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At least 181 records · Page 10

Charge-transfer excitations in low-gap systems under the influence of solvation and conformational disorder: Exploring range-separation tuning

Charge transfer excitations play a prominent role in the fields of molecular electronics and light harvesting. At the same time they have developed a reputation for being hard to predict with time-dependent density functional theory, which is the otherwise predominant method for calculating molecular structure and excitations. Recently, it has been demonstrated that range-separated hybrid functionals, in particular with an “optimally tuned” range separation parameter, describe charge-transfer excitations reliably for different molecules. Many of these studies focused on molecules in vacuum. Here we investigate the influence of solvation on the electronic excitations of thiophene oligomers, i.e., paradigm low gap systems. We take into account bulk solvation using a continuum solvation model and geometrical distortions from molecular dynamics. From our study, three main findings emerge. First, geometrical distortions increase absorption energies by about 0.5 eV for the longer thiophene oligomers. Second, combining optimal tuning of the range separation parameter with a continuum solvation method is not straightforward and has to be approached with great care. Third, optimally tuned range-separated hybrids without a short-range exchange component tend to inherit undesirable characteristics of semi-local functionals: with increasing system size the range separation parameter takes a smaller value, leading to a functional of effectively more semi-local nature and thus not accurately capturing, e.g., the saturation of the optical gap with increasing system size.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dissecting ion-specific dielectric spectra of sodium-halide solutions into solvation water and ionic contributions

Using extensive equilibrium molecular dynamics simulations we determine the dielectric spectra of aqueous solutions of NaF, NaCl, NaBr, and NaI. The ion-specific and concentration-dependent shifts of the static dielectric constants and the dielectric relaxation times match experimental results very well, which serves as a validation of the classical and non-polarizable ionic force fields used. The purely ionic contribution to the dielectric response is negligible, but determines the conductivity of the salt solutions. The ion-water cross correlation contribution is negative and reduces the total dielectric response by about 5%-10% for 1 M solutions. The dominating water dielectric response is decomposed into different water solvation shells and ion-pair configurations, by this the spectral blue shift and the dielectric decrement of salt solutions with increasing salt concentration is demonstrated to be primarily caused by first-solvation shell water. With rising salt concentration the simulated spectra show more pronounced deviations from a single-Debye form and can be well described by a Cole-Cole fit, in quantitative agreement with experiments. Our spectral decomposition into ionic and different water solvation shell contributions does not render the individual contributions more Debye-like, this suggests the non-Debye-like character of the dielectric spectra of salt solutions not to be due to the superposition of different elementary relaxation processes with different relaxation times. Rather, the non-Debye-like character is likely to be an inherent spectral signature of solvation water around ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unusual solvation through both p-orbital lobes of a carbene carbon

As a result of a configurational space search done to explain the experimental evidence of transient specific solvation of singlet fluorocarbene amide with tetrahydrofuran, we found that the most stable structures consist in a group in which each oxygen of two tetrahydrofuran molecules act as electron donor to its respective empty p-orbital lobe of the carbene carbon atom, located at each side of the carbene molecular plane. This kind of species, which to our knowledge has not been reported before, explains very well the particular experimental characteristics observed for the transient solvation of this system. We postulate that the simultaneous interaction to both p-orbital lobes seems to confer a special stability to the solvation complexes, because this situation moves away the systems from the proximity of the corresponding transition states for the ylide products. Additionally, we present an analysis of other solvation complexes and a study of the nature of the involved interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lieb-Liniger-like model of quantum solvation in CO-{sup 4}He{sub N} clusters

