases in the classical model due to lower energy barriers, as compared to the NNP model. The opposite trends between the electrostatic potential profile and PMF data indicate that, while electrostatic potential based on fixed point charges reveals local electric fields and potential wells at the interface, it does not fully capture the free energy landscape governing molecular transport. The latter includes electrostatic contributions from induced charges and polarization together with the thermally induced sur-face fluctuations, and solvent effects from asymmetric interactions with interfacial water molecules. To get more details into the solvent effects, we computed the radial distribution function (RDF) between the carbon atom of CO 2 (C CO2 ) and the oxygen atom of water (O H2O ) at the interface using instantaneous interface definitions. Likewise PMFs on Figure , the RDFs (Figure ) show stronger interactions between CO 2 and water in the NNP model compared to the classical model, pointing to differences in the solvent effects controlling CO 2 transport across the liquid phase boundary. In the classical model, the weaker total solvation effects at the interface results in CO 2 moving back and forth between the interface and either the air or bulk aqueous phase, decreasing its residence time in the truly interfacial layer and speeding up its dynamics at the interface. To investigate this behavior further, we computed the survival probability of CO 2 in the interfacial layer. Specifically, we calculated the probability of finding CO 2 at a later time t, given its presence in the instantaneous layer at t = 0 (Figure ). The results showed that the survival probability decayed more rapidly in the classical model compared to the NNP model, indicating faster dynamics of CO 2 at the air-water interface when modeled with classical potentials. Similarly, faster dynamics of H 2 O was observed in the classical system compared to the NNP system (Figure ). Moreover, we observed significant differences in the spread of the PMF and electrostatic potential (due to wider charge density distribution, Figure ), which we attribute to variations in the surface fluctuations at the interfaces modeled using classical and NNP potentials. To quantify the extent of these surface fluctuations, we employed a method similar to that described in ref. . First, we computed the density profiles of water and CO 2 in the instantaneous layers (Figure ). These density profiles were fitted to the Gaussian distribution function and the standard deviation σ is used to compute the Full Width at Half Maximum (FWHM) as 2 2 ln(2) σ, which is used to characterize the spread of the surface fluctuations (Figure ). The FWHM was calculated to be 2.94 Å for the classical model and 3.07 Å for the NNP model, indicating that water is more widely spread at the interface in the NNP model. This wider spread of interface leads to larger surface fluctuations compared to the classical model, possibly contributing to the free energy associated with the CO 2 transport from air to the aqueous phase. As a result, significant differences in the charge distribution (Figure ) and orientation of water at the interface were observed between the two models (Figure ). Specifically, in the NNP model, water molecules demonstrate a more pronounced spread of water tilted toward the air phase (with similar maximum cos values) within the interfacial region (the overall water orientation behavior is consistent with previously observed DFT-MD results ) compared to the classical model. This pronounced tilt-where the hydrogen atoms of H 2 O are more oriented (thicker water layer showing tilt in the NNP model compared to classical water model) toward the air-along with slower water dynamics (as shown by the water O-H vector orientation in Figure ), creates favorable configurations for stronger interactions between water and CO 2 . Consequently, the free energy barrier for CO 2 transport from the interface into the aqueous phase rises, driven by the combined effects of enhanced surface fluctuation-induced capillary waves, extended molecular orientation, and improved solvation. In summary, we studied the structure and dynamics of CO 2 at the air-water interface using machine learning simulations and compared the results with classical forcefields simulations. Our findings reveal significant differences in the distribution, dynamics, and free energy associated with CO 2 transport to the aqueous phase. Specifically, we observed that the classical force fields underestimated the free energy barrier for CO 2 transport and exhibited weaker interactions between CO 2 and H 2 O at the air-water interface compared to neural network potentials. First-principles accuracy is essential for computing CO 2 thermodynamics and kinetics at evolving interfaces, as these simulations inherently include explicit polarization effects necessary for accurately describing interfacial chemical and transport processes. Despite stronger interfacial electrostatic potential from a fixed point-charge model, CO 2 interacts weaker with classical water. These weaker interactions resulted in faster adsorption and desorption kinetics at the air-water interface. We observed enhanced surface fluctuations and interface broadening for the NNP compared to the classical model. The contributions from the thermal surface fluctuations and solvent rearrangements are often overlooked but are essential for accurately characterizing chemical reactions and transport processes at the interface, and should be considered when using computational methods to model interfacial chemical reactions and transport properties.
