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On the opposite effect of guanidinium chloride and guanidinium sulphate on the kinetics of the Diels-Alder reaction
Journal of Molecular Liquids 275 (2019) 100–104
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
On the opposite effect of guanidinium chloride and guanidinium sulphate on the kinetics of the Diels-Alder reaction Giuseppe Graziano Dipartimento di Scienze e Tecnologie, Università del Sannio, Via Port'Arsa 11, 82100 Benevento, Italy
a r t i c l e
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Article history: Received 20 August 2018 Received in revised form 13 October 2018 Accepted 13 November 2018 Available online 14 November 2018 Keywords: Transition state of Diels-Alder reaction Contact-minimum configuration of pairwise hydrophobic interaction Water and aqueous solutions of guanidinium salts
a b s t r a c t The transition state of Diels-Alder reactions resembles the contact-minimum configuration of pairwise hydrophobic interaction. On this ground, it has been possible to find a robust correlation between the experimental k2 values for the reaction between cyclopentadiene and methyl acrylate and the Gibbs energy estimates for the formation of this contact-minimum configuration. The enhancement of rate constant caused by Gdm2SO4 comes from the large density increase caused by the addition of this salt to water (i.e., the strong electrostrictive power of sulphate ions), that renders very large the Gibbs energy cost of cavity creation. The WASA decrease associated with the formation of the contact-minimum configuration leads to a decrease in the Gibbs energy cost of cavity creation with respect to the situation of the two molecules far apart from each other. This corresponds to a gain in translational entropy of ions and water molecules that is larger the greater the density or better the number density of the aqueous solution. This entropy gain in the case of Gdm2SO4 overwhelms the energy decrease associated with the loss of several attractive interactions between the Gdm + ions and the nonpolar solute molecules. © 2018 Elsevier B.V. All rights reserved.
1. Introduction For a long time it was believed that Diels-Alder reactions should not be sensitive to changes in the solvent selected as reaction medium [1]. Breslow and co-workers, however, discovered during the eighties that several Diels-Alder reactions are strongly accelerated in water [2,3]. Water affects also the stereoselectivity of Diels-Alder reactions: the endo product, which is already the dominant one in organic solvents, is even more favoured in water [2,3]. Breslow pointed out that the solvent effect is not a simple polarity effect, because a special effect occurs in water, namely the hydrophobic effect or better the so-called hydrophobic interactions: the tendency of nonpolar moieties to aggregate in water in order to reduce the contact surface with water [4]. Two hydrocarbon surfaces must be close to each other in the transition state of Diels-Alder reactions, and such an association is strongly favoured in water due to hydrophobic interactions. In fact, Breslow and Zhu found a correlation between the reaction rate and the nonpolar surface area that becomes inaccessible in the transition state [5]. This rationalization holds also for the stereoselectivity, because the transition state leading to the endo product is more compact than that for the exo product. Engberts and co-workers, by systematically investigating the effects of water and its mixtures with organic solvents on Diels-Alder reactions, rationalized the results in terms of an “enforced” pairwise hydrophobic interaction for the encounter of diene and dienophile [6–8]. They E-mail address: [email protected].
https://doi.org/10.1016/j.molliq.2018.11.054 0167-7322/© 2018 Elsevier B.V. All rights reserved.
introduced this expression to distinguish the association process leading to the transition state from the non-reactive ones. Even though “enforced” pairwise hydrophobic interaction is a more correct expression than “hydrophobic packing” used by Breslow, the two research groups fundamentally refer to the same physical process driven by the unique properties of water. Further evidence came from the analysis of the effects caused by the addition of salts to water [9,10]. It was found that: (a) salts decreasing the hydrocarbon solubility in water (salting out agents) cause an enhancement of the rate constant with respect to pure water; (b) salts increasing the hydrocarbon solubility in water (salting in agents) cause a decrease of the rate constant with respect to pure water [9,10]. This finding was rationalized on the basis of the Hofmeister series, according to which the ion size is the controlling factor: small ions decrease hydrocarbon solubility, while large ions increase solubility [11,12]. In an interesting investigation, Kumar and co-workers have verified the effect of different guanidinium salts on the kinetics of the Diels-Alder reaction between cyclopentadiene and methyl acrylate [13]. They found that all guanidinium salts cause a decrease of the rate constant with the respect to pure water, except guanidinium sulphate, and proposed some explanations. It is worth noting that Gdm2SO4 is different from the other guanidinium salts also because its addition to water causes a stabilization of the native state of globular proteins [14–16], whereas GdmCl, for instance, is a commonly used protein denaturant. Since I have devised a rationalization of the different behaviour of GdmCl and Gdm2SO4 towards the native state of globular proteins
G. Graziano / Journal of Molecular Liquids 275 (2019) 100–104
