Molecular Structure Descriptors Research Articles

The Euler Sombor index of a graph

AbstractA novel geometric method is proposed for constructing vertex‐degree‐based molecular structure descriptors, which is the perimeter of an ellipse whose focal points represent the degree‐point and its dual‐point of a pair of adjacent vertices in a graph . We first analyze the chemical applicability of this elliptic Sombor index, and then establish its mathematical properties and determine the extremal values for this elliptic Sombor index among all (molecular) trees and characterize the corresponding extremal graphs.

Insight to the prediction of CO2 solubility in ionic liquids based on the interpretable machine learning model

In this work, we investigated three different ML-based models, i.e., GPR, LightGBM, and CatBoost, for predicting the solubility of CO2 in various ionic liquids (ILs). Three molecular descriptors, i.e., group contribution (GC), molecular structure descriptors (MSD), and hybrid GC-MSD are used in our three models. The performance of our developed models were rigorously evaluated using mean absolute error (MAE), coefficient of determination (R2), and mean relative error (MRE) (i.e., relative deviation in percentage), with each model subjected to multiple tests employing different random state parameters. The dataset underwent partitioning into training and testing sets at an 80:20 ratio, with additional splits at various ratios to assess prediction performance sensitivity. Overall, all models exhibited proficient CO2 solubility prediction in ILs, with performance varying based on descriptor type. Notably, the hybrid GC-MSD consistently outperformed others, attributed to GC-MSD incorporates a broader array of molecular feature information. Particularly, the CatBoost-GC-MSD model excelled, achieving an impressive R2 of 0.9925, MAE of 0.0122, and MRE of 11.1550%. Comparing our models to previous studies revealed the superior performance of CatBoost-GC-MSD across all descriptor types. Furthermore, our model interpretation, employing SHAP analysis, identified pressure, temperature, Chi0, Kappa2, and EState_VSA10 as the top five influential input features. These findings provide valuable insights into the underlying molecular features affecting CO2 solubility in ILs and lay the foundation for future research in this field.

Unveiling the electronic and molecular structure of a trinuclear ruthenium cluster containing one nitrosyl ligand

The understanding of the Ru-NO bond in Ru nitrosyl systems is of great interest due to the non-innocent nature of the NO ligand, and because of the ability of such compounds to release nitric oxide, an essential physiological regulator. The Ru-NO bond description can be even more complicated when it comes to polynuclear systems such as the μ-oxo clusters of general formula [Ru3O(CH3COO)6(L)3]n, which can be electronically localized or delocalized themselves depending on the nature of the L ligands, or present unpaired electrons depending on the Ru ions oxidation state. Herein, we present a detailed electronic- and molecular-structure description of the [Ru3O(CH3COO)6(py)2NO]PF6 (py = pyridine) cluster using multiconfigurational approaches and X-ray diffraction analysis. The X-ray data unveil a linear Ru–NO moiety with a Ru-NO angle of 180°. Although most linear {RuNO}6 complexes have been largely described as RuII–NO+, our valence bond-type analysis based on a CASSCF ground state wavefunction, with an active space comprised of 18 electrons and 16 orbitals, showed a predominance of the RuIII–NO° configuration, with minor contributions from RuIV–NO– and RuII–NO+. These findings provide a more precise framework to rationalize the electronic properties of trinuclear ruthenium nitrosyls, aiding the planning of new NO releasers based on those clusters.

EKGDR: An End-to-End Knowledge Graph-Based Method for Computational Drug Repurposing.

The lengthy and expensive process of developing new drugs from scratch, coupled with a high failure rate, has prompted the emergence of drug repurposing/repositioning as a more efficient and cost-effective approach. This approach involves identifying new therapeutic applications for existing approved drugs, leveraging the extensive drug-related data already gathered. However, the diversity and heterogeneity of data, along with the limited availability of known drug-disease interactions, pose significant challenges to computational drug design. To address these challenges, this study introduces EKGDR, an end-to-end knowledge graph-based approach for computational drug repurposing. EKGDR utilizes the power of a drug knowledge graph, a comprehensive repository of drug-related information that encompasses known drug interactions and various categorization information, as well as structural molecular descriptors of drugs. EKGDR employs graph neural networks, a cutting-edge graph representation learning technique, to embed the drug knowledge graph (nodes and relations) in an end-to-end manner. By doing so, EKGDR can effectively learn the underlying causes (intents) behind drug-disease interactions and recursively aggregate and combine relational messages between nodes along different multihop neighborhood paths (relational paths). This process generates representations of disease and drug nodes, enabling EKGDR to predict the interaction probability for each drug-disease pair in an end-to-end manner. The obtained results demonstrate that EKGDR outperforms previous models in all three evaluation metrics: area under the receiver operating characteristic curve (AUROC = 0.9475), area under the precision-recall curve (AUPRC = 0.9490), and recall at the top-200 recommendations (Recall@200 = 0.8315). To further validate EKGDR's effectiveness, we evaluated the top-20 candidate drugs suggested for each of Alzheimer's and Parkinson's diseases.