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Group 13 complexes featuring the imide ligand, [NR] 2-, have attracted significant recent attention (particularly in the case of aluminium) both as probes of potential M-N multiple bonding, and as precursors to materials offering applications in H2 storage or as semiconductors. Thermolytic loss of H2 (or other small organic molecules) from amine adducts or metal amides was initially exploited synthetically; more recently, reactions of aluminium(I) reagents, Ln(X)Al, with organo-azides, RN3, have been developed, which proceed via release of N2 and net oxidation of the metal centre to Al(III). Structurally, the high polarity of the Al-N bond provides a strong thermodynamic incentive for aggregation, and terminal imide complexes of the type Ln(X)Al(NR) are often very labile, undergoing a range of onward reactions, including oligomerisation, ligand activation, or uptake of a further equivalent of azide. Isolated imides of this type are therefore rare, and have been obtained only when very bulky aryl azides are employed (Figure ). As such, the first example of an aluminium imide featuring both two-coordinate aluminium and nitrogen atoms (V) was isolated by employing extremely bulky terphenyl ligands at both centres. Another type of Al(I) precursor that has been employed in this chemistry are anionic aluminium(I) ('aluminyl') reagents, [AlX2] -, which give rise to negatively charged aluminium imide complexes, [X2Al(NR)] -stabilised through secondary interactions (typically) with alkali metal counter ions. Advances in aluminyl chemistry, mean that these anionic imide systems have formed the basis for a range of recent studies of small molecule reactivity. In preliminary reactivity studies, K2[VII]2 has been shown to be capable of cleaving strong bonds: activating H2 via 1,2-addition across the Al-N bond, or taking up two equivalents of CO via C-O cleavage and C-C bond-forming steps to generate a fourmembered AlOCC ring, featuring a pendant imine function (K2[X]2, Scheme 1). K2[VII]2 also undergoes cycloaddition reactions, and acts as a transfer reagent for the [NDipp] 2-function towards a range of unsaturated oxygen-containing substrates. As such, the conversion (by cycloaddition chemistry) of CO2, N2O and PhCHO to DippNCO, DippN3 and PhCHNDipp, respectively, has been demonstrated. In similar fashion, Coles has reported the [2+2] cycloaddition reaction between imide K2[VIa]2 and CO2, affording an isolable aluminium carbamate complex. Here we report the first examples of isolable terminal aluminium and gallium imides bearing a heteroatom substituent at nitrogen, and investigation of the effects of the substituent on electronic structure and reactivity. In particular, the reactivity of these imide systems towards CO and N2O is investigated, and we demonstrate that they can act as transfer reagents for the [N] 3- ion.
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Given that aluminyl compound K2[(NON)Al]2 reacts with trimethylsilyl azide to form a tetrazene complex by the uptake of two equivalents of substrate, we targeted the use of more sterically demanding silyl substituents to generate isolable aluminium silylimide compounds. We hypothesized that the cycloaddition of a second equivalent of azide would be less facile in the presence of greater steric bulk. Accordingly, the reaction of K2[(NON)Al]2 with triphenylsilyl azide in benzene leads to the rapid evolution of gas and the rapid precipitation of fine needles of the target imide K[(NON)Al{N(SiPh3)}], K[1a], as determined by H NMR spectroscopy and X-ray crystallography (Scheme 2 and Figure ). Pr methine signal at dH = 3.92, 2.87 ppm). Single crystals of the product K[1a] can be studied by X-ray crystallography, and although the quality of the data means that caution must be exercised with the structural metrics, the formation of the anionic [(NON)Al{N(SiPh3)}] -unit, bridged by K + cations (to give a 1-D coordination polymer) is unequivocally demonstrated (Figure ). K[1a] is sparingly soluble in hydrocarbon solvents, and attempts to dissolve it in THF lead immediately to the activation of the solvent via C-H bond cleavage across the Al-N bond, affording K[(NON)Al{NH(SiPh3)}(C4H7O)], K [2]. As such, K[1a] can be characterised by H NMR and X-ray diffraction only. The activation of THF in this way, effectively via deprotonation, mirrors the previously reported benzylic activation of toluene by the putative imide K[(NON)Al{N(SiMe3)}], and speaks to the strongly basic nature of the imide nitrogen.
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In the solid state THF-activation product K[2] also adopts a polymeric structure, in which K + counter ions bridge between the NON-Dipp group and the activated C4H7O moiety of one molecule and the SiPh3 unit of a neighbouring molecule (Figure ). The Al1-N3 distance is 1.871(3) Å, i. For comparison, gallium imide complex K[(NON)Ga{N(SiPh3)}], K [3], was also prepared via the reaction of the analogous potassium gallyl compound K2[(NON)Ga]2 with triphenylsilyl azide. Like its aluminium congener K[1a], K [3] rapidly crystallises as fine needles from benzene, although in this case these are unsuitable for X-ray crystallography. K [3] gives rise to a near identical 1 H NMR spectrum to K[1a], with characteristic resonances at dH = 6.75/6.39 (xanthene aromatic CH) and 3.77/2.94 ppm (Dipp i Pr methine). Unlike K[1a], K [3] is unreactive towards small amounts of THF, and it can be solubilized by reaction with 2.2.2-cryptand to enable the acquisition of C NMR data. Although its molecular structure in the solid state could not be determined crystallographically, the formulation K[(NON)Ga{N(SiPh3)}] is also implied by its onward reactivity (see below).