Small {sup 4}He clusters doped with various molecules allow for the study of “quantum solvation” as a function of cluster size. A peculiarity of quantum solvation is that, as the number of {sup 4}He atoms is increased from N = 1, the solvent appears to decouple from the molecule which, in turn, appears to undergo free rotation. This is generally taken to signify the onset of “microscopic superfluidity.” Currently, little is known about the quantum mechanics of the decoupling mechanism, mainly because the system is a quantum (N + 1)-body problem in three dimensions which makes computations difficult. Here, a one-dimensional model is studied in which the {sup 4}He atoms are confined to revolve on a ring and encircle a rotating CO molecule. The Lanczos algorithm is used to investigate the eigenvalue spectrum as the number of {sup 4}He atoms is varied. Substantial solvent decoupling is observed for as few as N = 5 {sup 4}He atoms. Examination of the Hamiltonian matrix, which has an almost block diagonal structure, reveals increasingly weak inter-block (solvent-molecule) coupling as the number of {sup 4}He atoms is increased. In the absence of a dopant molecule the system is similar to a Lieb-Liniger (LL) gas and we find a relatively rapid transition to the LL limit as N is increased. In essence, the molecule initially—for very small N—provides a central, if relatively weak, attraction to organize the cluster; as more {sup 4}He atoms are added, the repulsive interactions between the identical bosons start to dominate as the solvation ring (shell) becomes more crowded which causes the molecule to start to decouple. For low N, the molecule pins the atoms in place relative to itself; as N increases the atom-atom repulsion starts to dominate the Hamiltonian and the molecule decouples. We conclude that, while the notion of superfluidity is a useful and correct description of the decoupling process, a molecular viewpoint provides complementary insights into the quantum mechanism of the transition from a molecular cluster to a quantum solvated molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effective interactions between nanoparticles: Creating temperature-independent solvation environments for self-assembly

The extent to which solvent-mediated effective interactions between nanoparticles can be predicted based on structure and associated thermodynamic estimators for bulk solvents and for solvation of single and pairs of nanoparticles is studied here. As a test of the approach, we analyse the strategy for creating temperature-independent solvent environments using a series of homologous chain fluids as solvents, as suggested by an experimental paper [M. I. Bodnarchuk et al., J. Am. Chem. Soc. 132, 11967 (2010)]. Our conclusions are based on molecular dynamics simulations of Au{sub 140}(SC{sub 10}H{sub 21}){sub 62} nanoparticles in n-alkane solvents, specifically hexane, octane, decane and dodecane, using the TraPPE-UA potential to model the alkanes and alkylthiols. The 140-atom gold core of the nanocrystal is held rigid in a truncated octahedral geometry and the gold-thiolate interaction is modeled using a Morse potential. The experimental observation was that the structural and rheological properties of n-alkane solvents are constant over a temperature range determined by equivalent solvent vapour pressures. We show that this is a consequence of the fact that long chain alkane liquids behave to a good approximation as simple liquids formed by packing of monomeric methyl/methylene units. Over the corresponding temperature range (233–361 K), the solvation environment is approximately constant at the single and pair nanoparticle levels under good solvent conditions. However, quantitative variations of the order of 10%–20% do exist in various quantities, such as molar volume of solute at infinite dilution, entropy of solvation, and onset distance for soft repulsions. In the opposite limit of a poor solvent, represented by vacuum in this study, the effective interactions between nanoparticles are no longer temperature-independent with attractive interactions increasing by up to 50% on decreasing the temperature from 361 K to 290 K, accompanied by an increase in emergent anisotropy due to correlation of mass dipoles on the two nanoparticles. One expects therefore that during self-assembly using solvent evaporation, temperature can be used as a structure-directing factor as long as good solvent conditions are maintained. It also suggests that disordered configurations may emerge as solvent quality decreases due to increasing role of short-range attractions and ligand fluctuation-driven anisotropy. The possibilities of using structural estimators of various thermodynamic quantities to analyse the interplay of ligand fluctuations and solvent quality in self-assembly as well as to design solvation environments are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Incorporating Solvate and Solid Electrolytes for All‐Solid‐State Li 2 S Batteries with High Capacity and Long Cycle Life

