Nickel Bis(diselenolene) as a Catalyst for Olefin Purification

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Nickel Bis(diselenolene) as a Catalyst for Olefin Purification Rajesh K. Raju,‡ Dusan N. Sredojevic,‡ Salvador Moncho,‡ and Edward N. Brothers*,‡ ‡

Science Program, Texas A&M University at Qatar, Education City, Doha, Qatar S Supporting Information *

ABSTRACT: Nickel bis(dithiolene) reversibly binds olefins via a known interligand binding mechanism, but the complex has limited practical use, due to a competitive intraligand addition which results in decomposition. The present work examines an alternative nickel-based complex that eliminates the decomposition route. Specifically, we have examined the olefin binding processes of nickel bis(diselenolene) complexes using modern density functional theory. Both the inter- and intraligand adducts of the nickel bis(diselenolenes) are thermodynamically more stable than their dithiolene analogues. We have predicted that nickel bis(diselenolene) complexes do not decompose after the intraligand addition, and that the overall activation energies for the kinetically accessible products are quite small. In short, our computational work predicts that nickel bis(diselenolene) complexes are better electrocatalysts for olefin purification than the previous candidates, superior to the previously studied nickel bis(dithiolene) complexes.

1. INTRODUCTION Olefins, primarily ethylene and propylene, are the largest volume material produced in the chemical and petrochemical industries, and are widely used as building blocks for the manufacture of polymers, esters, alcohols, acids, and so forth.1,2 Olefins are typically produced from natural gas or crude oil via steam or catalytic cracking, and are then separated from impurities via cryogenic distillation. However, cryogenic distillation is an energy-intensive and costly process, which contributes approximately 75% of the total olefin production cost.3,4 Although alternative methods, such as reverse olefin complexation with redox metal salts (for example, copper and silver) have been proposed, their practical use is limited due to “poisoning” by impurities such as CO, H2, and H2S.5 A work by Wang and Stiefel in 2001 was a major breakthrough in costeffective olefin purification, as it reported that nickel bis(dithiolene) complexes [Ni(S2C2(R2))2 (R = CF3, CN)] can be used as an efficient electrocatalyst for olefin purification via reversible selective binding with olefins, and this complex appears to avoid deactivation in the presence of impurities.6 Wang and Stiefel proposed an electrocatalytic cycle comprising four distinct steps (Scheme 1): (i) [NiL2]− undergoes electrochemical oxidation to neutral [NiL2]. (ii) [NiL2] (L = substituted dithiolene) selectively binds the olefin to form the adduct [(olefin)NiL2]. (iii) [(olefin)NiL2] is electrochemically reduced to the anionic [(olefin)NiL2]− species. (iv) [(olefin)NiL2]− rapidly eliminates olefin to regenerate [NiL2]−. Several previous studies, including the X-ray structural characterization of cis-interligand adducts, have shown that bis(dithiolene) complexes have high cycloaddition reactivity toward strained and cyclic alkenes such as norbornadiene.7−18 Consistent with this, the cis-interligand adduct (addition of the CC bond across two sulfur atoms on different dithiolene rings) was believed to be formed in step (ii), while the © XXXX American Chemical Society

intraligand addition (addition of CC bond across two sulfur atoms on the same dithiolene ring) was considered a minor side reaction.6,18 However, this selectivity in favor of the interligand adduct violates the Woodward−Hoffmann addition rule, as the formation of the interligand adduct (2; see Scheme 2) is symmetry forbidden, whereas the formation of the intraligand adduct (3) is symmetry allowed.19 In 2002, Fan and Hall attempted to resolve this by proposing a two-step mechanism for the formation of 2 via a twisted interligand intermediate (2y), which then isomerizes into thermodynamically more stable 2.19 Such a two-step process could avoid the constraints imposed by orbital symmetry considerations. In 2006, new experiments by Fekl and co-workers demonstrated that the interligand adduct is recovered only in the presence of the reduced anionic species 1−, necessitating a revision of the Fan-Hall two-step mechanism, as it did not consider the anion’s role.20 In the absence of 1−, the binding of olefins leads to the symmetry-allowed intraligand adduct 3 which then decomposes, while with high concentrations of 1− the primary product is 2 (Scheme 2B). A revised mechanism was then developed by some of the authors via a combination of experimental and computational studies; this mechanism explains all current experimental observations for nickel bis(dithiolene)’s binding of olefins and includes other indirect routes such as binding directly to the nickel (4) or along the nickel sulfur bond (5).21−23 In a related work, and inspired by the nickel bis(dithiolene) electrocatalysis, Li et al. computationally investigated the possibilities of cobalt and copper analogues of nickel bis(dithiolene) complexes for olefin purification.24 Also in a related work, Dang et al. studied the binding of 1,3-butadiene with platinum bis(dithiolene) using Received: June 9, 2016