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Given the (coordination-) polymeric nature of K[1a], we hypothesized that employing less symmetric silyl substituents or those without a SiPhn moiety might result in less strongly aggregated (and by implication more soluble) imide derivatives. As such, aluminium imides bearing Si t BuPh2 or Si i Pr3 substituents were targeted. The reaction of K2[(NON)Al]2 with t BuPh2SiN3 can be shown by in situ 1 H NMR monitoring to lead to clean conversion to a single product. Uptake of only one Si t BuPh2 unit per NON ligand backbone is indicated by integration of the signals at dH = 1.28 ( t Bu) and 7.95 ppm (ortho CH) associated with the silyl group with respect to the NON backbone signals at dH = 6.38 and 6.73 ppm. Gratifyingly, the silylimide product in this case is soluble in aromatic solvents, and crystals suitable for X-ray diffraction (and elemental microanalysis) could be obtained from benzene solution, confirming the formation of K[(NON)Al{N(Si t BuPh2)}], K[1b] (Scheme 2 and Figure ). In the solid state, K[1b] also adopts a polymeric structure analogous to that of K[1a]. The Al-N and N-Si distances (1.7351(15)/1.7304(15) and 1.6576(14)/1.6584(15) Å, for the two molecules in the asymmetric unit) are also similar to those of K[1a] (1.740(6)/1.730(6) and 1.657(6)/1.644(5) Å). The Al-N-Si angle is somewhat wider for K[1b] than for K[1a] (138.73(9)/138.99(9)° vs 131.0(3)/130.9(3)°), presumably on steric grounds, although both are narrower than the corresponding Al-N-C angle observed for Dipp-substituted imide K2[VII]2 (146.43(17)°). Interestingly, the O-Al-N-Si dihedral angles (56.44(16), 55.00(16)°) measured for K[1b] differ significantly from those measured for either K[1a] or K2[VII]2 (37.6(5)/41.9(5) and 75.9(4)°), presumably reflecting not only the differing steric profiles of the imide substituents, but also a degree of angular flexibility consistent with the minor role of Al=N p bonding. Potassium aluminyl compound K2[(NON)Al]2 was also reacted with i Pr3SiN3 to afford K[(NON)Al{N(Si i Pr3)}], K[1c]. In this case, although the reaction proceeds quantitatively (as judged by in situ 1 H NMR monitoring), attempts to isolate the product at room temperature invariably lead to decomposition, and K[1c] was therefore prepared and used in situ for onward reactivity studies. The formulation of K[1c] as K[(NON)Al{N(Si i Pr3)}] is implied by its onward reactivity (see below). Finally, with a view to expanding the scope of heteroatom derived N-substituents, K2[(NON)Al]2 was reacted with {(HCNDipp)2B}N3 targeting the formation of an aluminium borylimide. While this proves to be feasible, the compound so generated K[(NON)Al{NB(NDippCH)2}], (K[1d]) is also extremely labile, decomposing rapidly in solution, and (more slowly) in the solid state. An in situ acquired 1 H NMR spectrum, features signals consistent with a symmetric NON ligand environment (e.g. two 2H doublets for the xanthene backbone at dH = 6.14 and 6.57 ppm), and an unsymmetrical diazabutadiene environment (e.g. two mutually coupled 1H NCH backbone signals at dH = 5.96 and 6.28 ppm). The 11 B NMR signal shifts from dB = 19.5 ppm for the parent azide compound to dB = 24.8 ppm. K[1d] is highly unstable, decomposing very rapidly in solution; nonetheless, the molecular structure of K[1d] could be determined from single crystals grown rapidly from supersaturated solution (minimal solvent) at 283 K and immediately harvested/manually separated for data collection (Scheme 3). In the solid state K[1d] adopts a monomeric structure (in contrast to K[1a] and K[1b]), with the tendency to aggregate via bridging K + /arene interactions being frustrated by encapsulation of the potassium counterion between the bulky boryl and aluminylderived Dipp groups of the same imide complex. Within the [(NON)Al{NB(NDippCH)2}] -unit, the Al-N distance (1.739(2) Å), Al-N-B angle (136.6(2)°), and O-Al-N-B torsion (61.8(3)°) mirror closely the corresponding geometric parameters measured for K[1b]. The B1-N3 distance, on the other hand is relatively short (1.387(4) Å; cf. 1.55 Å for the sum of the respective covalent radii, and 1.498(4)/1.510(4) Å for the other B-N distances associated with the diazaborolyl unit), suggesting that pdelocalization from the imide nitrogen into the B-centred heterocycle is structurally significant, (in contrast to Al=N p bonding).
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In order to probe the electronic structures of aluminium/gallium silyimides [1a] -, [1b] -, [1c] -and [3] -quantum chemical calculations were carried out using Density Functional Theory at the r2scan-3c level using the complete anionic component in each case (see ESI for details). The calculated geometries for crystallographically characterized imide anions, [1a] -and [1b] -, are in good agreement with those determined experimentally, in particular the key bond lengths and angle relating to the Al-N-X unit (Table ).
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1.724 1.740( q(M) 2.127 2.114 2.095 1.904 q(N) -1.919 - For all complexes examined, the HOMO is a p-symmetry orbital centred primarily on the imide nitrogen, and orientated perpendicular to the Al-N-X plane; the corresponding HOMO-1 in each case defines a second N-centred p-symmetry orbital lying perpendicular to the HOMO, and stabilised by the mixing in of N s-orbital character within the bent Al-N-X unit. The LUMO in all cases is xanthene ligand-based. Within the aluminium silylimide series [1a] -, [1b] -and [1c] -, sequential stabilization of both the HOMO and HOMO-1 orbitals is observed on going from N(Si i Pr3) derivative [1c] -to N(Si t BuPh2) system [1b] -and finally N(SiPh3) complex [1a] -(Table ). This trend reflects the possibility for pdelocalization involving the Si-C s* orbitals, and the relative pacceptor capabilities of the silyl substituents, Si i Pr3 < Si t BuPh2 < SiPh3. In addition, in the case of the HOMO-1 orbitals, the narrowing of the Al-N-Si angle (Si i Pr3 > Si t BuPh2 > SiPh3), presumably on steric grounds, would be expected to lead to greater N 2s character (less 2p character) in the N-centred lone pair and consequent energetic stabilization. The dominant overall effect appears to be the stabilization of the HOMO-1, such that the energetic separation between the two N-lone pairs increases in the order Si i Pr3 < Si t BuPh2 < SiPh3.
