Connotations of the fuzzy judgment of credit risk based on a scale of 0.1–0.9.

Connotations of the fuzzy judgment of credit risk based on a scale of 0.1–0.9.</p

S1 Appendix -

(DOCX)</p

The system of indicators for assessing the own credit risk of firms in the supply chain.

The system of indicators for assessing the own credit risk of firms in the supply chain.</p

Probability distribution of consistency index <i>CR</i>.

Probability distribution of consistency index CR.</p

Probability distributions of .

Probability distributions of .</p

The system of indicators of firm’s own credit risk.

The system of indicators of firm’s own credit risk.</p

Risk contagion network of the automotive supply chain.

Risk contagion network of the automotive supply chain.</p

The visual process to evaluate the credit risk of enterprises in the supply chain.

The visual process to evaluate the credit risk of enterprises in the supply chain.</p

Quantum Chemistry Study on the Extraction of Trivalent Lanthanide Series by Cyanex301: Insights from Formation of Inner- and Outer-Sphere Complexes

The extraction of lanthanide series by Cyanex301, i.e., bis­(2,4,4-trimethylpentyl)­dithiophosphinic acid (HC301), has been modeled by density functional theory calculation, taking into account the formation of both inner- and outer-sphere complexes. The inner-sphere complex Ln­(C301)₃ and the outer-sphere complex Ln­(H₂O)₉(C301)₃ are optimized, followed by the analysis of interaction energy, bond length, Laplacian bond orders, and Mulliken populations. The covalency degree increases in Ln–S and Ln–O bonds in the inner- and outer-sphere complexes, respectively, as the lanthanide series is traversed. Mulliken population analysis indicates the important role of the 5d-orbital participation in bonding in the formation of inner- and outer-sphere complexes. Two thermodynamic cycles regarding the formation of inner- and outer-sphere complexes are established to calculate the extraction Gibbs free energies (Δ<i>G</i>_extr), and relaxed potential energy surface scan is utilized to model the kinetic complexation of C301 anion with hydrated metal ions. Light lanthanides can form both inner- and outer-sphere complexes, whereas heavy lanthanides only form outer-sphere complexes in biphasic extraction. After adopting the data of forming inner-sphere complex for light Ln­(III) and that of forming outer-sphere complexes for heavy Ln­(III), the trend of the calculated −Δ<i>G</i>_extr agrees very well with that of the experimental distribution ratios on crossing the Ln­(III) series. Results from this work help to theoretically understand the extraction behavior of Cyanex301 with respect to different Ln­(III)

Weights of <i>S</i>₁, <i>S</i>₂,⋯,<i>S</i>₈ under the linear weighting coefficient.

Weights of S1, S2,⋯,S8 under the linear weighting coefficient.</p