[17], grounded in a general approach to the hydrophobic effect [18–20], I would like to use practically the same approach to shed light on the effect of these guanidinium salts on the kinetics of Diels-Alder reactions. Such an approach cannot shed light on π-electron rearrangement that is the heart of Diels-Alder reactions, but is aimed at providing an explanation of salt effects on reaction kinetics. 2. Theoretical approach By recognizing the kinetic mechanism of the Diels-Alder reaction, I have developed a simple approach based on the following fundamental assumption. Since the activation volume is negative for Diels-Alder reactions [21], the transition state of the latter should resemble the contact-minimum configuration of the pairwise hydrophobic interaction [22], HI, that is characterized by a decrease in water accessible surface area [23–25], WASA (i.e., a decrease in solvent-excluded volume). This implies that: (a) the second-order rate constant of the Diels-Alder reaction, k2, is related to the Gibbs energy cost associated with the formation of the transition state, ΔGǂ, via the Eyring equation; (b) the ΔGǂ quantity should be correlated to the indirect part (i.e., the one that depends upon the solvent [22,24]; see below for a complete definition) of the reversible work associated with the formation of the contact-minimum configuration (i.e., the transition state), starting from the two molecules at infinite distance, ΔGǂ ∝ δG(HI); (c) the latter relationship does not mean that k2 can really be calculated by means of the δG(HI) values; other things would be necessary, because the δG(HI) values do not account for the loss in translational, rotational and vibrational degrees of freedom of the two molecules on forming the transition state; (d) the knowledge of the δG(HI) values can be useful to rationalize solvent effects on the k2 magnitude. Pairwise HI corresponds to the process of forming, at constant temperature and pressure, a contact-minimum configuration of two nonpolar molecules at a fixed position in water starting from the two molecules at infinite separation [22]. The associated Gibbs energy change is given by: ΔGðHIÞ ¼ Ea ðcontactÞ þ δGðHIÞ
ð1Þ
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reorganization of water-water H-bonds upon nonpolar solute insertion does not appear in Eq. (3) because an almost complete enthalpyentropy compensation holds for such a reorganization process [28,29]. Since the occurrence of such enthalpy-entropy compensation is due to the weakness of solute-solvent attractions in comparison to the strength of solvent-solvent attractions [29] (i.e., water-water H-bonds are stronger than nonpolar molecule-water van der Waals attractions), its validity cannot be guaranteed in the case of strong ion-water electrostatic interactions. The assumption that enthalpy-entropy compensation holds for the structural reorganization of all the species present in the considered aqueous solutions has to be considered as a working hypothesis. The use of Eq. (3) in the definition of δG(HI) leads to: δGðHIÞ ¼ ½ΔGc ðtwoÞ−2 ΔGc ðoneÞ þ ½Ea ðtwoÞ−2 Ea ðoneÞ ¼ δGc þ δEa
ð4Þ
Eq. (4) shows that a quantitative estimate of ions and water contribution to pairwise HI can be obtained from: (a) the calculation of ΔGc to create in water and aqueous solutions a cavity suitable to host a couple of solute molecules in the contact-minimum configuration, and a cavity suitable to host a single solute molecule; (b) the calculation of Ea to turn on the attractive interactions between a couple of solute molecules in the contact-minimum configuration or a single solute molecule and all the surrounding ions and water molecules. Actually, a different route has been followed, by assuming that the diene and the dienophile can be described as spherical molecules with the same diameter σc = 5 Å. This choice, even though not strictly correct from the structural point of view, allows one to provide a proof of concept for the reliability of the proposed rationalization. Classic scaled particle theory [30], SPT, calculations have shown that: (a) by keeping fixed the van der Waals cavity volume, the ΔGc magnitude depends on the cavity shape, and proves to be proportional to cavity WASA, that is a measure of the solvent-excluded volume due to cavity creation; (b) the value of the ΔGc/WASA ratio calculated for spherical cavities can be used, to a good approximation, also for nonspherical cavities [31,32]. Thus, δGc is calculated from the knowledge of the WASA fraction buried upon association [18,24,25]: δGc ¼ −f WASA ΔGc ðone sphereÞ
ð5Þ
where Ea(contact) is the direct interaction energy of the two solute molecules in the contact-minimum configuration, and does not depend on the presence of the solvent and its nature; δG(HI) is the indirect part of the reversible work to carry out the process, and accounts for the specific features of the solvent in which pairwise HI occurs. A general relationship connects δG(HI) to the Ben-Naim standard hydration Gibbs energy of the two molecules in the contact-minimum configuration and of a single molecule [22,24,25], respectively:
The detailed analysis performed by Levy and colleagues indicates that also Ea scales linearly with WASA [33]; in addition, to achieve close agreement with the computer simulation results for the pairwise HI of some alkanes, it emerged that fWASA has to be multiplied times a factor equal to 1.2 [24]. On this basis, δEa is calculated by means of the following relationship:
δGðHIÞ ¼ ΔG• ðtwoÞ−2 ΔG• ðoneÞ
δEa ¼ −1:2 f WASA Ea ðone sphereÞ
ð2Þ