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Consistent with the relative p-acceptor capabilities (Si i Pr3 < Si t BuPh2 < SiPh3), the N-Si bond lengths decrease slightly (and To gain additional insight, the M-N bonds were analysed using the ETS-NOCV method, to identify the key contributions to the orbital interaction term DEorb (Table ; ESI). Cationic [(NON)M] + and dianionic [NR] 2-fragments were chosen as reference states. Within this scheme, the M-N bond is comprised of both s and p interactions, with the latter split into a pair of mutually orthogonal components. For the aluminium imides, s interactions account for ca. 52-57% of DEorb, and p interactions ca. 25-30%, while for
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The activation of carbon monoxide by amide reagents has recently proven to be of significant interest. For example, it has been shown that simple lithium amides can effect Fisher-Tropschlike CO homologation processes, while the introduction of silyl substituents (as in, e.g., K[N(SiMe3)2]) leads to the conversion of CO to cyanide salts or organic isocyanides. Previous work in our group has shown that aluminium imide K2[VII]2 reacts with CO via C-O bond cleavage and C-C bond formation steps, to give K2[X]2 in which the N-aryl linkage is retained (Scheme 2). Given the greater lability of N-Si (over N-C) bonds, we were keen to investigate the reactions of aluminium and silyl imides towards CO and other small molecules, with the aim of exploring the possibilities for nitride transfer chemistry.
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The reaction of K[1a] with CO in benzene unfortunately leads to the formation of an inseparable mixture of poorly soluble products. The analogous reaction of the more soluble imide K[1b] initially also produces several products; however over the course of two weeks, conversion to a single major compound, K2[(NON)Al{O2C(Si t BuPh2)}(CN)]2, K2[4b]2, is observed by 1 H NMR spectroscopy (Scheme 4). This compound could be crystallised only in relatively low yields (10-15%) due to its high solubility, but this did allow the molecular structure in the solid state to be determined, revealing the formation of cyano and silylcarboxylate ligands (Figure ). Moreover, consistent with the solid-state structure, the 13 C{ 1 H} NMR spectrum of K2[4b]2 features a signal at dC = 187.7 ppm associated with a silylcarboxylate group. NMR spectroscopy (Scheme 4). This compound could also be crystallised, in this case in ca. 35 % isolated yield. The molecular structure in the solid state was determined crystallographically (Figure ), and K2[4c]2 was also characterised by standard spectroscopic techniques and elemental analysis. The IR spectrum shows diagnostic bands at 2126, 1640, 1587, 1486 and 1417 cm -1 . The band at 2126 cm -1 is weak and corresponds to the CN stretch; the remaining four bands are stronger and correspond to the symmetric and asymmetric stretching modes of the carboxylate C-O bonds, and two vibrations of the ligand backbone. In a similiar fashion to K2[4b]2, the C NMR spectrum of K2[4c]2 features a signal at dC = 189.6 ppm assigned to the silylcarboxylate group.
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The cyanide moieties bridge between aluminium and both potassium ions, while the carboxylate groups bridge between aluminium and a single potassium cation. The Al1-C2 and Al1-O2 distances (e.g. 2.0263(18) and 1.7891( ) Å for K2[4b]2) are similar to those found in comparable complexes. The C2-N3 bond length The conversion of aluminium imides to carboxy/cyanide complex--es has been investigated by quantum chemical methods carried out using the model system [1a'] -(in which the K + cations were removed, and the NON backbone t Bu groups replaced by methyls for computational efficiency) (Scheme 5). The minimum energy reaction pathway closely resembles the previously reported and (experimentally supported) mechanism for the reaction of [VII] - with CO, both (i) in the formation of Int3 through the uptake of CO, and the formation and isomerization of a side-on bound isocyanate complex, and (ii For comparative purposes, we also examined the reactivity of gallium silylimide K [3] towards CO. Treatment of a suspension of gallium imide K [3] in benzene-d6 with CO, resulted in clean conversion to a single new product K2[(NON)Ga{O(SiPh3)}(CN)]2, K2 [5]2, over the course of six days as judged by in situ 1 H NMR spectroscopy (Scheme 6). The rate of this reaction is limited by the low solubility of the imide starting material in benzene-d6, but the cyanide-containing product K2 [5]2 can be crystallised in ca. 80% isolated yield. In the solid state K2 [5]2 adopts a dimeric structure related to that of K2[4b]2 and K2[4c]2, albeit with a metalbound siloxide, rather than a silylcarboxylate supporting ligand (Figure ). Within the dimeric framework of K2 [5]2, K + counter ions bridge between two anionic [(NON)Ga{O(SiPh3)}(CN)] -units through interactions with the Dipp and cyanide groups. The Ga1-C1 distance (2.0463(18) Å) is similar to those found in comparable complexes (e.g. {HC(MeCDippN)2}Ga( t Bu)CN, 2.028(8) Å), and the C1-N3 distance (1.148(2) Å) is statistically identical to those observed for the related aluminium cyanide complexes K2[4b]2 and K2[4c]2. The presence of the cyanide ligand is also confirmed by the presence of two closely spaced bands at 2070 and 2080 cm -1 in the IR spectrum of K2 [5]2.