A

DOI: 10.1021/acs.inorgchem.6b01295 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Scheme 1. Proposed Electrochemical Catalytic Cycle for Olefin Purification by Nickel Bis(dithiolene) Complexes6

Scheme 2. [A] Naming Conventions of the Ethylene Adducts with Nickel Bis(Dithiolene) Complexes; [B] Decomposition Route via Interligand Adduct Formation in the Absence of the Anionic Complexa

a

MM, MD, and CP are metal monomer, metal dimer, and cyclic product, respectively. B

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Inorganic Chemistry Table 1. Relative Free Energies (kcal/mol) for the Various Nickel Bis(dithiolene) and Bis(diselenolene) Complexes square planar complex Ni(Se2C2(CF3)2)2 Ni(Se2C2(CN)2)2 Ni(S2C2(CF3)2)2c Ni(S2C2(CN)2)2

abbreviation Ni(tds)2 Ni(mns)2 Ni(tfd)2 Ni(mnt)2

S

1

0.0 0.0 0.0 0.0

tetrahedral

T

S

1

10.9 7.9 0.9 4.7

1

square planar T

1

6.6 6.6

a

a

a

b

b

a

D −

1

0.0 0.0 0.0 0.0

tetrahedral

Q −

D −

24.3 19.0

b

a

b

a

d

a

15.1

a

15.3 10.7

1

Q −

1

1

a Converged to other high energy isomers. bOptimization converges to square planar geometry. cValue taken from ref 22. dGeometry optimization failed to converge. Note that superscript S, D, T and Q corresponds to singlet, doublet, triplet, and quartet electronic state.

DFT.25 The balance of this work is thus leveraging this knowledge to design a better catalyst, preferably one that does not decompose but is related to the original nickel bis(dithiolene). Although their chemical reactions with olefins are as of yet unstudied, the existence of the synthetic routes to nickel bis(diselenolene) complexes such as Ni(Se2C2(CF3)2)2, Ni(Se2C2(CN)2)2, Ni(Se2C2(CH3)2)2, and Ni(Se2C2(CH3)H)2 are established in the literature.26−32 Given the proximity of selenium to sulfur on the periodic table, the synthetic accessibility of the nickel bis(diselenolene) complexes, and the ability of nickel bis(dithiolene) to reversibly complex olefins, we studied the possible applications of these complexes as olefin purification catalysts by evaluating their ability to reversibly complex olefins via modeling their respective mechanisms. Ideally, the catalyst should reversibly bind olefins, avoid decomposition, and not require the use of an anionic cocatalyst.

Table 2. Binding Free Energies (kcal/mol) for the Binding of Ethylene with Nickel Bis(dithiolene) and Nickel Bis(diselenolene) Complexesa complex

abbreviation

2y

2

3

Ni(Se2C2(CF3)2)2 Ni(Se2C2(CN)2)2 Ni(S2C2(CF3)2)2 Ni(S2C2(CN)2)2

Ni(tds)2 Ni(mns)2 Ni(tfd)2 Ni(mnt)2

−22.9 −24.1 −16.7 −16.9

−26.2 −28.3 −18.4 −18.9

−30.0 −27.8 −15.8 −13.0

a

Binding free energy values for the dithiolene complex Ni(tfd)2 are taken from ref 22. We have computed the binding free energies for Ni(mnt)2.