where ΔG• represents the Gibbs energy change associated with the transfer of a species from a fixed position in the ideal gas phase to a fixed position in water, at constant temperature and pressure, ΔG• (one) is the hydration Gibbs energy change of one molecule, and ΔG• (two) is the hydration Gibbs energy change of two molecules in the contact-minimum configuration. Application of a physical concept and of statistical mechanics allows the exact splitting of ΔG• into two contributions [26,27]: ΔG• ¼ ΔGc þ Ea
ð3Þ
where ΔGc is the reversible work to create at a fixed position in water or aqueous solution a cavity suitable to host the solute molecule, and Ea is the reversible work to turn on the attractive interactions between the solute molecule inserted in the cavity and all the surrounding ions and water molecules (the second step is conditional to the first: there is no additivity of independent contributions [26,27]). Of course, ΔGc is always a positive quantity and Ea is always a negative quantity. The
ð6Þ
The WASA fraction of the two spherical cavities, fWASA, that becomes buried in the contact-minimum configuration, is exactly given by [24]: f WASA ¼ 1−½σ c =ðσ c þ σ Þ
ð7Þ
where σc = 5 Å is the diameter of one spherical cavity (solute molecule), and ⟨σ⟩ = ∑χj⋅σj is the average effective diameter of the different particles constituting the considered aqueous solution, where χj is the molar fraction of species j and σj is the corresponding hard sphere diameter. Eqs. (5) and (6) show that δGc provides a negative Gibbs energy change favouring the formation of the contact-minimum configuration, whereas δEa provides a positive Gibbs energy change contrasting the formation of the contact-minimum configuration. The rationale is that bringing two spherical solute molecules from a fixed position at infinite distance to a fixed position at contact distance in aqueous solution causes: (a) a decrease in the solvent-excluded volume, measured by the WASA decrease upon association, that causes a translational entropy gain for ions and water molecules; (b) a decrease in the number of ions
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G. Graziano / Journal of Molecular Liquids 275 (2019) 100–104
and water molecules contacting the two spherical solute molecules, that causes the loss of attractive solute-ions and solute-water energetic interactions [18,24,25]. 3. Calculation procedure Estimates of ΔGc[σc = 5 Å] have been calculated by means of classic SPT formulas [17,30], using the experimental values of the density of water [34], and of all the considered aqueous salt solutions [35], at 25 °C and 1 atm (see the second column of Table 1). The following effective hard sphere diameters have been selected: σ = 2.80 Å for water molecules [17,18], close to the location of the first peak in the oxygen‑oxygen radial distribution function of water [36]; σ = 2.02 Å for Na + ions [37]; 4.70 Å for Gdm + ions, which is the diameter of the sphere possessing the same WASA of Gdm + ion [17]; 3.62 Å for Cl- ions; 4.80 Å for ClO4ions; 4.60 Å for SO42-ions (all the anionic values correspond to the Pauling-type diameters listed by Marcus in Table XIII of [38]). These diameters serve to arrive at the volume packing density of the considered solutions, ξ3 = (π/6)⋅∑ρj⋅σ3j , where ρj is the number density of the species j; ξ3 represents the fraction of the total liquid volume really occupied by ions and molecules, and is a fundamental ingredient of classic SPT calculations [17,37]. The obtained ξ3 values are reported in the fourth column of Table 1. The Ea value for the nonpolar spherical solute of 5 Å diameter has been fixed to −30.0 kJ mol−1 in pure water at 25 °C and 1 atm, in line with the numbers obtained for alkanes of similar size by means of Monte Carlo or molecular dynamics simulations in detailed water models [33,39,40]. By considering that both Na + and SO42-ions are strongly hydrated and should not interact with the nonpolar solute, the Ea value in aqueous 1 M Na2SO4 solution has been calculated by means of the following relationship: Ea ðsolutionÞ ¼ Ea ðwaterÞ ½ξ3 ðsolutionÞ=ξ3 ðwaterÞ
ð8Þ
whose reliability comes from the formula originally proposed by Pierotti [30]. Application of Eq. (8) leads to Ea(1 M Na2SO4) = −32.0 kJ mol−1. In the case of aqueous GdmCl solutions, it is necessary to consider that guanidinium ions are weakly hydrated in view of their low charge density [41], and interact preferentially with the nonpolar solute [17,42]. This should imply that the Ea magnitude in aqueous GdmCl solutions has to be larger than that in water and aqueous Na2SO4 solution. On this physical ground, I have deliberately fixed: Ea(1 M GdmCl) = −34.0 kJ mol−1, and Ea(2 M GdmCl) = −38.0 kJ mol−1. Since in aqueous 1 M Gdm2SO4 solution, the Gdm + concentration corresponds to that in aqueous 2 M GdmCl solution and the sulphate ions should not interact with the nonpolar solute, I have used Eq. (8) to arrive at: Ea(1 M Gdm2SO4) = Ea(2 M GdmCl)·(0.4675/0.4242) = −42.0 kJ mol−1. In
Table 1 Experimental values, at 25 °C and 1 atm, of the density and water molar concentration for pure water, aqueous 1 M and 2 M GdmCl solutions, aqueous 1 M and 2 M Gdm2SO4 solutions, aqueous 1 M and 2 M GdmClO4 solutions, and aqueous 1 M Na2SO4 solution [34,35]; values of the volume packing density for all these solutions, calculated using the effective hard sphere diameters reported in the text; classic SPT estimates of the reversible work ΔGc to create in these liquid solutions, at 25 °C and 1 atm, a spherical cavity of 5 Å diameter; estimates of the Ea quantity and values of ΔGc + Ea in all these solutions; values of the average effective hard sphere diameter ⟨σ⟩ of these solutions.