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Mechanistically, this reaction is thought to proceed along a similar pathway to that determined for the aluminium imide systems to generate an intermediate similar to Int3 (Scheme 5), at which point the silyl group migrates from N to O. The difference in reactivity between these aluminium and gallium systems is presumably related to the greater migratory aptitude of the SiPh3 group compared to the Si t BuPh2 and Si i Pr3 groups, and potentially the greater electronegativity of gallium over aluminium.
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Given the ability of both aluminium and gallium silylimides to convert CO to cyanide, we wanted to examine the reactivity of these systems towards N2O, hypothesizing that a further example of O/N -metathesis might lead to the generation of azide, N3 -. In the event, the reactivity displayed diverges more markedly between the aluminium and gallium silylimides. When aluminium imides K[1a], K[1b] or K[1c] are exposed to an atmosphere of N2O, clean conversion is observed within 10 min to yield the previously reported
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and one equivalent of the corresponding silyl azide (Schemes 1 and 7). Similar reactivity has been reported for the reaction of Dipp-imide complex K2[VII]2 with N2O, which also generates K2[VIIIb]2 together with DippN3. By contrast, when a suspension of gallium silylimide K [3] in benzene is exposed to N2O, no reaction is observed at room temperature. Heating this mixture at 80 °C for 3 d leads to the formation of a single new species, K2[(NON)Ga{O(SiPh3)}(N3)]2, K2[6]2 (Scheme 7), which can be isolated as a microcrystalline precipitate in 61% yield and characterised by standard spectroscopic techniques and elemental microanalysis. Single crystals can be obtained by recrystallization from benzene: in the solid state, azide complex K2[6]2 adopts a dimeric structure, closely related to that of its cyanide analogue K2 [5]2: two anionic [(NON)Ga{O(SiPh3)}(N3)] -fragments are bridged by potassium counter ions to give a centrosymmetric dimer. Both structures feature a five-coordinate gallium centre, the geometry of which lies between trigonal bipyramidal and square pyramidal (t = 0.54 for K2[6]2; 0.78 for K2 [5]2). Approximating to the trigonal pyramidal limit, both complexes feature the OSiPh3 ligand in the equatorial plane, with the CN -/N3 -ligand occupying the apical site trans to the xanthene O-donor. The Ga1-N3 distance is 1.989(2) Å, and the Ga-O2 and Ga-N1/2 distances for K2[6]2 (1.8345( ) and 1.960(2)/1.969(2) Å) are equal within error those measured for K2 [5]2 (1.8312( ) and 1.959(1)/1.965(2) Å). The N3-N4 and N4-N5 distances (1.182(3) Å and 1.152(3) Å) are typical of a terminally-bound azide ligand, and the IR spectrum of K2[6]2 shows a strong absorption band at 2127 cm -1 , which is also consistent with the N3 -ligand. The reactions of both aluminium and gallium silylimides with N2O are postulated to proceed via the formation of a transient metal oxide intermediate, together with an equivalent of silylazide. In the case of the aluminium silylimides, K[1a], K[1b] and K[1c], the (common) oxide intermediate so generated has previously been shown to undergo a [2+3] cycloaddition with further N2O to yield the observed hyponitrite product, K2[VIIIb]2. The putative gallium oxide intermediate, by contrast, would be expected to feature a less polarized Ga-O bond, and instead activates the Si-N bond of the initially generated silylazide 1,2-fashion (to generate azide, N3 -, and siloxide ligands, Ph3SiO -, at gallium). Conceptually similar 1,2-addition reactions of the N-Si bond of a silylazide across M-NR units have previously been reported, leading to the formation of metal-bound azide and silylamide ligands.
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The first examples of terminal aluminium and gallium imides bearing heteroatom substituents have been synthesised via the reactions of formally anionic aluminium(I) and gallium(I) precursors with silyl and boryl azides. These systems vary significantly in their lability in solution, with the N(Si i Pr3) and N(Boryl) complexes K[1c] and K[1d] being extremely labile, on account of the strong s-donor capabilities of the trialkylsilyl and boryl substituents and the consequently high basicity at nitrogen. Phenylsilylimido derivatives offer greater stabilization through the p-acceptor capabilities of the SiR3 group. The N(Si t BuPh2) system K[1b] represents a usable compromise between stability and solubility, and has been completely characterized by spectroscopic, analytical and crystallographic methods. All of the systems examined feature minimal p-bonding between the imide ligand and aluminium/gallium, with the HOMO and HOMO-1 orbitals effectively comprising orthogonal lone pairs centred at N.
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In terms of reactivity, both aluminium and gallium silylimides are found to act as viable sources of nitride, [N] 3-. Aluminium systems react with CO to afford complexes featuring a cyanide unit (together with a silyl carboxylate moiety), while the product of the analogous reaction with a gallium silylimide also contains a cyanide ligand, in this case partnered by a siloxide group. The mechanisms for these transformations are thought to be substantially similar to that determined for the related aluminium NDipp imide (in the presence of CO), with the different ultimate products rationalized in the final mechanistic steps on the basis of the lability of the N-Si bond. Interestingly, the aluminium and gallium silylimides show more divergent reactivity towards N2O, with the gallium system alone being capable of oxide/nitride exchange to generate the azide ion, N3 -. In the aluminium analogues, the imide ([N(SiR3)]
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Artificial Intelligence, sometimes called machine intelligence, is a concept that pertains to the ability of a computer system to acquire knowledge and skills through the analysis of past data ( ). Machine Learning (ML) techniques have been widely employed across various domains, including but not limited to assisted autonomous vehicles, improved speech recognition, medical applications, natural language processing and drug discovery and development ( ).