Fe2+-NTA synergized UV254 photolytic defluorination of perfluorooctane sulfonate (PFOS): Enhancing through intramolecular electron density perturbation via electron acquisition

Perfluorooctane sulfonate (PFOS) is a persistent organic pollutant posing a risk in environmental persistence, bioaccumulation and biotoxicity. This study was to reach a comprehensive and deeper understanding of PFOS elimination in a UV254 photolytic treatment with the co-presence of Fe2+ and nitrilotriacetic acid trisodium salt (NTA). PFOS defluorination was noticeably enhanced in the UV/Fe2+-NTA treatment compared with UV/NTA, UV/Fe2+ and our previously studied UV/Fe3+ treatments. UV–vis, FTIR, and UPLC/MS-MS results indicated the formation of PFOS-Fe2+-NTA complex in PFOS, Fe2+ and NTA mixture. The transition energy gap of PFOS-Fe2+-NTA decreased below the excitation energy supplied by UV254 irradiation, corresponding with red shift appearing in UV–vis scanning spectrum. This favored intramolecular electron transfer from Fe2+-NTA to PFOS under UV254 irradiation to form electron-accepting PFOS. Molecular electrostatic potential and atom charge distribution analyses suggested electron density rearrangement and perturbation in the perfluorinated carbon chain of electron-accepting PFOS, leading to the decrease in bond dissociation energies. Intermediate products detection suggested the parallel defluorination pathways of PFOS desulfonation, middle carbon chain scission and direct C-F cleavage. NTA exhibited crucial functions in the UV/Fe2+-NTA treatment by holding Fe2+/Fe3+ in soluble form as a chelant and favoring water activation to generate hydrated electrons (eaq−) under UV irradiation as a photosensitizer. Fe2+ acting as the conduit for electron transfer and the bridge of PFOS anion and NTA was thought functioning best at 200 µM in this study. The degree of UV/Fe2+-NTA -synergized PFOS defluorination also depended on eaq− yield and UV254 photon flux. The structure dependence on the electron transfer process of PFOS and PFOA was explored incorporating molecular structure descriptors. Because of possessing greater potential to acquire electrons or less likeliness to donate its electrons than PFOA, PFOS exhibited faster defluorination kinetics in the published “reduction treatments” than “oxidation” ones. Whereas, PFOA defluorination kinetics were at similar level in both “reduction” and “oxidation” treatments.

Study for Some Eccentricity-based Topological Indices of Second Type of Dominating David-derived Network.

Dominating David-derived networks are widely studied due to their fractal nature, with applications in topology, chemistry, and computer sciences. The use of molecular structure descriptors is a standard procedure that is used to correlate the biological activity of molecules with their chemical structures, which can be useful in the field of pharmacology. This article's goal is to develop analytically closed computing formulas for eccentricity-based descriptors of the second type of dominating David-derived derived network. Thermodynamic characteristics, physicochemical properties, and chemical and biological activities of chemical graphs are just a few of the many properties that may be determined using these computation formulas. Vertex sets were initially divided according to their degrees, eccentricities, and cardinalities of occurrence. The eccentricity-based indices are then computed using some combinatorics and these partitions. Total eccentricity, average eccentricity, and the Zagreb index are distance-based topological indices utilized in this study for the second type of dominating David-derived network, denoted as D_2 (m). These calculations will assist the readers in estimating the fractal and difficult-to-handle thermodynamic and physicochemical aspects of chemical structure. Apart from configuration and impact resistance, the D_2 (m) design has been used for fundamental reasons in a variety of technical and scientific advancements.