H2O 1 M GdmCl 2 M GdmCl 1 M Gdm2SO4 2 M Gdm2SO4 1 M GdmClO4 2 M GdmClO4 1 M Na2SO4
ρ g L−1
[H2O] M
ξ3
ΔGc kJ mol−1
Ea kJ mol−1
ΔGc + Ea kJ mol−1
⟨σ⟩ Å
997 1022 1047 1183 1353 1060 1121 1117
55.3 51.4 47.5 53.7 51.1 50.0 44.5 54.1
0.3830 0.4035 0.4242 0.4675 0.5460 0.4137 0.4432 0.4103
37.9 39.8 42.0 53.4 75.7 40.4 43.1 42.6
−30.0 −34.0 −38.0 −42.0 −52.0 −36.0 −41.0 −32.0
7.9 5.8 4.0 11.4 23.7 4.4 2.1 10.6
2.80 2.85 2.91 2.90 3.00 2.87 2.96 2.80
aqueous 2 M Gdm2SO4 solution, I have deliberately fixed Ea = −52.0 kJ mol−1, a value markedly larger than that in water because [Gdm+] = 4 M and it interacts preferentially with the nonpolar solute [17,42]. Finally, since the perchlorate ions are weakly hydrated due to their low charge density [11,12], the Ea magnitude in aqueous GdmClO4 solutions has been considered to be larger than that in aqueous GdmCl solutions. Specifically, Ea(1 M GdmClO4) = −36.0 kJ mol−1, and Ea(2 M GdmClO4) = −41.0 kJ mol−1. All these numbers are listed in the sixth column of Table 1. Even though they do not come from a precise formula or detailed computer simulations, their magnitude should be more-than-qualitatively correct; nevertheless, significant changes to these Ea values might have marked effects on the final results of the present analysis. A last point. According to Eq. (7) and the ⟨σ⟩ estimates listed in the last column of Table 1, 0.36 ≤ fWASA ≤ 0.38. Therefore, I have fixed fWASA = 0.37 for water and all the considered aqueous solutions. 4. Results and discussion The calculated ΔGc[σc = 5 Å] values are listed in the fifth column of Table 1. They are large positive and increase markedly with the volume packing density of the solution. As a consequence, the smallest ΔGc occurs in pure water (i.e., 37.9 kJ mol−1 with ξ3 = 0.383) and the largest in 2 M Gdm2SO4 (i.e., 75.7 kJ mol−1 with ξ3 = 0.546). In comparing the ΔGc magnitude in aqueous solutions, the size of solvent molecules and ions does not play a fundamental role [18,37], because the average effective diameter ⟨σ⟩ is always close to 2.8 Å, the effective size of water molecules, as can be appreciated on looking at the numbers listed in the last column in Table 1. The fundamental role is played by the volume packing density ξ3 whose value reflects the density of such solutions [37,43]. By looking at the second and third columns of Table 1, it is evident that: (a) all the considered salts cause a density increase in view of the strength of ion-water electrostatic interactions; (b) the presence of the sulphate ion causes a marked density increase due to its high charge density and so a marked increase in the ΔGc magnitude. The SPT result that all the considered salts increase the ΔGc magnitude is in line with the experimental fact that all these salts cause an increase of the liquid-vapour surface tension of water, and Gdm2SO4 proves to be the most effective among the guanidinium salts [44]. On the other hand, the Ea estimates are large negative but always smaller in magnitude than the corresponding ΔGc numbers. As a consequence, the ΔGc + Ea values prove to be positive in all cases, but they are small in aqueous GdmClO4 and GdmCl solutions, and large in aqueous Gdm2SO4 solutions (see the numbers listed in the seventh column of Table 1). This is in line with the salting in effect of GdmClO4 and GdmCl, and the salting out effect of Gdm2SO4 experimentally determined by Kumar and co-workers for the solubility of methyl acrylate (see Figure 2 in [13]). It is worth noting that the salting out effect of Gdm2SO4 occurs even though the Ea magnitude in such solutions proves to be the largest among the considered solutions (see Table 1). The salting out effect is due to the ΔGc magnitude, whose marked increase on adding Gdm2SO4 to water is caused by the large density increase [17], that manifests also in the increase of the total number density: 55.3 mol l−1 in water, 56.7 mol l−1 in 1 M Gdm2SO4, and 57.1 mol l−1 in 2 M Gdm2SO4. The ΔGc and Ea values can be used to obtain estimates of the Gibbs energy change δG(HI) associated with the formation of the contactminimum configuration of the two spheres by means of Eqs. (4)–(7). The obtained δG(HI) estimates, listed in the fourth column of Table 2, are positive in aqueous GdmClO4 and GdmCl solutions, but negative in water, and aqueous Gdm2SO4 and Na2SO4 solutions. Clearly, a negative δG(HI) value favours the formation of the contact-minimum configuration of the two spheres, whereas a positive δG(HI) value means that the formation of the contact-minimum configuration is not favoured. It is worth noting that the δG(HI) values are small in comparison to what is expected for ΔGǂ, which would be of the order of several tens of
G. Graziano / Journal of Molecular Liquids 275 (2019) 100–104 Table 2 Estimates, at 25 °C and 1 atm, of the δGc, δEa, and δG(HI) terms, calculated by means of Eqs. (4)–(7) for the contact-minimum configuration of two spherical molecules in all the considered aqueous solutions. In the last two columns, are reported the experimental values, determined by Kumar and co-workers [13], of the second-order rate constant and of the percentage endo yield for the Diels-Alder reaction between cyclopentadiene and methyl acrylate, at 25 °C and 1 atm.