Abstract The development of all‐solid‐state lithium–sulfur batteries is hindered by the poor interfacial properties at solid electrolyte (SE)/electrode interfaces. The interface is modified by employing the highly concentrated solvate electrolyte, (MeCN) 2 −LiTFSI:TTE, as an interlayer material at the electrolyte/electrode interfaces. The incorporation of an interlayer significantly improves the cycling performance of solid‐state Li 2 S batteries compared to the bare counterpart, exhibiting a specific capacity of 760 mAh g −1 at cycle 100 (330 mAh g −1 for the bare cell). Electrochemical impedance spectroscopy shows that the interfacial resistance of the interlayer‐modified cell gradually decreases as a function of cycle number, while the impedance of the bare cell remains almost constant. Cross‐section scanning electron microscopy (SEM)/ energy dispersive X‐ray spectroscopy (EDS) measurements on the interlayer‐modified cell confirm the permeation of solvate into the cathode and the SE with electrochemical cycling, which is related to the decrease in cell impedance. In order to mimic the full permeation of the solvate across the entire cell, the solvate is directly mixed with the SE to form a “solvSEM” electrolyte. The hybrid Li 2 S cell using a solvSEM electrolyte exhibits superior cycling performance compared to the solid‐state cells, in terms of Li 2 S loading, Li 2 S utilization, and cycling stability. The improved performance is due to the favorable ionic contact at the battery interfaces.

Shin, Minjeong↗

Solvation Rule for Solid‐Electrolyte Interphase Enabler in Lithium‐Metal Batteries

Abstract Despite the exceptionally high energy density of lithium metal anodes, the practical application of lithium‐metal batteries (LMBs) is still impeded by the instability of the interphase between the lithium metal and the electrolyte. To formulate a functional electrolyte system that can stabilize the lithium‐metal anode, the solvation behavior of the solvent molecules must be understood because the electrochemical properties of a solvent can be heavily influenced by its solvation status. We unambiguously demonstrated the solvation rule for the solid‐electrolyte interphase (SEI) enabler in an electrolyte system. In this study, fluoroethylene carbonate was used as the SEI enabler due to its ability to form a robust SEI on the lithium metal surface, allowing relatively stable LMB cycling. The results revealed that the solvation number of fluoroethylene carbonate must be ≥1 to ensure the formation of a stable SEI in which the sacrificial reduction of the SEI enabler subsequently leads to the stable cycling of LMBs.

Su, Chi‐Cheung↗

Synthesis and Structural Features of [4,4'-Diisopropoxyester-2,2'-bipyridine], [Dichloro(4,4'-diisopropoxyester-2,2'-bi-pyridine)-platinum(ii)] and Its Dichloromethane Solvated Pseudo-Polymorph: Versatile Supramolecular Interactions

We report that the organic ligand 4,4'-diisopropoxyester-2,2'-bipyridine, C 18 H 20 N 2 O 4 (1), crystallizes in the triclinic crystal system P-1 and the molecule occupies a special position in the unit cell. In the crystal, molecules form stacks with partial overlapping of the pyridine rings. The Pt(II) dichloro complex of 1 crystallizes from a mixture of ethanol/hexane and from dichloromethane to form orange and yellow crystals, respectively. The orange non-solvated crystals of the (bipyridine)(dichloro)platinum(II) complex C 18 H 20 N 2 O 4 PtCl 2 (2) crystallize in the triclinic crystal system P-1 as well with two independent molecules in the unit cell. In the crystal packing, molecules form two types of dimers with Pt1 ··· Pt1A and Pt2···Pt2A distances of 3.478 and 5.186 angstrom respectively. The yellow crystals, as a solvated pseudo-polymorph C 18 H 20 N 2 O 4 PtCl 2 ·1.5 CH 2 Cl 2 (3) also crystallize in the triclinic crystal system P-1 with two independent molecules in the unit cell. In the crystal packing, molecules form Pt2 ···Pt1 ···Pt1A ···Pt2A intermolecular contacts with alternating distances 3.501 and 3.431 angstrom, respectively, forming infinite chains. Graphical Abstract The dichloro(bipyridine)platinum complex, dichloro(4,4'-diisopropoxyester-2,2'-bipyridine)platinum(II), forms single crystals as a stable non-solvated form and a solvated polymorph with dramatically different supramolecular structure and short contacts.

