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. 2020 May 22;5(22):13219–13223. doi: 10.1021/acsomega.0c01252

Sulfonation Mechanism of Polysulfone in Concentrated Sulfuric Acid for Proton Exchange Membrane Fuel cell Applications

Yidong Hu †, Liuming Yan ‡,*, Baohua Yue ‡,*
PMCID: PMC7288593  PMID: 32548508

Abstract

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The sulfonated polysulfone is a competitive proton-conducting material for proton exchange membrane fuel cells because of its relatively low cost and adequate performance compared with the perfluorinated sulfonic acid ionomers. This material can be economically synthesized by postsulfonation of commercial polysulfone; however, the inadequate sulfonation degree and the chain-scission degradation during sulfonation prevent the further optimization of its overall performance. In this work, the sulfonation mechanism of polysulfone is studied in terms of the transition state and activation energy based on density functional theory calculations, and the optimization of sulfonation processing parameters are discussed.

1. Introduction

Proton exchange membrane fuel cells (PEMFCs) are promising technology for vehicle applications in the post-fossil-fuel world.1,2 However, the large-scale commercialization of PEMFCs is hindered by the high cost of the essential materials, including the proton exchange membranes (PEMs) and the electrocatalysts.3,4 Therefore, the cost reduction or the development of low-cost PEMs and electrocatalysts is of great priority for the commercialization of PEMFCs.5

The perfluorinated sulfonic acid (PFSA) ionomers, e.g., NAFION, represent the state-of-the-art materials for PEMs, owing to their outstanding performances; however, PFSA ionomers are notorious for their high cost.6,7 In order to cut down the cost of PEMs, sulfonated polysulfone (SPSF) is developed as one substituent of PFSA because of its chemical and thermal stability, excellent mechanical property of its aromatic backbone, adequate proton conductivity contributed by the high concentration of the sulfonic acid groups, and low cost.8−18 For example, Lurrano et al. synthesized SPSF from commercial polysulfone using trimethylsilyl chlorosulfonate as the sulfonation agent at room temperature and achieved a proton conductivity of 43 mS·cm–1 at 80 °C, glass-transition temperature between 200 and 220 °C, and power density of 400 and 500 mW·cm–2, respectively, in H2/air and H2/O2 fuel cells.19,20 By optimization of the sulfonation degree, SPSF can exhibit comparable performances in a direct methanol fuel cell (DMFC) with NAFION 115.21 Furthermore, sulfonated poly(ether sulfone) (SPES),22,23 sulfonated poly(aryl ether sulfone) (SPAES),24,25 and sulfonated poly(phenyl sulfone) (SPPS)26−28 are also synthesized, which partially fulfill the PEMFC applications.

Though sulfonated polysulfone can be synthesized by postsulfonation of commercial polysulfone, the adequate sulfonation degree is difficult to achieve as the insufficient sulfonation will limit the overall proton conductivity, and oversulfonation will lead to chain-scission breakage of the polymeric backbone thus degradation of the molecular weight, the water resistance, and the chemical and mechanical performances.29−31 Therefore, it is important to study the sulfonation mechanisms to improve the overall performances of sulfonated polysulfone. Galabov et al. optimized the transition states of the sulfonation of aromatic molecules by SO3 using high-level ab initio calculations and verified that the sulfonation is a trimolecular process consisting of one aromatic molecule and two SO3 molecules.32,33 Morkovnik and Akopova optimized the transition states for the processes of single-stage isomerization of bimolecular π complex that associates with a H2SO4 molecule into corresponding associates of sulfonic acids, which indicated that the initial associates of the benzene π complex may result from the addition of bimolecular π complexes and H2SO4.34 Recently, Shi suggested that the trimolecular σ complex is formed directly from the rearrangement of a weak trimolecular π complex instead of the reaction of a bimolecular σ complex and SO3.35

In this work, we will study the sulfonation mechanisms of model molecules, which emulate the typical commercialized polysulfone, using concentrated H2SO4 as the sulfonation agent on the basis of density functional theory (DFT) calculations. We will search for transition states of the model systems and evaluate the activation barriers, and the solvation effect will also be evaluated by application of an implicit solvation model for the calculations.