H2O 1 M GdmCl 2 M GdmCl 1 M Gdm2SO4 2 M Gdm2SO4 1 M GdmClO4 2 M GdmClO4 1 M Na2SO4
δGc kJ mol−1
δEa kJ mol−1
δG(HI) kJ mol−1
k2⋅104 M−1 s−1
endo %
−14.0 −14.7 −15.5 −19.8 −28.0 −15.0 −16.0 −15.8
13.7 15.1 16.9 18.6 23.1 16.0 18.2 14.2
−0.7 0.4 1.4 −1.2 −4.9 1.0 2.2 −1.6
25.0 17.0 11.0 33.1 39.3 10.5 4.1 37.3
67 58 53 75 82 52 -79
103
between the transition state of Diels-Alder reactions and the contactminimum configuration of pairwise HI. It was proposed, mainly on the basis of molecular dynamics results [47], that the stabilizing effect of Gdm2SO4 towards the native state of globular proteins is due to the formation of ion-pairs in water that lead to the formation of nanoscale aggregates, rendering the Gdm + ions not available to directly interact with the protein surface. However, a detailed conductance study concluded that the observed ion association is rather weak and cannot explain the different behaviour of Gdm2SO4 with respect to the other guanidinium salts towards the native state of globular proteins [48]. This conclusion is in line with that emerged earlier from my theoretical approach [17]. As a consequence, the formation of ion-pairs cannot be invoked to rationalize the special behaviour of Gdm2SO4 towards the kinetics of Diels-Alder reactions. 5. Conclusion
kJ mol−1 [45,46]. Most of the ΔGǂ magnitude depends upon the rearrangement of chemical bonds during the formation of the transition state. This rearrangement of π-electrons should be little affected by changes in the solvent medium and should represent a common ground for a given Diels-Alder reaction. The δG(HI) values represent a small perturbation to this common ground, but important to increase or decrease the rate constant. Importantly, the calculated δG(HI) values prove to be correlated with the experimental values of both the second order rate constant k2 and the percentage endo yield of the Diels-Alder reaction of cyclopentadiene with methyl acrylate. The latter numbers, determined by Kumar and co-workers at 25 °C and 1 atm [13], are listed in the last two columns of Table 2. A plot of the correlation between the experimental k2 values and the present δG(HI) estimates is shown in Fig. 1. The correlation is reasonably good, indicating the reliability of the present approach, even though it is stretched very far from its range of applicability. As already underscored in the Theoretical approach section, this is solely a correlation because there is no straightforward formula to pass from δG(HI) to the k2 values. In general, Diels-Alder reactions are characterized by negative activation volumes [21], indicating that the transition state occupies less volume in solution than the two separated reactants. The activation volumes determined by Kumar and co-workers for the Diels-Alder reaction between cyclopentadiene and methyl acrylate at 25 °C proved to be negative and to follow the same rank order of the k2 values (see Table 5 in [13]). The present approach is in line with experimental data on activation volumes, as expected due to the geometric similarity
By assuming that the transition state of Diels-Alder reactions can be described as the contact-minimum configuration of pairwise HI, it has been possible to find a robust correlation between the δG(HI) estimates and the experimental k2 values for the reaction between cyclopentadiene and methyl acrylate. The enhancement of rate constant caused by Gdm2SO4 is due to the large density increase caused by its addition to water (i.e., the strong electrostrictive power of sulphate ions), that renders very large the Gibbs energy cost of cavity creation. Indeed, the WASA decrease associated with the formation of the contact-minimum configuration leads to a decrease in the Gibbs energy cost of cavity creation with respect to the situation of the two molecules far apart from each other. This corresponds to a gain in translational entropy of ions and water molecules (for the increase in the accessible configurational space) that is larger the greater the density or better the number density of the aqueous solution. This entropy gain in the case of Gdm2SO4 overwhelms the energy decrease associated with the loss of several attractive interactions between the Gdm + ions and the nonpolar solute molecules. Acknowledgements I would like to thank the two reviewers for their useful comments on the original version of the manuscript. The present work has been supported by the fund for research activity of the Università del Sannio. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
Fig. 1. Plot of the second order rate constant k2 values for the Diels-Alder reaction between cyclopentadiene and methyl acrylate, at 25 °C and 1 atm, in water and different aqueous salt solutions [13] versus the δG(HI) estimates obtained in the present study. See Table 2 for the precise numbers.