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Drug discovery and development pipelines are extensive, intricate, and contingent upon many factors ( ). ML methodologies offer a range of tools that have the potential to enhance the process of exploration and decision-making for precisely defined inquiries, utilising ample and reliable data. Machine learning (ML) can be applied at several stages of the drug discovery process. Before implementing ML approaches, it is crucial to have a profound understanding of the foundational principles of Machine Learning. Therefore, the application of ML in the various stages of drug development will be examined in the subsequent sixteen subsections.
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Modern drug research now depends on machine learning-based virtual screening to effectively find biologically active molecules from large chemical libraries. Two main strategies are used in this technique to find therapeutic candidates: (i) ligand-based drug design, which depends just on ligand information, and (ii) receptor-based drug design, which combines target and ligand data ( ) (Table . Whereas receptor-based methods use molecular docking to forecast binding affinities and interactions, ligand-based techniques examine molecular similarity and structure-activity connections. These techniques, taken together, improve the accuracy and scope of virtual screening, therefore hastening the identification of possible drug candidates with specific pharmacological effects ( ).
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One must have a representation of the drug candidate and targets if one is training a machine learning model utilising ligand and receptor (target) information ( ). Ligandbased drug design is the machine learning-based analysis of molecular characteristics and chemical fingerprints of active and inactive compounds ( ). By matching newly discovered compounds to known active molecules, ML systems can use patterns found from this data to forecast their activity. This approach is practical when there is a shortage of particular and thorough structural data about the receptor being targeted or when one wants to target several receptors with similar binding sites for ligands ( ).
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Conversely, receptor-based drug design uses molecular docking simulations with machine learning. Under these conditions, machine learning techniques use simulations to predict the degree of attraction between a small molecule ligand and a target receptor from their spatial and electrostatic compatibility. These models help to identify potential therapy candidates with excellent specificity and potency by using known ligandreceptor interactions and structural data to forecast the most favourable binding locations and strengths ( ).
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The different methods for displaying molecular data routinely used in computational approaches for drug discovery and molecular modelling are briefly summarised in this table. Among the representations are atomic coordinates, chemical descriptions, fingerprints, graph-based models, and other specialised forms. Every representation has different advantages and is selected depending on the particular needs of the computing activity. The table provides a thorough overview of the characteristics and applications of every data representation method, helping researchers select the most suitable approach for their computational study ( ).
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By utilising these representations (Table ), a substantial amount of drug exploration has been accomplished thus far. An instance of identifying novel antibiotics was achieved through a deep neural network model, which underwent training utilising an extensive database comprising chemical compounds and their corresponding efficacy against various bacterial strains ( ). The development of a generative tensorial reinforcement learning (GENTRL) model by Insilico Medicine resulted in the rapid identification of new highly effective DDR1 kinase inhibitors ( ). Machine learning techniques have been utilised in several applications, such as exploring potential drugs for Alzheimer's disease ( ). The research on Alzheimer's disease showcased the capacity of machine learning-based virtual screening approaches for drug discovery.
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Toxicity continues to be a significant factor contributing to the failure of medication candidates in drug development, leading to the exorbitant expenses associated with the drugs that successfully reach the market ( ). For example, it has been observed that a significant proportion, specifically 90%, of medication candidates that have undergone clinical trials experience failure during phases I, II, or III of the trial process or throughout the process of drug licensure ( ). For example, clinical trials have revealed that uncontrollable toxicity accounts for 90% of medication development failures ). Despite receiving approval, some medications are subsequently pulled from the market due to their shown health concerns. This phenomenon engenders a decline in trust and assurance within the healthcare sector among patients, healthcare practitioners, investors, and regulatory bodies ( ). In the given context, the utilisation of computational toxicity prediction proves to be highly beneficial during the initial phases of drug exploration, as it enables the exclusion of compounds that possess a substantial likelihood of experiencing failure in clinical trials ( ). Figure : An example of ML application in RNA-seq data's toxicity prediction RNA-seq data's toxicity prediction: a deep learning method using RNA-seq data to precisely project toxicity. This complex model uses deep learning techniques to estimate toxicity levels accurately, therefore offering important data on possible harmful effects and helping to produce safer drugs and chemicals ( ).
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Quantitative structure-activity relationship (QSAR) models have long been used to predict pharmacological promiscuity and toxicity ( ). These models show that the biological characteristics of these substances are related to different functional groupings. The spread of toxicity databases in the current setting has helped to adopt machine learning (ML) algorithms to predict the toxicity of small molecules. As such, these models have become somewhat popular recently. Consequently, the scholarly literature has recorded many toxicity prediction methods based on machine learning, including MolToxPred ( ) and DeepTox ( ), a neural network model. Although the examples demonstrate the ML models provide promising performance in toxicity predictions, they still have limitations, such as low interpretability.
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Modern drug development depends critically on target predictions since they identify particular biological molecules or cellular processes that drugs can reasonably control to produce therapeutic benefits. Despite the developments in omic and experimental technologies over recent years, the challenge of pinpointing suitable therapeutic targets still exists ( ). Target predictions have lately attracted attention as a possible approach by combining multi-omic data with artificial intelligence systems ( ).