complex in comparison to the more electronegative sulfur, resulting in more positive charge on selenium atoms, which is in favor of the approach of ethylene, which acts as a nucleophile. Mulliken charges (Table S1) qualitatively confirm this observation. The NBO analysis on adducts 2 and 3 also leads to similar observations. For both complexes Ni(tds)2 and Ni(mns)2, NBO reveals that there is a net positive charge of ∼ +1.4 on the two sulfur atoms which form the bonds with ethylene carbon atoms for both the adducts 2 and 3, which can be compared to the net positive charge of ∼1.0 on the two similar sulfur atoms. This leads to the conclusion that, being less electronegative in comparison with sulfur, selenium has more electron delocalization which leads to the greater stability of the adducts. As a generalization, we can suggest that more electropositive donor atoms can make the approach of ethylene more favorable and leads to greater stabilization of the adducts. In fact, if the reaction of the bare ligand with ethylene is modeled at the same level of theory used here, the complexation of mns and ethylene is more exergonic (−48.4 kcal/mol) than the complexation of mnt and ethylene (−41.7 kcal/mol). It should be noted in passing that the LUMOs and HOMO−LUMO gaps of the selenium and sulfur compounds are similar and hence not the cause of this difference (Table S2). By looking at Table 2, it can be seen that 2 is always more stable than 3 for sulfur complexes, while this is not the case for selenium. The discrepancies in the stabilities of various adducts for nickel bis(diselenolene) complexes compared to those of the dithiolene complexes can be explained on the basis of the distortion energies (Table S3) of the monomeric nickel complex when forming these adducts. Distortion energy, in this case, is the energetic cost of the nickel complex adjusting its geometry to bind the olefin. It is calculated by optimizing the complex with the bound ethylene, then removing the ethylene and doing a single point calculation on the distorted nickel bearing structure, then taking the difference in energy between the optimized bare complex and the distorted complex. The energetic costs for the distortion of the nickel bis(diselenolene) complexes for forming 2 are 13.2 and 14.5 kcal/mol for Ni(tds)2 and Ni(mns)2, respectively, whereas 3 costs 31.4 kcal/

2. RESULTS AND DISCUSSION As a starting point, and following previous studies on Ni(S2C2(CF3)2)2 and Ni(S2C2(CN)2)2, we studied the binding of olefins with the selenolene analogues, namely, Ni(Se2C2(CF3)2)2 and Ni(Se2C2(CN)2)2. The relative free energy difference for the two low-lying electronic states for both neutral and reduced dithiolene and diselenolene complexes are given in Table 1. In addition to square planar complexes, we have also examined tetrahedral geometries. From Table 1, it is clear that, for all the neutral species, the singlet state is the lowest energy electronic state, while for all the reduced complexes, the doublet state is the lowest energy electronic state. While we could find tetrahedral species for some of the complexes, they are higher energy species compared to the stable square planar complexes. Also, for selenolene complexes, the singlet and triplet electronic states are widely separated compared to dithiolene complexes. The most stable singlet electronic states are taken for binding free energy calculations with the parent complex 1. The comparative binding free energies of ethylene on nickel bis(dithiolene) and nickel bis(diselenolene) complexes are given in Table 2. It can be seen from Table 2 that the binding of ethylene with the selenium complexes is more exergonic compared to the dithiolene analogues. This can be attributed to the stronger bond formed between the selenium and the carbon than between the sulfur and the carbon. Natural bond orbital (NBO) analysis on Ni(tds)2 and Ni(mns)2 shows that there is an overall positive charge of ∼ +1.0 on the two selenium atoms of the diselenolene ligand compared to an overall positive charge of ∼ +0.6 on the two sulfur atoms of the dithiolene ligand for Ni(tfd)2 and Ni(mnt)2. Being less electronegative, selenium can have greater electron delocalization into the C

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Figure 1. Free energy profile (solvent corrected, kcal/mol) for the binding of ethylene with Ni(tds)2. The Fan-Hall path is shown in blue, the indirect pathway via intermediate 5 is shown in red, and the direct path for 3 is shown with a dotted line.

Figure 2. Comparison between the solvent corrected free energy values (kcal/mol) for Ni(tds)2 [red] and Ni(tfd)2 [blue].

energies account for the reduction in thermodynamic stability for the intraligand adducts (3) on the nickel bis(dithiolenes). The computed free energy profiles for the binding of ethylene with Ni(tds)2 is shown in Figure 1, while a graph comparing the free energy values for Ni(tds)2 and the

mol each. For dithiolene analogues, the distortion energies remain almost the same (14.2 and 14.7 kcal/mol) for the formation of 2. However, the distortion energies for the formation of intraligand adducts (39.5 and 37.7 kcal/mol) are higher than for the diselenolene complex. These high distortion D