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On the opposite effect of guanidinium chloride and guanidinium sulphate on the kinetics of the Diels-Alder reaction Giuseppe Graziano Dipartimento di Scienze e Tecnologie, Università del Sannio, Via Port'Arsa 11, 82100 Benevento, Italy
a r t i c l e
i n f o
Article history: Received 20 August 2018 Received in revised form 13 October 2018 Accepted 13 November 2018 Available online 14 November 2018 Keywords: Transition state of Diels-Alder reaction Contact-minimum configuration of pairwise hydrophobic interaction Water and aqueous solutions of guanidinium salts
a b s t r a c t The transition state of Diels-Alder reactions resembles the contact-minimum configuration of pairwise hydrophobic interaction. On this ground, it has been possible to find a robust correlation between the experimental k2 values for the reaction between cyclopentadiene and methyl acrylate and the Gibbs energy estimates for the formation of this contact-minimum configuration. The enhancement of rate constant caused by Gdm2SO4 comes from the large density increase caused by the addition of this salt to water (i.e., the strong electrostrictive power of sulphate ions), that renders very large the Gibbs energy cost of cavity creation. The WASA decrease associated with the formation of the contact-minimum configuration leads to a decrease in the Gibbs energy cost of cavity creation with respect to the situation of the two molecules far apart from each other. This corresponds to a gain in translational entropy of ions and water molecules that is larger the greater the density or better the number density of the aqueous solution. This entropy gain in the case of Gdm2SO4 overwhelms the energy decrease associated with the loss of several attractive interactions between the Gdm + ions and the nonpolar solute molecules. © 2018 Elsevier B.V. All rights reserved.
1. Introduction For a long time it was believed that Diels-Alder reactions should not be sensitive to changes in the solvent selected as reaction medium [1]. Breslow and co-workers, however, discovered during the eighties that several Diels-Alder reactions are strongly accelerated in water [2,3]. Water affects also the stereoselectivity of Diels-Alder reactions: the endo product, which is already the dominant one in organic solvents, is even more favoured in water [2,3]. Breslow pointed out that the solvent effect is not a simple polarity effect, because a special effect occurs in water, namely the hydrophobic effect or better the so-called hydrophobic interactions: the tendency of nonpolar moieties to aggregate in water in order to reduce the contact surface with water [4]. Two hydrocarbon surfaces must be close to each other in the transition state of Diels-Alder reactions, and such an association is strongly favoured in water due to hydrophobic interactions. In fact, Breslow and Zhu found a correlation between the reaction rate and the nonpolar surface area that becomes inaccessible in the transition state [5]. This rationalization holds also for the stereoselectivity, because the transition state leading to the endo product is more compact than that for the exo product. Engberts and co-workers, by systematically investigating the effects of water and its mixtures with organic solvents on Diels-Alder reactions, rationalized the results in terms of an “enforced” pairwise hydrophobic interaction for the encounter of diene and dienophile [6–8]. They E-mail address: [email protected].
https://doi.org/10.1016/j.molliq.2018.11.054 0167-7322/© 2018 Elsevier B.V. All rights reserved.
introduced this expression to distinguish the association process leading to the transition state from the non-reactive ones. Even though “enforced” pairwise hydrophobic interaction is a more correct expression than “hydrophobic packing” used by Breslow, the two research groups fundamentally refer to the same physical process driven by the unique properties of water. Further evidence came from the analysis of the effects caused by the addition of salts to water [9,10]. It was found that: (a) salts decreasing the hydrocarbon solubility in water (salting out agents) cause an enhancement of the rate constant with respect to pure water; (b) salts increasing the hydrocarbon solubility in water (salting in agents) cause a decrease of the rate constant with respect to pure water [9,10]. This finding was rationalized on the basis of the Hofmeister series, according to which the ion size is the controlling factor: small ions decrease hydrocarbon solubility, while large ions increase solubility [11,12]. In an interesting investigation, Kumar and co-workers have verified the effect of different guanidinium salts on the kinetics of the Diels-Alder reaction between cyclopentadiene and methyl acrylate [13]. They found that all guanidinium salts cause a decrease of the rate constant with the respect to pure water, except guanidinium sulphate, and proposed some explanations. It is worth noting that Gdm2SO4 is different from the other guanidinium salts also because its addition to water causes a stabilization of the native state of globular proteins [14–16], whereas GdmCl, for instance, is a commonly used protein denaturant. Since I have devised a rationalization of the different behaviour of GdmCl and Gdm2SO4 towards the native state of globular proteins
G. Graziano / Journal of Molecular Liquids 275 (2019) 100–104