2 '-bipyridine)-platinum(II)] Supramolecular inter↗

Impact of fluorination on Li + solvation and dynamics in ionic liquid-hydrofluoroether locally concentrated electrolytes

The thermal, physical, structural, and transport properties of ionic liquid (IL) electrolytes based on n-methyl-n-butylpyrrolidinium bis(trifluoromethanesulfonyl)imide [PYR14][TFSI] and Li-salts of lithium (nonafluorobutane)(trifluoromethanesulfonyl)imide [Li][IM14] and [Li][TFSI] (0 ≤ x Li ≤ 0.3), with addition of 1,1,2,2-tetrafluoroethyl 2,2,3,3-tetrafluoropropyl ether (TTE) (0 ≤ x TTE ≤ 0.45) were studied. While [IM14] increases glass transition, TTE improves conductivity over a wider liquidus range. Li + is solvated primarily by [TFSI] with some contribution by [IM14]. However, both 7 Li- 19 F HOESY NMR and spatial distribution functions (SDFs) derived from molecular dynamics (MD) indicate short contacts between the fluorines of TTE and Li + . This is a result of tighter anion-solvated Li + without aggregation of the Li + solvates, consistent with Raman measurements, thus confirming the existence of fluorous domains in the bulk which leads to improved fluidity and a Li + diffusivity of 1.26 x 10 –12 m 2 /s at 0 °C (x Li = 0.20) with a Li + transference of 0.16. Improved transport properties translated to a higher capacity of the TTE/IL electrolyte in a Li||LiFePO 4 half-cell with 95mAh/g at 0.1C, compared to the IL electrolyte without TTE (60 mAh/g). Furthermore, this study demonstrates the tunability of solvation and transport properties in IL electrolytes by asymmetric fluorinated anions and hydrofluoroether co-solvents for low temperature Li-ion batteries.

25 ENERGY STORAGE↗

Solvation-guided inhibition of manganese dissolution of lithium- and manganese- rich cathode via cyclic carbonate molecular engineering

Lithium and manganese-rich (LMR) layered oxides represent a leading class of high-energy cathode materials, but their practical realization is fundamentally limited by severe manganese (Mn) dissolution, a process that triggers structural degradation and rapid capacity fade. While mitigation efforts have predominantly focused on interfacial engineering, the intrinsic contribution of bulk electrolyte solvation to this degradation pathway remains largely unexplored, primarily due to the difficulty of deconvolving its effects from concurrent cathode-electrolyte interphase (CEI) formation. Here, we report an experimental design to isolate the role of solvation. We systematically varied the electrolyte solvent solvation power by substituting the strongly coordinating ethylene carbonate (EC) with its weaker coordinating fluorinated derivatives, fluoroethylene carbonate (FEC) and trans-4,5-Difluoro-1,3-dioxolan-2-one (DFEC), while maintaining a consistent interfacial chemistry. Remarkably, the electrolyte formulated with the weakest solvent, DFEC, exhibits superior cycling stability, suppressing Mn dissolution by up to 63% relative to the conventional EC-based system. Post-mortem analysis unequivocally attributes this performance enhancement to the preservation of the LMR cathode's structural integrity, a direct consequence of mitigated Mn dissolution. This work provides conclusive evidence that modulating bulk electrolyte solvation is a potent and direct strategy for stabilizing LMR cathodes, establishing a vital design principle for next-generation battery systems.

25 ENERGY STORAGE↗

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a method for quantifying this uncertainty in solvation energies using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space required compressed sensing combined with an iterative rotation method to enhance problem sparsity. We present results for the uncertainty in small molecule solvation energies based on these approaches. Additionally, we explore the correlation between uncertainties due to radii and charges which motivates the need for future work in uncertainty quantification methods for high-dimensional parameter spaces.

Yang, Xiu↗

Dicarbonyl Electrolyte for High-Voltage Lithium Metal Batteries: Importance of the Entropy of Solvation in Bidentate Solvent