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Figure 3. Computed free energies of reaction for the model decomposition process of intraligand adduct 3 for Ni(tds)2 [A] and Ni(tfd)2 [B]. All energy values are solvent corrected and in kcal/mol. Note that these are stationary points on the energy surface for various decomposition species in their most stable form, i.e., this is a thermodynamic path with no transition states shown. The superscripts “S” and “T” on the decomposed species MM, CP, and MD represent the spin states in their most stable form.

position of diselenolene complexes to the experimental decomposition of dithiolenes into the cyclic product (CP) and the metal dimer (MD). Surprisingly, we have found that, compared to the dithiolene complex Ni(tfd)2, the intraligand adduct 3 of the diselenolene complex Ni(tds)2 is less likely to decompose. The intraligand adduct 3 for the dithiolene complex Ni(tfd)2 decomposes into a metal monomer (MM) and cyclic product (CP), which are 20.9 kcal/mol less stable than 3. The metal monomer then forms a more stable dimer (MD). However, for diselenolene analogue Ni(tds)2, the decomposition products MM and CP are highly unstable intermediates, 44.7 kcal/mol less stable than the intraligand adduct 3. Because nickel bis(diselenolene) complexes do not easily generate decomposition products via intraligand addition, both interligand and intraligand complexes may be equally useful, assuming they can release the olefin upon reduction. The computed binding free energies for the reduced selenolene complex Ni(tds)2− with ethylene show that 2− and 3− are less stable than the unbound reactants by 7.5 and 11.0 kcal/mol, respectively. This is thermodynamically sufficient to result in dissociation, as upon electrochemical reduction the complex will expel the bound olefin. The dissociation pathways of ethylene from 2− and 3− for Ni(tds)2− are depicted in Figure 4. The reduced interligand adduct 2− first forms the twisted intermediate 2y−, overcoming a barrier of 24.5 kcal/mol. However, there is not a simple reversal of the Fan-Hall path that connects 2y− and the dissociated products. Instead, a two-step mechanism has been proposed for the release of ethylene from 2y−. In the first step, 2y− first forms an intermediate Int2y−, which then breaks the second C−Se bond, releasing 1−, and ethylene. The breaking of the first bond C−Se bond from 2y− requires an activation of 19.1 kcal/mol, while breaking the second C−Se bond requires a very small activation energy of only 0.7 kcal/mol. However, there is a more kinetically favored pathway via intermediate 5−, which requires an overall activation of 18.5 kcal/mol; this is a simple pathway of 2− going to 5− which then dissociates. A similar two-step

corresponding sulfur complex Ni(tfd)2 is shown in Figure 2. With regard to the selenium-bearing complex Ni(tds)2 first, the formation of 2 requires an activation of 16.9 kcal/mol (TS2y) to form the twisted intermediate 2y via the Fan-Hall pathway. The twisted intermediate 2y then isomerizes into 2 after crossing a barrier of 21.4 kcal/mol. The direct route to 3 has an activation barrier of 3.8 kcal/mol (TS3). However, there also exists an indirect route for the formation of 2 and 3 via intermediate 5; the creation of 5 is nearly barrierless (1.0 kcal/ mol), and relative free energy of 5 is quite exergonic. Intermediate 5 can then isomerize into 2 and 3, overcoming barriers of 8.4 and 14.3 kcal/mol, respectively. Overall, the kinetically favored pathway is the formation of 2 via 5 with a rate-determining barrier of 8.4 kcal/mol. However, the overall activation energy for the formation of 2 via 5 is 1.0 kcal/mol. The direct route for the intraligand addition is also competitive as the activation barrier is only 3.8 kcal/mol. A comparison between nickel bis(dithiolene) and nickel bis(diselenolene) complexes shows that the reaction profiles follow very similar patterns. The indirect pathway for the dithiolene complex Ni(tfd)2 begins with the formation of weak complex 4 (binding only to the nickel) which then isomerizes into the stable intermediate 5 (Ni−S bound complex) via transition state TS45. The overall kinetic barrier for this indirect pathway is 20.0 kcal/mol. However, the direct addition pathway for the formation of intraligand adduct 3 is the kinetically favored route with an overall activation barrier of 18.3 kcal/mol. On the other hand, for nickel bis(diselenolene) complex Ni(tds)2, we could locate direct formation of 5 via transition state TS5. In addition, there are considerable reductions in activation barriers for diselenolene complexes (Figure 2). Moreover, the kinetically preferred route is almost barrierless for nickel bis(diselenolene) complexes. We then examined the decomposition profiles for nickel bis(diselenolene)’s intraligand complex (3) and compared them with the decomposition of the nickel bis(dithiolene) analogues (Figure 3). Specifically, we compared the decomE