On the Entire Harmonic Index and Entire Harmonic Polynomial of Graphs

A topological descriptor is a numerical parameter that describes a chemical structure using the related molecular graph. Topological descriptors have significance in mathematical chemistry, particularly for studying QSPR and QSAR. In addition, if a topological descriptor has a reciprocal link with a molecular attribute, it is referred to as a topological index. The use of topological indices can help to examine the physicochemical features of chemical compounds because they encode certain attributes of a molecule. The Randić index is a molecular structure descriptor that has several applications in chemistry and medicine. In this paper, we introduce a new version of the Randić index to the inclusion of the intermolecular forces between bonds with atoms, referred to as an entire Harmonic index (EHI), and we present the entire Harmonic polynomial (EHP) of a graph. Specific formulas have been obtained for certain graph classes, and graph operations have been obtained. Bounds and some important results have been found. Furthermore, we demonstrate that the correlation coefficients for the new index lie between 0.909 and 1. In the context of enthalpy of formation and π-electronic energy, the acquired values are significantly higher than those observed for the Harmonic index and the Randić index.

Geometric approach to vertex‐degree‐based topological indices–Elliptic Sombor index, theory and application

AbstractA novel geometric method is proposed for constructing vertex‐degree‐based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices. This approach enables a geometric interpretation of several previously known topological indices, and lead to design of a few new. The area of the ellipse induces a vertex‐degree‐based topological index of remarkable simplicity, which we call elliptic Sombor index(). The main mathematical properties of are established, especially its relations to other, earlier known, indices. Then the applicative potential of is analyzed.

The minimal chemical tree for the difference between geometric–arithmetic and Randić indices

AbstractTopological indices are numerical parameters derived from the structural information of chemical compounds. By providing a quantitative description of molecular structures, topological indices enable researchers to predict various properties and behaviors of molecules. The Randić index () and the geometric–arithmetic index () are widely recognized topological indices. It is observed that, for any given graph . We aim to investigate the gap between and for chemical tree. The complete characterization of minimal chemical tree for is carried out here. This article offers an interesting finding that, whereas and provide same minimal chemical trees, yields minimal tree structures that are totally different from and . Moreover is observed to correlate well with physico‐chemical properties of octanes.

Molecules structure and viscosity relationship of nematic liquid crystal and BPNN-QSAR model

Nematic liquid crystal materials designed for optics, microwave communication tuning, etc. need high response speed, which is related to the rotational viscosity and the birefringent index of the liquid crystal. In order to achieve a wide tuning range of phase modulation, the nematic liquid crystals often employ large π-electron conjugated systems and large polar groups to enhance the birefringence and dielectric anisotropy of the liquid crystal molecule, which, however, increases the viscosity of the liquid crystal material, deteriorating the response speed of the microwave device. Herein, we explore the viscosity of the nematic liquid crystal from the perspective of liquid crystal compound structure by testing the viscosity of our designed and synthesized forty-two different nematic liquid crystals by using a rotating rheometer at 25 ℃. To the best of our knowledge, the BPNN-QSAR quantitative structure-activity model between nematic liquid crystal molecular structure and viscosity is established for the first time. The correlation coefficient between the predicted value and the experimental value is <i>q</i><sup>2</sup> = 0.607 > 0.5, indicating that the model can be used to predict the viscosity performances of liquid crystal compounds. Besides, the molecular structure descriptors affecting the viscosity properties are explored. Based on the practical application and this model, seven liquid crystal molecules of two series with large birefringent index are designed and tested. The viscosity predicted by the BPNN model is smaller than that of the molecules of the same type and matches with the measured viscosity.

Fe(VI) oxidation of synthetic phenolic antioxidants: Kinetics, influencing factors, transformation mechanism and toxicity