An electrolyte system based on dicarbonyl solvents has been proposed and implemented in lithium metal batteries (LMBs). Among several dicarbonyl solvents explored, dimethyl dicarbonate (DMDC) emerged as the most promising electrolyte candidate. Interestingly, despite the structural similarities between DMDC and its monocarbonyl counterpart DMC, the DMDC electrolyte exhibits higher solvent coordination, even at the same lithium-to-carbonyl ratio. Further, this leads to the formation of a more robust solid-electrolyte interphase and enhances the anodic stability of the electrolyte. Notably, in various electrolyte systems, the solvation energy is typically enthalpy-driven. However, the bidentate nature of DMDC introduces a significant role for the entropy of solvation because the Li + -DMDC complexes release fewer free molecules. With the addition of non-solvating co-solvent 1,1,2,2-tetrafluoro-ethyl 2,2,3,3-tetrafluoro-propyl ether (TTE), which reduces the viscosity of the electrolyte, the DMDC-TTE system enables remarkably stable cycling of the lithium anode by manipulating the entropy of solvation. This introduces a new strategy for tailoring functional electrolyte systems.

25 ENERGY STORAGE↗

Weakly Solvating Electrolyte to Enable Lithium- and Manganese-Rich Cathode-Based Li-Ion Batteries

Traditional ethylene carbonate (EC)-based electrolytes exhibit strong solvation power at the surface of the layered transition metal oxide cathodes, which accelerates transition metal dissolution. The subsequent migration and deposition of dissolved transition metal species on the anode surface lead to significant capacity fading. To overcome this difficulty, we report a weakly solvating, all-fluorinated electrolyte designed to mitigate transition metal dissolution. For the first time, the role of electrolyte solvation in suppressing transition metal dissolution is systematically investigated. The tailored electrolyte significantly reduces transition metal dissolution and enhances the electrochemical performance of Li- and Mn-rich (LMR) cathode/graphite cells. This solvation-modulating strategy offers a broadly applicable framework for stabilizing interphases in other earth-abundant cathode chemistries, which similarly demand kinetic protection against interfacial degradation.

25 ENERGY STORAGE↗

Role of Solvation on Diffusion of Ions in Diblock Copolymers: Understanding the Molecular Weight Effect through Modeling

Salt-doped diblock copolymers with microphase-separated domains of both an ion conductive and a mechanically strong polymer have been extensively studied due to their potential in transport applications. Several unusual or counterintuitive trends regarding their transport properties have been observed experimentally, such as increasing ion conduction as a function of molecular weight. A vital feature of these systems is the strong solvation of ions in the conducting microphase due to its higher dielectric constant. Herein, we perform molecular dynamics simulations using a coarse-grained model that includes a 1/r 4 potential form to generically represent ion solvation, allowing us to reproduce experimentally observed trends and explore their molecular underpinnings. We find that increasing ion concentration can increase or decrease ion diffusion, depending on solvation strength. We further show that the trend of increasing diffusion with molecular weight becomes more dramatic as ions are solvated in one polymer block more strongly or as the ion-ion interactions get stronger. In contrast to expectations, the interfacial width or the overlap of ions with the nonconductive polymer block do not adequately explain this phenomenon; instead, local ion agglomeration best explains reduced diffusion. Interfacial sharpening, controlled by the Flory chi parameter and molecular weight, tends to allow ions to spread more uniformly, and this increases their diffusion.

36 MATERIALS SCIENCE↗

Nanosecond solvation dynamics in a polymer electrolyte for lithium batteries

Solvation dynamics critically affect charge transport. Spectroscopic experiments and computer simulations show that these dynamics in aqueous systems occur on a picosecond timescale. In the case of organic electrolytes, however, conflicting values ranging from 1 to several 100 picoseconds have been reported. We resolve this conflict by studying mixtures of an organic polymer and a lithium salt. Lithium ions coordinate with multiple polymer chains, resulting in temporary crosslinks. Relaxation of these crosslinks, detected by quasielastic neutron scattering, are directly related to solvation dynamics. Simulations reveal a broad spectrum of relaxation times. The average timescale for solvation dynamics in both experiment and simulation is one nanosecond. Here we present the direct measurement of ultraslow dynamics of solvation shell break-up in an electrolyte.