2. Results and Discussion

The sulfonation pathways may involve various possible moieties that exist in the sulfonation environment. In concentrated H2SO4, it is widely accepted that there exist both SO3 and H2SO4, and the actual sulfonation agent may be SO3 or H2SO4 or both. The trimolecular transition states being composed of arene, SO3, and H2SO4 have been optimized in the literature.35 In the present work, we are going to optimize the transition states involving M1 (or M2), SO3, and H2SO4 for the trimolecular mechanism.

2.1. Sulfonation Mechanism of M1

During the sulfonation of M1, the sulfonation agents attack at two positions of M1@a and M1@b via two reactions of R1@a and R1@b, leading to two transition states of TS1@a and TS1@2 and two position isomeric products of P1@a and P1@b.

The transition state of TS1@a is characterized by a six-membered ring (the hydrogen atoms are not counted) as shown in Figure 1a. From TS1@a, it can be seen that the electrophile SO3 attacks at the M1@a carbon from one side of the arylene ring, and H2SO4 attacks the hydrogen atom from the other side of the arylene ring. The complexation interaction between the SO3 and H2SO4 reduces the energy barrier of TS1@a by sharing two hydrogen atoms via two hydrogen bonds. The forming C–S(SO3) bond has a distance of 1.881 Å, closing to the C–S bond in the final product P1@a. The leaving hydrogen atom has passed the center of the C–S(H2SO4), and breaking the C–H bond is elongated from its initial distance of 1.07 to 1.328 Å.

Figure 1.

Figure 1

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Transition states of (a) TS1@a and (b) TS1@b for the sulfonation of M1.

The transition state of TS1@b possesses similar characteristics to the TS1@a (Figure 1b). The forming C–S(SO3) bond has a distance of 1.957 Å, slightly longer than the corresponding distance in TS1@a. Also, the breaking C–H bond is 1.312 Å, slightly shorter than the corresponding distance in TS1@a. In addition, the leaving hydrogen atom reaches almost the center of the C–S(H2SO4). By comparison with TS1@a and TS1@b, it can be concluded that TS1@b resembles the reactant more, and TS1@a resembles the product more.

Since the sulfonation attack at M1@b is hindered by steric repulsion from the bulky sulfonyl linkage between the two arylene rings, the activation energy for TS1@b is much higher than TS1@a in both the gaseous phase and solvated state by H2SO4. The activation energy of TS1@a is low at 39.5 kJ·mol–1 in the gaseous phase and slightly reduces to 33.7 kJ·mol–1 under the solvated state in the sulfonation environment of H2SO4 (Figure 2). For contrast, the activation energy of TS1@b is high at 117.2 kJ·mol–1 in the gaseous phase and reduces to 97.9 kJ·mol–1 under the solvated state in the sulfonation environment. An activation energy of 97.9 kJ·mol–1 is high enough to exclude the sulfonation at M1@b; therefore, it is concluded that the sulfonation product is exclusively P1@a and rarely P1@b.

Figure 2.

Figure 2

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Energetics for R1@a and R1@b evaluated at a theory level of M06-2X/6-311 + G(d) and the PCM solvation model of H2SO4 (inset: IRC for the transition state calculations, unit: kJ·mol–1).

2.2. Sulfonation Mechanism of M2

Similar to the sulfonation of M1, there are also two potential attacking positions for the sulfonation of M2. However, we only optimized on the transition state of TS2@a but failed to locate the transition state of TS2@b. This failure is attributed to the fact that the dimethyl methylene linkage is bulkier than the sulfonyl linkage and thus the more powerful steric repulsion. The powerful steric repulsion from the dimethyl methylene linkage has excluded the formation of TS2@b and thus the formation of P2@b. From Figure 3, it can be seen that TS2@a is also a trimolecular transition state resembling TS1@a. In TS2@a, the forming C–S(SO3) bond has a distance of 1.863 Å, close to the corresponding bond distance of TS1@a, and the breaking C–H bond is elongated to 1.354 Å, which also resembles that of TS1@a.

Figure 3.

Figure 3

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Transition state of TS2@a for the sulfonation of M2.

In Figure 4, it depicts the energetics of the sulfonation reaction of R2@a. The activation energy for TS2@a is at 49.8 kJ·mol–1 in the gas phase, 10.3 kJ·mol–1 higher than that for TS1@a. Under the solvated state of H2SO4, this activation energy slightly decreases to 48.4 kJ·mol–1, and the difference between TS2@a and TS1@a increases to 14.7 kJ·mol–1. That is to say, the solvation effect for TS2@a is insignificant in comparison with TS1@a. This phenomenon is attributed to the difference in polarizability of the dimethyl methylene linkage and the sulfonyl linkage. The sulfonyl linkage can form a hydrogen bond with H2SO4 in the sulfonation environment; thus it greatly interacts with H2SO4. On the other hand, the dimethyl methylene linkage interacts weakly with the sulfonation medium and thus possesses an almost untouched activation energy.