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Figure 4. Dissociation pathways (solvent corrected, kcal/mol) for the release of ethylene from reduced adducts 2− and 3− for Ni(tds)2.

mechanism is proposed for the release of ethylene from 3−. The reduced intraligand adduct 3− first forms an intermediate Int3− after breaking one C−Se bond, overcoming an activation barrier of 17.7 kcal/mol. This intermediate then relases 1− and ethylene quite rapidly, as the breaking of the second C−Se bond has an activation barrier of only 0.7 kcal/mol. The

indirect route via 5− also exists as in the decomposition of 2−; however, it requires a higher free energy of activation of 21.7 kcal/mol. The important point is that both 2 and 3, which are stable for bis(diselenolene), dissociate upon reduction with approximately the same barrier. Similar dissociation profiles for 2− and 3− for the dithiolene complex Ni(tfd)2 are shown in F

DOI: 10.1021/acs.inorgchem.6b01295 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 5. Dissociation pathways (solvent corrected, kcal/mol) for the release of ethylene from reduced adducts 2− and 3− for Ni(tfd)2.

contrast with the diselenolene complex, we have found a reversal of the Fan-Hall pathway for the dissociation of ethylene from the dithiolene complex. However, the activation barrier is quite high for this dissociation route compared to the indirect pathway via intermediate 5−. The dissociation pathways for the loss of ethylene from the reduced intraligand adduct 3− is similar for both Ni(tfd)2 and Ni(tds)2. As in the case of the

Figure 5. The dissociation of ethylene from the anionic adduct 2− is preferred via the indirect pathway. The reduced interligand adduct 2− first forms the intermediate 5− by overcoming a kinetic barrier of 18.7 kcal/mol and then dissociates. The overall activation energies required for the dissociation of ethylene from dithiolene and diseleonolene complexes are similar (18.7 and 18.5 kcal/mol, respectively). In G

DOI: 10.1021/acs.inorgchem.6b01295 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry diselenolene complex, a two-step dissociation route via Int3− is preferred over the indirect route via 5−. It is also interesting to note that the overall activation energy required for the dissociation of ethylene from 2− is also quite similar (17.5 kcal/mol for Ni(tfd)2 and 17.7 kcal/mol for Ni(tds)2) as in the case of 3−. The reaction profile for the complex with a CN substituent in place of the CF3 groups is very similar, save minor changes in the free energy values. In addition, we have investigated the binding of ethylene with Ni(C2Se2H2)2 and Ni(C2Se2(CH3)2)2. The free energy profiles for these complexes also show no significant changes in the results except for the upshift of free energy values, which is an expected result when the strong electron withdrawing groups CN and CF3 are replaced by H or the electron donating group CH3. These results are included in the Supporting Information, as they are of interest to workers in the field, but do not add to the overall arguments of this work.

correction. The solvation corrected free energy values (ΔG) were used throughout the paper unless otherwise stated. Taking Ni(tds)2 as a representative case, we have shown that the difference between the solvent corrected free energy values and the free energy values obtained by performing the full calculation (optimization and vibrational analysis) in solvent are relatively small (see Supporting Information Table S5). The differences range from −0.7 to −2.2 for all the geometries except for one transition state for which the difference is −2.8 kcal/mol.

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b01295. Average Mulliken charges; HOMO−LUMO energies; distortion energies for the formation of interligand and intraligand adducts; binding free energies; comparison between solvent corrected binding free energy values and the free energies obtained by performing the full optimization in solvent; relative free energies; free energy profiles for the binding of ethylene with Ni(mns)2, Ni(Se2C2H2)2 and Ni(Se2C2(CH3)2)2; comparison between the solvent corrected free energy values for Ni(mns)2 and Ni(mnt)2, and for Ni(tds)2 and Ni(tfd)2; computed free energy surfaces for the model decomposition process of intraligand adduct 3 for Ni(mns)2, Ni(mnt)2, Ni(Se2C2H2)2 and Ni(Se2C2(CH3)2)2; dissociation pathways; optimized geometries for reactants, products, intermediates, and transition states; IRC plot for the transition states TS52 and TS53 for Ni(tds)2 and Ni(mns)2; Cartesian coordinates of the optimized geometries of different complexes (PDF)