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Novel biological targets for small compounds have been predicted via pharmacophore screening ( ), structure similarity assessment ( ), reverse docking ( ) and ML ( ), depending on the availability of protein structure and the chemical structure of the drug of interest. Despite the rest of the methods, ML is an essential element of artificial intelligence that can be utilised with or without oversight. Supervised learning uses annotated datasets to train models to classify data and accurately predict outcomes.
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Unsupervised learning, in contrast, investigates the concealed organisation of unlabeled data without human involvement ( ) (Figure ). With the utilisation of ML in the analysis and resolution of intricate biological data networks, such as (Figure ), ML algorithms have the potential to unveil latent patterns and correlations within the data that may elude human perception. Therefore, ML can potentially enhance comprehension and therapeutic approaches for various diseases. ML has significantly advanced target prediction. Besides target prediction, ML has demonstrated its effectiveness in indication prioritisation, biomarker and target discovery, pharmacokinetics prediction, drug-like molecule creation, clinical trial design, and drug-target interaction. The examples demonstrate that ML has great potential not only in target pre-dictions but also for other steps in drug discovery.
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Structure-based drug design (SBDD) is widely used in the search for possible medicinal agents. Usually referred to as ligands, the procedure involves evaluating the docking posture and calculating the degree of interaction between target proteins and small molecules ( ). Generally referring to binding affinity, the computation of interaction strength uses several scoring systems. Target protein physiological activity is directly proportional to the intensity of their interactions in relation to ligands. Therapeutic candidates thus are selected depending on their capacity to firmly attach to the target protein ( ). Accurate binding affinity prediction with the help of ML models can decrease the cost of a de novo drug design by utilising the projected binding affinity of the ligand in a library for virtual screening or lead optimisation ( ). To achieve this objective, conventional scoring functions have been suggested, such as empirical scoring functions ( ), knowledgebased ( ), and force-field-based ( ); typically, these characteristics encompass hydrogen bonds involving desolvation, van der Waals forces (view), and hydrophobic interactions. The coefficient of each descriptor is determined by considering the established binding affinity of protein-ligand complexes ( ). ML-based scoring functions have been developed to enhance the performance of conventional scoring functions.
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Machine learning-based scoring systems have been proposed as substitutes to improve the prediction performance of conventional scoring systems. RF-Score is a prominent machine learning-based grading system ( ). The present approach quantifies intermolecular interactions by use of atom pair counting comprising nine different heavy-atom types: C, N, O, F, P, S, Cl, Br, and I. Evaluated on the PDBbind ( ) v2007 benchmark set, the RF-Score shows significant improvement over the existing techniques. Moreover, among the six additional parameters of the RF-Score v3 model ( ), it shows better prediction accuracy than the original model. As described in reference ( ), the Structural Interaction Fingerprints (SIFt) method is a machine learning technique using a format akin to fingerprints to document intermolecular interactions.
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Drug discovery and development have significantly benefited from conventional methods for optimising chemical processes, which are essential for synthesising and improving prospective pharmacological compounds ( ). These methods rely on well-founded ideas of organic chemistry, which include empirical rules and refined reaction conditions throughout decades of laboratory work. The optimised reaction conditions maximise desired product reaction yields, purity, and selectivity through exact control of variables, including temperature, pressure, and catalysts. Although the optimisation of chemical reactions that are expensive and ineffective is still an essential feature of pharmaceutical synthesis, the conventional approach has generated a significant number of possible medications ( ). Luckily, ML applications in chemical reaction optimisation can efficiently solve the restrictions of conventional approaches. Therefore, machine learning applications overcome the limitations of conventional approaches, such as LabMate.ML ( ) is shown in Figure . LabMate.ML simplifies the process of optimising reaction conditions using a repetitive computational method. At first, the user inputs reactants and reaction parameters into LabMate.ML, which is shown as the left pathway in the picture. The software begins with an initial exploration phase (iterations 1-10), during which it selects starting experiments based on predictions that have the most considerable variability in output without considering the target value (measured AUC in LC-MS traces). The exploratory phase enables LabMate.ML will collect various data points and enhance its predictive model. During iterations 11-20, LabMate.ML adopts an exploitative (greedy) strategy, prioritising selecting conditions that maximise the target value of the reaction output. The selection approach entails selecting reactions with the most minor variability among the top five anticipated high-yielding reactions, given that the highest target value from the exploratory phase is four times higher than that of randomly chosen starting trials. Alternatively, if the goal value fails to exceed this threshold, LabMate.ML chooses conditions with the most significant variability among the top ten predictions that generate high results. During each iteration, LabMate.ML consistently enhances its predictive model by retraining it with fresh data points, optimising hyperparameters (such as the number of trees, tree depth, and amount of features in RF regressors), and improving forecasts for untested circumstances that still need to be evaluated-the optimised synthesis protocol derived by LabMate.ML following repeated refinement is represented by the right pathway in the picture. This protocol enables efficient and informed experiment selection without requiring specialised gear. This method democratises the field of synthetic chemistry by combining chemical intuition with computational automation, resulting in improved efficiency and reduced resource usage ( ).
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Conventional, time-consuming, and expensive approaches have been proposed to be improved using machine learning techniques, such as LabMate.ML ( ). Also, Aspuru-Guzik et al. effectively implemented automated chemical design utilising data-driven approaches ( ) by using graph convolutional neural networks, especially specialised for molecular analysis. Building on graph convolution, Kearnes et al. ( ) proposed one-shot learning as a tool to support drug discovery. The example shows how ML applied in chemical reaction optimisation can overcome the restrictions of conventional approaches for optimising chemical reactions.