[17], grounded in a general approach to the hydrophobic effect [18–20], I would like to use practically the same approach to shed light on the effect of these guanidinium salts on the kinetics of Diels-Alder reactions. Such an approach cannot shed light on π-electron rearrangement that is the heart of Diels-Alder reactions, but is aimed at providing an explanation of salt effects on reaction kinetics. 2. Theoretical approach By recognizing the kinetic mechanism of the Diels-Alder reaction, I have developed a simple approach based on the following fundamental assumption. Since the activation volume is negative for Diels-Alder reactions [21], the transition state of the latter should resemble the contact-minimum configuration of the pairwise hydrophobic interaction [22], HI, that is characterized by a decrease in water accessible surface area [23–25], WASA (i.e., a decrease in solvent-excluded volume). This implies that: (a) the second-order rate constant of the Diels-Alder reaction, k2, is related to the Gibbs energy cost associated with the formation of the transition state, ΔGǂ, via the Eyring equation; (b) the ΔGǂ quantity should be correlated to the indirect part (i.e., the one that depends upon the solvent [22,24]; see below for a complete definition) of the reversible work associated with the formation of the contact-minimum configuration (i.e., the transition state), starting from the two molecules at infinite distance, ΔGǂ ∝ δG(HI); (c) the latter relationship does not mean that k2 can really be calculated by means of the δG(HI) values; other things would be necessary, because the δG(HI) values do not account for the loss in translational, rotational and vibrational degrees of freedom of the two molecules on forming the transition state; (d) the knowledge of the δG(HI) values can be useful to rationalize solvent effects on the k2 magnitude. Pairwise HI corresponds to the process of forming, at constant temperature and pressure, a contact-minimum configuration of two nonpolar molecules at a fixed position in water starting from the two molecules at infinite separation [22]. The associated Gibbs energy change is given by: ΔGðHIÞ ¼ Ea ðcontactÞ þ δGðHIÞ
ð1Þ
101
reorganization of water-water H-bonds upon nonpolar solute insertion does not appear in Eq. (3) because an almost complete enthalpyentropy compensation holds for such a reorganization process [28,29]. Since the occurrence of such enthalpy-entropy compensation is due to the weakness of solute-solvent attractions in comparison to the strength of solvent-solvent attractions [29] (i.e., water-water H-bonds are stronger than nonpolar molecule-water van der Waals attractions), its validity cannot be guaranteed in the case of strong ion-water electrostatic interactions. The assumption that enthalpy-entropy compensation holds for the structural reorganization of all the species present in the considered aqueous solutions has to be considered as a working hypothesis. The use of Eq. (3) in the definition of δG(HI) leads to: δGðHIÞ ¼ ½ΔGc ðtwoÞ−2 ΔGc ðoneÞ þ ½Ea ðtwoÞ−2 Ea ðoneÞ ¼ δGc þ δEa
ð4Þ
Eq. (4) shows that a quantitative estimate of ions and water contribution to pairwise HI can be obtained from: (a) the calculation of ΔGc to create in water and aqueous solutions a cavity suitable to host a couple of solute molecules in the contact-minimum configuration, and a cavity suitable to host a single solute molecule; (b) the calculation of Ea to turn on the attractive interactions between a couple of solute molecules in the contact-minimum configuration or a single solute molecule and all the surrounding ions and water molecules. Actually, a different route has been followed, by assuming that the diene and the dienophile can be described as spherical molecules with the same diameter σc = 5 Å. This choice, even though not strictly correct from the structural point of view, allows one to provide a proof of concept for the reliability of the proposed rationalization. Classic scaled particle theory [30], SPT, calculations have shown that: (a) by keeping fixed the van der Waals cavity volume, the ΔGc magnitude depends on the cavity shape, and proves to be proportional to cavity WASA, that is a measure of the solvent-excluded volume due to cavity creation; (b) the value of the ΔGc/WASA ratio calculated for spherical cavities can be used, to a good approximation, also for nonspherical cavities [31,32]. Thus, δGc is calculated from the knowledge of the WASA fraction buried upon association [18,24,25]: δGc ¼ −f WASA ΔGc ðone sphereÞ
ð5Þ
where Ea(contact) is the direct interaction energy of the two solute molecules in the contact-minimum configuration, and does not depend on the presence of the solvent and its nature; δG(HI) is the indirect part of the reversible work to carry out the process, and accounts for the specific features of the solvent in which pairwise HI occurs. A general relationship connects δG(HI) to the Ben-Naim standard hydration Gibbs energy of the two molecules in the contact-minimum configuration and of a single molecule [22,24,25], respectively:
The detailed analysis performed by Levy and colleagues indicates that also Ea scales linearly with WASA [33]; in addition, to achieve close agreement with the computer simulation results for the pairwise HI of some alkanes, it emerged that fWASA has to be multiplied times a factor equal to 1.2 [24]. On this basis, δEa is calculated by means of the following relationship:
δGðHIÞ ¼ ΔG• ðtwoÞ−2 ΔG• ðoneÞ
δEa ¼ −1:2 f WASA Ea ðone sphereÞ
ð2Þ
where ΔG• represents the Gibbs energy change associated with the transfer of a species from a fixed position in the ideal gas phase to a fixed position in water, at constant temperature and pressure, ΔG• (one) is the hydration Gibbs energy change of one molecule, and ΔG• (two) is the hydration Gibbs energy change of two molecules in the contact-minimum configuration. Application of a physical concept and of statistical mechanics allows the exact splitting of ΔG• into two contributions [26,27]: ΔG• ¼ ΔGc þ Ea
ð3Þ