Figure 4.

Figure 4

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Energetics for R2@a evaluated at a theory level of M06-2X/6-311 + G(d) and the PCM solvation model of H2SO4 (inset: IRC for the transition state calculations, unit: kJ·mol–1).

The structural parameters for the transition states are summarized in Table 1 where lC – S is the forming bond between C, S, lC – H is the breaking bond between C and H, and lO – H is the distance between O and the leaving H. These structural parameters are consistent with each other, indicating that these transition states are concerted.

Table 1. Structural Parameters for the Transition States.

TS lC – S (Å) lC – H (Å) lO – H (Å)
TS1@a 1.881 1.328 1.307
TS1@b 1.957 1.312 1.322
TS2@a 1.863 1.354 1.281
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3. Conclusions

From the DFT study of the sulfonation mechanisms of model molecules, it is concluded that the sulfonation is a trimolecular process involving one substrate molecule, one SO3, and one H2SO4 in the transition state. The SO3 and H2SO4 attack simultaneously from both sides of the arylene ring of the polysulfone, forming a six-membered ring at the transition state without counting the hydrogen atoms, and the activation barrier is compensated by the hydrogen-bonding interaction between the attacking SO3 and H2SO4 molecules. The sulfonation attacks favorably at the ortho position of the ether bond linkage, rarely at the ortho position of the sulfonyl linkage, and not at the ortho position of the dimethyl methylene linkage attributing to the steric hindrance. For the two ortho positions of the ether bond linkage, the sulfonation attacks preferentially at the arylene ring with a sulfonyl linkage instead of that with a dimethyl methylene linkage.

Under the solvation of the sulfonation environment, the sulfonyl interacts more intensively with the solvation medium than the dimethyl methylene, and the activation barrier for the previous reaction is depressed more significantly than that for the latter. Therefore, it is concluded that the sulfonation attacks preferentially at the arylene ring with a sulfonyl linkage to that with a dimethyl methylene ring.

Furthermore, the sulfonation process is more complicated except for the sulfonation reaction. The detrimental side reactions, such as chain-scission breakage and/or cross-linking, are also possible at high temperatures for a long time in the sulfonation medium.36 These side reactions are beyond the scope of this short paper but will be covered in our future study.

4. Calculation Method

The DFT calculations are applied to the study of sulfonation mechanisms of polysulfone. All the geometries of reactants, reactant complexes, transition states, and products are optimized at a theory level of B3LYP/6-31G(d), and the energies are corrected at a theory level of M06-2X/6-311 + G(d) without further optimization as implemented in the Gaussian 09 package of programs.37,38 The solvation effects are evaluated using the implicit PCM model of H2SO4 with a dielectric constant of 101 and a refractive index of 1.4183 at a theory level of M06-2X/6-311 + G(d) without further optimization.39−42 Finally, internal reaction coordination (IRC) is evaluated to connect the transition states with both the reactant complexes and products.

The bisphenol A type polysulfone (BPA-PSF) is the most produced polysulfone and thus is also the most frequently sulfonated polysulfone for the preparation of SPSF. The repeat unit of BPA-PSF consists of four arylene rings, and the two arylene rings from bisphenol A are equivalent and two from bis(4-fluorophenyl) sulfone are also equivalent. The sulfonation attacks at four possible positions (1, 2, 3, or 4 position), forming four position isomers of monosulfonated BPA-PSF as depicted in Figure 5.

Figure 5.

Figure 5

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Sulfonation positions of the BPA-PSF and the emulation model molecules for the DFT study

In the DFT study of the sulfonation mechanism of polysulfone, it is possible to use a short piece of the polymeric molecule or model molecule instead of the whole polysulfone molecule since chemical reactions are usually dependent only on near range interactions. For this reason, two model molecules, M1 and M2, are designed to emulate the BPA-PSF for the DFT study of sulfonation mechanisms (Figure 5). The model molecules consist of three arylene rings, and sulfonation attacks at the middle ring. For the model molecule M1 (or M2), the two possible sulfonation positions are labeled as M1@a (or M2@a) and M1@b (or M2@b), and the corresponding sulfonation reactions, transition states, and final products are labeled as R1@a (or R2@a) and R1@b (or R2@b), TS1@a (or TS2@a) and TS1@b (or TS2@b), and P1@a (or 2@a) and P1@b (or P2@b), respectively.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (grant nos. 21706156 and 21573143) and NSAF (grant no. U1630102). The authors also acknowledge the International Center for Quantum and Molecular Structures and the High-Performance Computing Center of Shanghai University for computing service.