25 ENERGY STORAGE↗

Probing the Early Stages of Solvation of cis-Pinate Dianions by Water, Acetonitrile, and Methanol: A Photoelectron Spectroscopy and Theoretical Study

Cis-pinic acid is one of the most important oxidation products of α-pinene – a key monoterpene compound in biogenic emission processes affecting the atmosphere. Molecular level understanding of interactions involved in the cluster formations around cis-pinic acid is an important and necessary prerequisite toward ascertaining its role in the aerosol formation processes. In this work, we studied the structures and energetics of the solvated clusters of cis-pinate (cis-PA²⁻), the doubly deprotonated dicarboxylate of cis-pinic acid, with H₂O, CH₃OH, and CH₃CN by negative ion photoelectron spectroscopy and ab initio theoretical calculations. We found that cis-PA²⁻ prefers being solvated alternately on the two -CO₂⁻ groups with increase of solvent coverage, a well-known solvation pattern that has been observed in microhydrated linear dicarboxylate dianion (DC n ²⁻) clusters. Experiments and calculations further reveal an intriguing feature for the existence of the asymmetric type isomers for cis-PA2–(H2O)2 and cis-PA²⁻(CH₃OH)₂, in which both solvent molecules interact with only one of the -CO²⁻ groups – a phenomena that has not been observed in DCn²⁻ water clusters and exhibits the subtle effect of the rigid four-membered carbon ring brought in on the cis-PA²⁻ solvation. The dominant interactions between cis-PA²⁻ and solvent molecules are forming bidentate O–···H–O H-bonds for H₂O, O–···H–O and O–···H–C H-bonds for CH₃OH, and tridentate O–···H–C H-bonds for CH₃CN. The formation of inter-solvent H-bonds between H₂O and CH₃CN is found to be favorable in mixed solvent clusters, distinctly different from that between H₂O and CH₃OH. These findings have important implications for understanding the mechanism of cluster growth and nucleation of atmospheric organic aerosols and the nature of structure-function relationship of proteins containing carboxylate groups under various solvent environments.

Environmental Molecular Sciences Laboratory↗

Exploring local solvation environments of a heme protein using the spectroscopic reporter 4-cyano- L -phenylalanine

The vibrational reporter unnatural amino acid (UAA) 4-cyano-L-phenylalanine (pCNF) was genetically incorporated individually at three sites (5, 36, and 78) in the heme protein Caldanaerobacter subterraneus H-NOX to probe local hydration environments. The UAA pCNF was incorporated site-specifically using an engineered, orthogonal tRNA synthetase in E. coli. The ability of all of the pCNF-containing H-NOX proteins to form the ferrous CO, NO, or O 2 ligated and unligated states was confirmed with UV-Vis spectroscopy. The solvation state at each site of the three sites of pCNF incorporation was assessed using temperature-dependent infrared spectroscopy. Specifically, the frequency–temperature line slope (FTLS) method was utilized to show that the nitrile group at site 36 was fully solvated and the nitrile group at site 78 was de-solvated (buried) in the heme pocket. The nitrile group at site 5 was found to be partially solvated suggesting that the nitrile group was involved in moderate strength hydrogen bonds. These results were confirmed by the determination of the X-ray crystal structure of the H-NOX protein construct containing pCNF at site 5.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Graphical Gaussian Process Regression Model for Aqueous Solvation Free Energy Prediction of Organic Molecules in Redox Flow Battery

The solvation free energy of organic molecules is a critical parameter in determining emergent properties such as solubility, liquid-phase equilibrium constants, and pKa and redox potentials in an organic redox flow battery. In this work, we present a machine learning (ML) model that can learn and predict the aqueous solvation free energy of an organic molecule using Gaussian process regression method based on a new molecular graph kernel. To investigate the performance of the ML model on electrostatic interaction, the nonpolar interaction contribution of solvent and the conformational entropy of solute in solvation free energy, three data sets with implicit or explicit water solvent models, and contribution of conformational entropy of solute are tested. We demonstrate that our ML model can predict the solvation free energy of molecules at chemical accuracy with a mean absolute error of less than 1 kcal/mol for subsets of the QM9 dataset and the Freesolv database. To solve the general data scarcity problem for a graph-based ML model, we propose a dimension reduction algorithm based on the distance between molecular graphs, which can be used to examine the diversity of the molecular data set. It provides a promising way to build a minimum training set to improve prediction for certain test sets where the space of molecular structures is predetermined.

25 ENERGY STORAGE↗