Synthetic phenolic antioxidants (SPAs) have been commonly used in industrial and domestic products to prevent the adverse effects of oxidants such as oxygen. However, attention to the removal of SPAs is scarcely attracted. In this paper, the removal kinetics, influencing factors, transformation mechanisms and toxicity in Fe(VI) oxidation of 18 SPA congeners were investigated in detail. Results showed that propyl gallate (PG), butylated hydroxyanisole (BHA), and tert-butylhydroquinone (TBHQ) had the highest reactivities with Fe(VI), while the reaction rate constant (kapp) value of 2,4-di-tert-butylphenyl 3,5-di-tert-butyl-4-hydroxybenzoate (UV120) was the lowest (221.3 M−1 s−1). A robust quantitative structure–activity relationship (QSAR) model between kapp and molecular structural descriptors of SPAs was established. The energy gap between the lowest unoccupied molecular orbital (ELUMO) and the highest occupied molecular orbital (EHOMO) was a vital parameter to determine the removal efficiencies of the SPA congeners. Furthermore, the numbers of oxygen atoms and alkyl groups in SPA structures also determined their reactivities with Fe(VI) to some extent. In addition, aqueous 2,6-di-tert-butyl-4-methylphenol (BHT, a representative of SPAs) could be efficiently removed with the increased amount of oxidant, and decreased substrate concentration and slightly alkaline conditions. Seventeen intermediates were identified, and oxidation routes including H-abstraction, single- and double-oxygen(s) transfer, and coupling were deduced. However, H-abstraction inevitably led to the generation of BHT-Q with higher toxicity than parent. These findings provide novel insights into the production and removal of SPA analogs.

Decolourization and degradation of azo-dyes by the NaClO/NiOOH catalytic oxidation system

ABSTRACT Azo dyes are highly toxic and difficult to degrade. Decolourization of acid red 18 (AR18) and reactive yellow 4 (RY4) dye wastewater by the NaClO/NiO x (OH) y catalytic system was studied. The influence of reaction conditions was investigated. Their degradation mechanism was discussed by free radical scavenging experiment, and the degradation pathways were proposed. The continuous flow experiment was conducted. The results showed that the catalytic oxidation has a good decolourization effect on AR18, but it is not ideal for RY4. The continuous flow experiment of 3000 min showed that the decolourization effect was stable. The concentration of Ni2+ in the effluent from the reactor was always up to the standard, and the catalyst was not deactivated. The decolourization mechanism of the two dyes is different: AR18 is mainly decolourized by atomic oxygen/singlet oxygen, while RY4 is mainly decolourized by NaClO. The catalysts were characterized by XPS and XRD. The surface contains the largest proportion of chemisorbed oxygen. With the extension of the catalyst service time, chemisorbed oxygen decreased slightly and was converted into atomic oxygen/singlet oxygen, which was consumed in the decolourization process. Compared with the used catalysts, the β-NiOOH crystallinity of the fresh catalyst is better. The quantitative structure–property relationship analysis based on the decolourization data shows that there is a good linear correlation between the decolourization rate of azo dyes and their molecular structure descriptors. The inorganic–organic properties balance (IOB) value was determined as the main molecular descriptor that affected the decolourization of dyes.

Study on quantitative structure–activity relationship of amine surfactants in coal reverse flotation

AbstractWith the deterioration of underground coal quality, hundreds of millions of tons of coal slime in China need to be treated using flotation methods every year. However, the design and selection of coal slurry flotation collectors lack theoretical guidance. In this paper, the quantitative structure–activity relationship (QSAR) model between the molecular structure descriptors of collectors and the flotation recovery and selectivity index is established by using pure kaolinite/clean coal flotation experiments and molecular simulation techniques. Flotation results showed that the flotation recovery rate of kaolinite by collectors with larger head group size, such as DDMAC, DDP, and DTAC, is higher than that of the other collectors with smaller head group size. DDA, DDP, and DD have similar flotation capabilities for clean coal, and their selectivity was slightly better than others. The QSAR model between the molecular structure descriptor and the selectivity index was successfully constructed by combining flotation experiments and molecular simulation results. The reliability of this model has been proven through theoretical analysis and flotation experiments. The molecular simulation results indicate that all eight collectors can advertise on 001 (−) surface of kaolinite, but the final advertisement configuration is different. DDA has less coverage on the surface of kaolinite. When the collector is DDA, the concentration of water molecules near the 001 (−) surface of kaolinite is the highest, indicating that the collector DDA has the weakest effect on improving the hydrophobicity of the 001 (−) surface of kaolinite. DDMAC and DDBAC have the best facilitation to the surface hydrophobicity of kaolinite 001 (−). The research results have theoretical guidance significance for the selection and design of mineral flotation collectors.