The authors declare no competing financial interest.

References

  1. Lü X.; Qu Y.; Wang Y.; Qin C.; Liu G. A comprehensive review on hybrid power system for PEMFC-HEV: Issues and strategies. Energy Convers. Manage. 2018, 171, 1273–1291. 10.1016/j.enconman.2018.06.065. [DOI] [Google Scholar]
  2. Steele B. C. H.; Heinzel A. Materials for fuel-cell technologies. Nature 2001, 414, 345–352. 10.1038/35104620. [DOI] [PubMed] [Google Scholar]
  3. Kraytsberg A.; Ein-Eli Y. Review of advanced materials for proton exchange membrane fuel cells. Energy Fuels 2014, 28, 7303–7330. 10.1021/ef501977k. [DOI] [Google Scholar]
  4. Ghosh P. C. High platinum cost: obstacle or blessing for commercialization of low-temperature fuel cell technologies. Clean Technol. Environ. Policy 2017, 19, 595–601. 10.1007/s10098-016-1254-4. [DOI] [Google Scholar]
  5. Sopian K.; Daud W. R. W. Challenges and future developments in proton exchange membrane fuel cells. Renewable Energy 2006, 31, 719–727. 10.1016/j.renene.2005.09.003. [DOI] [Google Scholar]
  6. Mauritz K. A.; Moore R. B. State of understanding of Nafion. Chem. Rev. 2004, 104, 4535–4586. 10.1021/cr0207123. [DOI] [PubMed] [Google Scholar]
  7. Esmaeili N.; Gray E. M.; Webb C. J. Non-fluorinated polymer composite proton exchange membranes for fuel cell applications - A review. ChemPhysChem 2019, 20, 2016–2053. 10.1002/cphc.201900191. [DOI] [PubMed] [Google Scholar]
  8. Scherer G. G. Sulfonated aromatic polymers for fuel cell membranes. Adv. Polym. 2008, 222, 1–62. [Google Scholar]
  9. Wang C.; Zhou Y.; Shen B.; Zhao X.; Li J.; Ren Q. Proton-conducting poly(ether sulfone ketone)s containing a high density of pendant sulfonic groups by a convenient and mild post-sulfonation. Polym. Chem. 2018, 9, 4984–4993. 10.1039/C8PY00996A. [DOI] [Google Scholar]
  10. Bose S.; Kuila T.; Nguyen T. X. H.; Kim N. H.; Lau K. T.; Lee J. H. Polymer membranes for high temperature proton exchange membrane fuel cell: Recent advances and challenges. Prog. Polym. Sci. 2011, 36, 813–843. 10.1016/j.progpolymsci.2011.01.003. [DOI] [Google Scholar]
  11. di Vona M. L.; Knauth P. Sulfonated aromatic polymers as proton-conducting solid electrolytes for fuel cells: a short review. Z. Phys. Chem. 2013, 227, 595–614. 10.1524/zpch.2013.0337. [DOI] [Google Scholar]
  12. Ghosh A.; Banerjee S. Sulfonated fluorinated-aromatic polymers as proton exchange membranes. e-Polymers 2014, 14, 227–257. 10.1515/epoly-2014-0049. [DOI] [Google Scholar]
  13. Feng S.; Sasaki K.; Nishihara M. Effect of sulfonation level on sulfonated aromatic poly(ether sulfone) membranes as polymer electrolyte for high-temperature polymer electrolyte membrane fuel cells. Macromol. Chem. Phys. 2016, 217, 2692–2699. 10.1002/macp.201600397. [DOI] [Google Scholar]
  14. Paradesi D.; Gandhimathi S.; Krishnan H.; Jeyalakshmi R. A novel proton conducting polymer electrolyte membrane for fuel cell applications. High Perform. Polym. 2017, 30, 116–125. 10.1177/0954008316684931. [DOI] [Google Scholar]
  15. Yu L.; Yue B.; Yan L.; Zhao H.; Zhang J. Proton conducting composite membranes based on sulfonated polysulfone and polysulfone-g-(phosphonated polystyrene) via controlled atom-transfer radical polymerization for fuel cell applications. Solid State Ionics 2019, 338, 103–112. 10.1016/j.ssi.2019.05.012. [DOI] [Google Scholar]