3. CONCLUSIONS In summary, we have investigated the binding pathways of ethylene with various nickel bis(diselenolene) complexes. We have found that these complexes are better candidates for olefin purification catalysts than nickel bis(dithiolene) complexes, as the selenium-bearing complexes do not decompose via intraligand addition. In addition, we have found that the various steps in the catalytic cycle also do not require high energies of activation. It is our hope that this complex and accompanying mechanism will have role to play in future technology in olefin purification, which is critical to the petrochemical industry. 4. COMPUTATIONAL DETAILS

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All calculations were performed using the development version of the Gaussian suite of programs.33 Previous benchmark studies on Ni(S2C2H2)2 showed that the ωB97XD34 density functional, which contains both long-range exact exchange and empirical dispersion corrections, gave results similar to that of coupled cluster (CCSD) calculations.35 We thus employed ωB97XD in combination with the 631++G(d,p) basis set. All geometries (reactants, products, intermediates, and transition states) were optimized in the gas phase, and vibrational analysis was performed to confirm that the optimized geometries correspond to minima or transition states based on the number of imaginary frequencies. Intrinsic reaction coordinate (IRC)36 calculations were also performed whenever necessary to demonstrate that a given transition state connects to reactants, products, or intermediates of interest. Gas phase vibrational frequencies (unscaled) were used to compute the enthalpic and entropic parts of the free energy. Stability calculations were performed to ensure that optimal electronic structures were found.37,38 Stability issues are solved by employing unrestricted ωB97XD calculations as in the case of open-shell systems; i.e., we perform a series of stability calculations and geometry reoptimizations until stability is achieved. In the rare case that we could not find a stable solution for a particular geometry even by performing unrestricted calculations, we employed the Yamaguchi broken-spin-symmetry procedure39,40 to calculate the energy of the spin-purified low-spin (LSE) state from the computed energies of the broken-symmetry solution (BSE) and the high-spin coupled state (HSE), according to the following formula LS

BS

E=

E( HS⟨S2 ⟩ −

LS

⟨S2 ⟩) − HSE( BS⟨S2 ⟩ − ⟨S2 ⟩ − BS⟨S2 ⟩

ASSOCIATED CONTENT

S Supporting Information *

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This publication was made possible by the NPRP award 5-3181-063 from the Qatar National Research Fund (a member of The Qatar Foundation). The IT Research Computing group in Texas A&M University at Qatar provided the computational resources and services used in this work.

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REFERENCES

(1) National Research Council. Separation and Purification: Critical Needs and Opportunities; National Academy Press: Washington, DC, 1987. (2) Sundaram, K. M.; Sreehan, M. M.; Olszewski, E. F. Kirk-Othmer Encyclopedia of Chemical Technology, 4th ed.; Wiley: New York, 1995. (3) Grantom, R. L.; Royer, D. J. In Ullmann’s Encyclopedia of Industrial Chemistry, 5th ed.; VCH: New York, 1987. (4) Ladwig, P. K. Chapter 3.1. In Hanbook of Petroleum Refining Processes, 2nd ed.; Meyers, R. A., Ed.; McGraw-Hill: New York, 1997. (5) Suzuki, T.; Noble, R. D.; Koval, C. A. Electrochemistry, Stability, and Alkene Complexation Chemistry of Copper(I) Triflate in Aqueous Solution. Potential for Use in Electrochemically Modulated Complexation-Based Separation Processes. Inorg. Chem. 1997, 36, 136−140.

LS

⟨S2 ⟩)

HS

Solvent effects were incorporated by using gas phase geometries and employing the SMD41 solvation model with chloroform as solvent; this solvation energy was then added to the gas phase results as a H

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Article

Inorganic Chemistry

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DOI: 10.1021/acs.inorgchem.6b01295 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry (41) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J. Phys. Chem. B 2009, 113, 6378−6396.

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DOI: 10.1021/acs.inorgchem.6b01295 Inorg. Chem. XXXX, XXX, XXX−XXX