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The binding site refers to a specific localised location on a protein or biomolecule that helps other molecules, including ligands, connect and interact. Since binding sites define the drug's efficacy, strength, and specificity in controlling biological processes, the interactions between a drug molecule and its target binding site play a crucial part in deciding the medicine's mechanism of action ( ). The most common approach to the identification of a binding site is the usage of structural information, such as dSPRINT ( ) (Figure ) Undergraduate student Anat Etzion-Fuchs from Mona Singh's lab at Princeton University leads the dSPRINT project, which forecasts the sites where ligands connect to protein domains using a range of traits, including amino acid patterns and physiochemical properties. Even for proteins without crystal structures, dSPRINT precisely forecasts interactions between domains and ligands by combining machine learning classifiers with a stacking approach. Cross-valuation validates the model's performance and reveals its capacity to forecast known interaction sites precisely. Furthermore, the forecasts of dSPRINT provide fresh insights into the interactions between proteins and ligands and expose new roles for proteins whose study has not been much investigated. This helps us to understand cellular processes and project protein functions better. One may easily review and investigate the dSPRINT architecture and its predictions ( ).
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Besides dSPRINT ( ) (Figure ), several structure-based approaches have been developed to find residues within protein binding sites and solve the time-consuming and expensive nature of conventional techniques ( ). For instance, the FunFold methods use binding residues ( ) to superimpose structural templates with significant ligands onto the target model. Combining domestically developed TM-SITE and S-SITE algorithms with outside prediction tools, including COFACTOR, FINDSITE, and Con-Cavity, the COACH consensus approach combines One and achieves this integration by using a supervised learning technique ( ). P2Rank ( ) is another instance of structural-based approaches applied in binding site identification. Designed especially for predicting the sites of ligand binding to protein structures, P2Rank is a powerful computer tool. P2Rank investigates protein surface physicochemical and geometric properties using machine learning (ML) approaches. This work helps to identify likely binding locations precisely. Trained on a large dataset of known protein-ligand interactions, the ML component of P2Rank gains knowledge of patterns and features separating binding sites from non-binding regions ( ). P2Rank can generate exact forecasts even in the absence of such comparable structures. Among P2Rank's various advantages are its excellent accuracy, potency, and ability to manage several protein structures. These traits make drug discovery and development valuable. P2Rank aids in the identification of fresh binding sites, enabling the synthesis of new drugs and reusing existing compounds ( ). At last, this accelerates the whole drug development process ( ). The examples show that using ML for binding site predictions offers a good substitute for past methods' time-consuming and costly character.
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Drug repositioning is the technique of assigning indications for drugs meant for another use than their initial one. One of the most well-known instances, for instance, is sildenafil citrate, first recommended for angina and then developed into Viagra, a commonly used drug for erectile dysfunction ( ). Many drugs have been moved throughout early medical history, including some ancient ones. The formal coining of medication repositioning can be found in a 2004 paper by Ashburn and Thor ( ). Initially, this paper described the method used to investigate new ways to effectively administer present medications for yet-unknown disease indications ( ). Drug repositioning studies the possible efficacy of existing medications and their application to treat diseases outside their current therapeutic reach. Among the advantages of drug repositioning over more traditional methods of drug development include less time and money needed for the latter. Furthermore, the medication employed has already been tested initially and has shown safety in human subjects, enabling the elimination of Phase I clinical studies. Drug repositioning shortens the cycle of pharmacological development ( ).
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Traditional ML in drug repositioning often involves utilising illness manifestations, drug targets, and genes as features. This is achieved by establishing a dichotomous network of links between features and medications, where similar disease targets are observed for similar drug actions ( ). In the field of drug repurposing, various machinelearning methodologies have been employed, such as Linear regression and logistic regression ( ), Support Vector Machines (SVMs) ( ), Random Forest (RF) ( ), and deep learning models ( ). The published studies prove that utilising ML drug repurposing presents a potent approach to discovering novel therapeutic applications for existing pharmaceuticals, thus expediting the drug development procedure.
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In the last decade, most drug development research has concentrated on identifying compounds that operate on a singular target ( ). Nevertheless, the selective affinity for a specific target consistently results in the instability of the cellular metabolic system, significantly impacting the regular physiological processes of cells and subsequently giving rise to detrimental effects. The selective affinity development of single-target medicines is subject to significant limitations ( ). Conversely, certain intricate illnesses, including drug-induced liver damage (DILI), are controlled by numerous targets and frequently pose challenges for treatment with a medicine that targets only one of them ( ). Therefore, the necessity of multi-target medications in treating complicated disorders has been established ( ). For example, Lim et al. developed a model to design multi-target drug prediction ([67]) (Figure ). (A) Illustration of a one-drug-multi-target-multi-indication strategy aimed at identifying drugs that enhance therapeutic effects while mitigating side effects, leveraging drug-off-target interactions. (B) Schema of 3D-REMAP, a robust multi-target screening platform integrating structural and chemical genomics data. The framework combines bioinformatics, chemoinformatics, protein-ligand docking, and machine-learning tools. Matrices R and Q represent observed and predicted protein-chemical interactions, respectively, used as inputs for the weighted imputed neighborhood-regularized One-Class Collaborative Filtering (winOCCF) algorithm to predict genome-wide drug-target interactions. Detailed methodologies are described in the Methods section ( ).
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