  16. Yue B.; Zeng G.; Zhang Y.; Tao S.; Zhang X.; Yan L. Improved performance of acid-base composite of phosphonic acid functionalized polysulfone and triazolyl functionalized polysulfone for PEM fuel cells. Solid State Ionics 2017, 300, 10–17. 10.1016/j.ssi.2016.11.011. [DOI] [Google Scholar]
  17. Zeng G.; Yue B.; Li X.; Yan L. Astonishing synergetic effect of proton conducting between phosphonic acid groups and triazolyl groups tethered simultaneously on poly(ether sulfone) backbone. Solid State Ionics 2018, 320, 100–112. 10.1016/j.ssi.2018.02.025. [DOI] [Google Scholar]
  18. Zhang X.; Yue B.; Yan L.; Zeng G.; Tao S. Improving the comprehensive performances of phosphonic acid functionalized poly(ether sulfone) by compositing with 1H-1,2,3-triazol-4-yl functionalized poly(ether sulfone). Int. J. Hydrogen Energy 2016, 41, 4740–4750. 10.1016/j.ijhydene.2016.01.076. [DOI] [Google Scholar]
  19. Lufrano F.; Squadrito G.; Patti A.; Passalacqua E. Sulfonated polysulfone as promising membranes for polymer electrolyte fuel cells. J. Appl. Polym. Sci. 2000, 77, 1250–1256. . [DOI] [Google Scholar]
  20. Lufrano F.; Gatto I.; Staiti P.; Antonucci V.; Passalacqua E. Sulfonated polysulfone ionomer membranes for fuel cells. Solid State Ionics 2001, 145, 47–51. 10.1016/S0167-2738(01)00912-2. [DOI] [Google Scholar]
  21. Fu Y. Z.; Manthiram A. Synthesis and characterization of sulfonated polysulfone membranes for direct methanol fuel cells. J. Power Sources 2006, 157, 222–225. 10.1016/j.jpowsour.2005.08.007. [DOI] [Google Scholar]
  22. Guan R.; Zou H.; Lu D.; Gong C.; Liu Y. Polyethersulfone sulfonated by chlorosulfonic acid and its membrane characteristics. Eur. Polym. J. 2005, 41, 1554–1560. 10.1016/j.eurpolymj.2005.01.018. [DOI] [Google Scholar]
  23. Kim I. C.; Choi J. G.; Tak T. M. Sulfonated polyethersulfone by heterogeneous method and its membrane performances. J. Appl. Polym. Sci. 1999, 74, 2046–2055. . [DOI] [Google Scholar]
  24. Wang F.; Hickner M.; Kim Y. S.; Zawodzinski T. A.; McGrath J. E. Direct polymerization of sulfonated poly(arylene ether sulfone) random (statistical) copolymers: Candidates for new proton exchange membranes. J. Membr. Sci. 2002, 197, 231–242. 10.1016/S0376-7388(01)00620-2. [DOI] [Google Scholar]
  25. Yuk J.; Lee S.; Nugraha A. F.; Lee H.; Park S. H.; Yim S. D.; Bae B. Synthesis and characterization of multi-block poly(arylene ether sulfone) membranes with highly sulfonated blocks for use in polymer electrolyte membrane fuel cells. J. Membr. Sci. 2016, 518, 50–59. 10.1016/j.memsci.2016.06.037. [DOI] [Google Scholar]
  26. Dyck A.; Fritsch D.; Nunes S. P. Proton-conductive membranes of sulfonated polyphenylsulfone. J. Appl. Polym. Sci. 2002, 86, 2820–2827. 10.1002/app.11264. [DOI] [Google Scholar]
  27. Schuster M.; Kreuer K. D.; Andersen H. T.; Maier J. Sulfonated poly(phenylene sulfone) polymers as hydrolytically and thermooxidatively stable proton conducting ionomers. Macromolecules 2007, 40, 598–607. 10.1021/ma062324z. [DOI] [Google Scholar]
  28. Schuster M.; de Araujo C. C.; Atanasov V.; Andersen H. T.; Kreuer K.-D.; Maier J. Highly sulfonated poly(phenylene sulfone): Preparation and stability issues. Macromolecules 2009, 42, 3129–3137. 10.1021/ma900333n. [DOI] [Google Scholar]