Quantitative structure-biotransformation relationships of organic micropollutants in aerobic and anaerobic wastewater treatments

Biotransformation is one of the dominant processes to remove organic micropollutants (OMPs) in wastewater treatment. However, studies on the role of molecular structure in determining the biotransformation rates of OMPs are limited. We evaluated the biotransformation of 14 OMPs belonging to different chemical classes under aerobic and anaerobic conditions, and then explored the quantitative structure-biotransformation relationships (QSBRs) of the OMPs based on biotransformation rates using valid molecular structure descriptors (electrical and physicochemical parameters). Pseudo-first-order kinetic modeling was used to fit the biotransformation rate, and only 2 of the 14 OMPs showed that the biotransformation rate constant (kbio) values were higher under anaerobic conditions than aerobic conditions, indicating that aerobic conditions were more favorable for biotransformation of most OMPs. QSBRs infer that the electrophilicity index (ω) is a reliable predictor for OMPs biotransformation under aerobic conditions. ω corresponds to the interaction between OMPs and microbial enzyme active sites, this process is the rate-limiting step of biotransformation. However, under anaerobic conditions the QSBR based on ω was not significant, indicating that specific functional groups may be more critical than electrophilicity. In conclusion, QSBRs can serve as alternative tools for the prediction of the biotransformation of OMPs and provide further insights into the factors that influence biotransformation.

Mathematical aspects and molecular descriptors for anti-tumour and anti-COVID drugs medications

The COVID-19 pandemic has significantly affected both the global economy and human health. COVID-19 is a single-stranded RNA virus that spreads through the inhalation of viral droplets. Its genome encodes four structural proteins: the envelop protein, spike protein, membrane protein, and nucleocapsid protein. The virus's capsid is a protein shell that contains a positive RNA strand that allows it to take control of human cell machinery. Currently, the only treatments for COVID-19 are preventative measures and immunization. Some of the anti-COVID and anti-cancer medications used to combat this virus include Camptothecin Polymer, Hyaluronic Acid-curcumin, and Hydroxychloroquine. Graphs are used extensively in chemical investigation to provide a mathematical model of molecules. The selection of graph invariants, formerly known as molecular structure descriptor's, is the mathematical modelling of chemical compounds’ physio-chemical, pharmacologic, and toxicological aspects. This paper presents a new technique to compute topological indices for three types of chemical networks for a few anti-COVID and anti-cancer medications. Our findings suggest that these indices show a strong association with the acentric factor and entropy, which make them effective in QSPR and QSAR analysis with high accuracy.

Application of machine learning algorithms in drug screening

At present, in the medical field, drug screening is usually performed using in vivo drug experiments. However, it is very time-consuming and laborious to conduct in vivo experiments on a large number of drugs to be screened one by one. This paper attempts to propose using machine learning algorithms to perform preliminary screening of a large number of compounds to be screened and their molecular structures to reduce the workload of in vivo experiments. Among them, it is internationally recognized that there is an important association between breast cancer progression and the alpha subtype of the estrogen receptor. Anti-breast cancer drug candidates with excellent efficacy need to contain compounds that can better antagonize ERα activity. In this paper, the research object is narrowed down from compounds to the molecular structure of the compounds, and then the random forest regression algorithm is used to develop the molecular structure-ERα activity prediction model. Molecular structures with significant effects on biological activity were screened from molecular structure descriptors in numerous compounds. Four different kernel functions were used to conduct comparative experiments, and finally a support vector regression algorithm based on radial basis kernel function was established, which realized the quantitative prediction of compounds on biological activity of ERα, and could find potential compounds beneficial to breast cancer treatment. This is a novel, computer-based method for preliminary drug screening, which can help medical researchers effectively narrow the scope of experiments and achieve more accurate optimization of drugs.

Generalization of Randic ́ Index of the Non-commuting Graph for Some Finite Groups

Randić index is one of the classical graph-based molecular structure descriptors in the field of mathematical chemistry. The Randić index of a graph is calculated by summing the reciprocals of the square root of the product of the degrees of two adjacent vertices in the graph. Meanwhile, the non-commuting graph is the graph of vertex set whose vertices are non-central elements and two distinct vertices are joined by an edge if and only if they do not commute. In this paper, the general formula of the Randić index of the non-commuting graph associated to three types of finite groups are presented. The groups involved are the dihedral groups, the generalized quaternion groups, and the quasi-dihedral groups. Some examples of the Randić index of the non-commuting graph related to a certain order of these groups are also given based on the main results.