  29. Liu B.; Robertson G. P.; Kim D.-S.; Guiver M. D.; Hu W.; Jiang Z. Aromatic poly(ether ketone)s with pendant sulfonic acid phenyl groups prepared by a mild sulfonation method for proton exchange membranes. Macromolecules 2007, 40, 1934–1944. 10.1021/ma061705+. [DOI] [Google Scholar]
  30. Liu B.; Robertson G. P.; Kim D. S.; Sun X.; Jiang Z.; Guiver M. D. Enhanced thermo-oxidative stability of sulfophenylated poly(ether sulfone)s. Polymer 2010, 51, 403–413. 10.1016/j.polymer.2009.12.014. [DOI] [Google Scholar]
  31. Unveren E. E.; Erdogan T.; Çelebi S. S.; Inan T. Y. Role of post-sulfonation of poly(ether ether sulfone) in proton conductivity and chemical stability of its proton exchange membranes for fuel cell. Int. J. Hydrogen Energy 2010, 35, 3736–3744. 10.1016/j.ijhydene.2010.01.041. [DOI] [Google Scholar]
  32. Koleva G.; Galabov B.; Kong J.; Schaefer F. S. III; von R. Schleyer P. Electrophilic aromatic sulfonation with SO3: Concerted or classic SEAr mechanism?. J. Am. Chem. Soc. 2011, 133, 19094–19101. 10.1021/ja201866h. [DOI] [PubMed] [Google Scholar]
  33. Galabov B.; Nalbantova D.; von R. Schleyer P.; Schaefer F. S. III Electrophilic aromatic substitution: New insights into an old class of reactions. Acc. Chem. Res. 2016, 49, 1191–1199. 10.1021/acs.accounts.6b00120. [DOI] [PubMed] [Google Scholar]
  34. Morkovnik A. S.; Akopova A. R. Low-barrier concerted electrophilic aromatic substitution under the action of sulfur trioxide. Dokl. Chem. 2013, 450, 122–126. 10.1134/S0012500813050054. [DOI] [Google Scholar]
  35. Shi H. Sulfonation mechanism of benzene with SO3 in sulfuric acid or oleum or aprotic solvent: Obeying the transition state theory via a trimolecular electrophilic substitution clarified by density functional theory calculation. Comput. Theor. Chem. 2017, 1112, 111–122. 10.1016/j.comptc.2017.04.012. [DOI] [Google Scholar]
  36. Xing P.; Robertson G. P.; Guiver M. D.; Mikhailenko S. D.; Wang K.; Kaliaguine S. Synthesis and characterization of sulfonated poly(ether ether ketone) for proton exchange membranes. J. Membr. Sci. 2004, 229, 95–106. 10.1016/j.memsci.2003.09.019. [DOI] [Google Scholar]
  37. Frisch M. J.; Pople J. A.; Binkley J. S. Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets. J. Chem. Phys. 1984, 80, 3265–3269. 10.1063/1.447079. [DOI] [Google Scholar]
  38. Zhao Y.; Truhlar D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 2008, 120, 215–241. 10.1007/s00214-007-0310-x. [DOI] [Google Scholar]
  39. York D. M.; Karplus M. Smooth solvation potential based on the conductor-like screening model. J. Phys. Chem. A 1999, 103, 11060–11079. 10.1021/jp992097l. [DOI] [Google Scholar]
  40. Scalmani G.; Frisch M. J. Continuous surface charge polarizable continuum models of solvation I. General formalism. J. Chem. Phys. 2010, 132, 114110–114125. 10.1063/1.3359469. [DOI] [PubMed] [Google Scholar]
  41. Dean J. A.Lange’s Handbook of Chemistry; 15th Ed.; Esposito R., Eds.; Mcgraw-Hill, Inc.: New York, 1998; pp 5.105–5.129. [Google Scholar]
  42. Haynes W. M.; Lide D. R.; Bruno T. J.. CRC Handbook of Chemistry and Physics. 97th Ed.; Haynes W. M., Ed. CRC Press: Boca Raton, 2017; pp 6.199–6.220. [Google Scholar]

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