Predicting the acute toxicity of organophosphate esters (OPEs) to aquatic organisms by modelling the structure-toxicity relationships using partial least square regression

Organophosphate esters (OPEs) have been used worldwide as organophosphate flame retardants (OPFRs) since brominated flame retardants (BFRs) were banned. Due to the toxicity of these OPEs, environmental concerns and ecological risks arose. However, there are still large gaps in the understanding of their toxicity to organisms and the mechanisms of toxicity. After collecting the existing toxicity information and obtaining molecular descriptors of OPEs, a partial least square (PLS) regression model was used in this study to quantify the structure-toxicity relationships of OPEs. Based on the regression results, the acute toxicity of the remaining OPEs lacking acute toxicity data was predicted, and the risk level of total common OPEs was classified. The acute toxicity of 15 chemicals was collected, and >1660 molecular structure descriptors were obtained. The cross-validation results of the partial least square regression indicated that two principal components met the regression requirements with the selected features, and the regression equations of these chemicals were generated with selected molecular descriptors. The influence of physicochemical properties, such as hydrophobicity/molecular weight, in traditional perception of OPE toxicity was not that obvious, and acute toxicity was mainly influenced by the autocorrelation coefficients. However, the regression results indicated that the correlation between autocorrelation coefficients calculated based on different physicochemical properties and toxicity was different. According to the prediction result based on PLS regression, CDP may pose a high risk and halogenated alkyl-substituted OPEs such as TCEP may be less toxic. The results of the present study may help inform the environmental management and risk assessment of emerging chemicals such as OPEs.

A Perspective Approach to Study the Valency-Based Irregular Indices for Benzenoid Planar Octahedron Structures

The molecular topology and the chemical structures which are not regular perform a dominant character in designing the compound in connection with their physical and chemical properties. The study of topological descriptors of molecular structures is widely used in the field of cheminformatics, information technology, biomedical science, and many more. Numerous topological indices have been evolved in the theory of chemistry. Graphs which are not regular can be specified using irregular measures. In this article, we find some irregularity indices, which are useful in Quantitative structure activity relationship for benzenoid structures. Based on the exact analytic expressions, the numerical and graphical comparison for benzenoid structures is also provided.

Bioaccumulation, Trophic Transfer, and Biotransformation of Polychlorinated Diphenyl Ethers in a Simulated Aquatic Food Chain.

Polychlorinated diphenyl ethers (PCDEs) are detected in aquatic environments and demonstrate adverse effects in aquatic organisms. However, data regarding the environmental behavior of PCDEs in aquatic ecosystems are lacking. In the present study, a simulated aquatic food chain (Scenedesmus obliquus-Daphnia magna-Danio rerio) was constructed in a lab setting, and the bioaccumulation, trophic transfer, and biotransformation of 12 PCDE congeners were quantitatively investigated for the first time. The log-transformed bioaccumulation factors (BCFs) of PCDEs in S. obliquus, D. magna, and D. rerio were in the range of 2.94-3.77, 3.29-4.03, and 2.42-2.89 L/kg w.w., respectively, indicating the species-specific bioaccumulation of PCDE congeners. The BCF values increased significantly with the increasing number of substituted Cl atoms, with the exception of CDE 209. The number of Cl atoms at the para and meta positions were found to be the major positive contributing factors for BCFs in the case of the same number of substituted Cl. The lipid-normalized biomagnification factors (BMFs) of S. obliquus to D. magna, D. magna to D. rerio, and the whole food chain for the 12 PCDE congeners ranged at 1.08-2.27, 0.81-1.64, and 0.88-3.64, respectively, suggesting that some congeners had BMFs comparable to PBDEs and PCBs. Dechlorination was the only metabolic pathway observed for S. obliquus and D. magna. For D. rerio, dechlorination, methoxylation, and hydroxylation metabolic pathways were observed. 1H nuclear magnetic resonance (NMR) experiments and theoretical calculations confirmed that methoxylation and hydroxylation occurred at the ortho position of the benzene rings. In addition, reliable quantitative structure-property relationship (QSPR) models were constructed to qualitatively describe the relationships between molecular structure descriptors and BCFs for PCDEs. These findings provide insights into the movement and transformation of PCDEs in aquatic ecosystems.