where ΔGc is the reversible work to create at a fixed position in water or aqueous solution a cavity suitable to host the solute molecule, and Ea is the reversible work to turn on the attractive interactions between the solute molecule inserted in the cavity and all the surrounding ions and water molecules (the second step is conditional to the first: there is no additivity of independent contributions [26,27]). Of course, ΔGc is always a positive quantity and Ea is always a negative quantity. The
ð6Þ
The WASA fraction of the two spherical cavities, fWASA, that becomes buried in the contact-minimum configuration, is exactly given by [24]: f WASA ¼ 1−½σ c =ðσ c þ σ Þ
ð7Þ
where σc = 5 Å is the diameter of one spherical cavity (solute molecule), and ⟨σ⟩ = ∑χj⋅σj is the average effective diameter of the different particles constituting the considered aqueous solution, where χj is the molar fraction of species j and σj is the corresponding hard sphere diameter. Eqs. (5) and (6) show that δGc provides a negative Gibbs energy change favouring the formation of the contact-minimum configuration, whereas δEa provides a positive Gibbs energy change contrasting the formation of the contact-minimum configuration. The rationale is that bringing two spherical solute molecules from a fixed position at infinite distance to a fixed position at contact distance in aqueous solution causes: (a) a decrease in the solvent-excluded volume, measured by the WASA decrease upon association, that causes a translational entropy gain for ions and water molecules; (b) a decrease in the number of ions
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G. Graziano / Journal of Molecular Liquids 275 (2019) 100–104
and water molecules contacting the two spherical solute molecules, that causes the loss of attractive solute-ions and solute-water energetic interactions [18,24,25]. 3. Calculation procedure Estimates of ΔGc[σc = 5 Å] have been calculated by means of classic SPT formulas [17,30], using the experimental values of the density of water [34], and of all the considered aqueous salt solutions [35], at 25 °C and 1 atm (see the second column of Table 1). The following effective hard sphere diameters have been selected: σ = 2.80 Å for water molecules [17,18], close to the location of the first peak in the oxygen‑oxygen radial distribution function of water [36]; σ = 2.02 Å for Na + ions [37]; 4.70 Å for Gdm + ions, which is the diameter of the sphere possessing the same WASA of Gdm + ion [17]; 3.62 Å for Cl- ions; 4.80 Å for ClO4ions; 4.60 Å for SO42-ions (all the anionic values correspond to the Pauling-type diameters listed by Marcus in Table XIII of [38]). These diameters serve to arrive at the volume packing density of the considered solutions, ξ3 = (π/6)⋅∑ρj⋅σ3j , where ρj is the number density of the species j; ξ3 represents the fraction of the total liquid volume really occupied by ions and molecules, and is a fundamental ingredient of classic SPT calculations [17,37]. The obtained ξ3 values are reported in the fourth column of Table 1. The Ea value for the nonpolar spherical solute of 5 Å diameter has been fixed to −30.0 kJ mol−1 in pure water at 25 °C and 1 atm, in line with the numbers obtained for alkanes of similar size by means of Monte Carlo or molecular dynamics simulations in detailed water models [33,39,40]. By considering that both Na + and SO42-ions are strongly hydrated and should not interact with the nonpolar solute, the Ea value in aqueous 1 M Na2SO4 solution has been calculated by means of the following relationship: Ea ðsolutionÞ ¼ Ea ðwaterÞ ½ξ3 ðsolutionÞ=ξ3 ðwaterÞ
ð8Þ
whose reliability comes from the formula originally proposed by Pierotti [30]. Application of Eq. (8) leads to Ea(1 M Na2SO4) = −32.0 kJ mol−1. In the case of aqueous GdmCl solutions, it is necessary to consider that guanidinium ions are weakly hydrated in view of their low charge density [41], and interact preferentially with the nonpolar solute [17,42]. This should imply that the Ea magnitude in aqueous GdmCl solutions has to be larger than that in water and aqueous Na2SO4 solution. On this physical ground, I have deliberately fixed: Ea(1 M GdmCl) = −34.0 kJ mol−1, and Ea(2 M GdmCl) = −38.0 kJ mol−1. Since in aqueous 1 M Gdm2SO4 solution, the Gdm + concentration corresponds to that in aqueous 2 M GdmCl solution and the sulphate ions should not interact with the nonpolar solute, I have used Eq. (8) to arrive at: Ea(1 M Gdm2SO4) = Ea(2 M GdmCl)·(0.4675/0.4242) = −42.0 kJ mol−1. In
Table 1 Experimental values, at 25 °C and 1 atm, of the density and water molar concentration for pure water, aqueous 1 M and 2 M GdmCl solutions, aqueous 1 M and 2 M Gdm2SO4 solutions, aqueous 1 M and 2 M GdmClO4 solutions, and aqueous 1 M Na2SO4 solution [34,35]; values of the volume packing density for all these solutions, calculated using the effective hard sphere diameters reported in the text; classic SPT estimates of the reversible work ΔGc to create in these liquid solutions, at 25 °C and 1 atm, a spherical cavity of 5 Å diameter; estimates of the Ea quantity and values of ΔGc + Ea in all these solutions; values of the average effective hard sphere diameter ⟨σ⟩ of these solutions.
H2O 1 M GdmCl 2 M GdmCl 1 M Gdm2SO4 2 M Gdm2SO4 1 M GdmClO4 2 M GdmClO4 1 M Na2SO4
ρ g L−1
[H2O] M
ξ3
ΔGc kJ mol−1
Ea kJ mol−1
ΔGc + Ea kJ mol−1
⟨σ⟩ Å
997 1022 1047 1183 1353 1060 1121 1117
55.3 51.4 47.5 53.7 51.1 50.0 44.5 54.1
0.3830 0.4035 0.4242 0.4675 0.5460 0.4137 0.4432 0.4103
37.9 39.8 42.0 53.4 75.7 40.4 43.1 42.6
−30.0 −34.0 −38.0 −42.0 −52.0 −36.0 −41.0 −32.0
7.9 5.8 4.0 11.4 23.7 4.4 2.1 10.6
2.80 2.85 2.91 2.90 3.00 2.87 2.96 2.80
aqueous 2 M Gdm2SO4 solution, I have deliberately fixed Ea = −52.0 kJ mol−1, a value markedly larger than that in water because [Gdm+] = 4 M and it interacts preferentially with the nonpolar solute [17,42]. Finally, since the perchlorate ions are weakly hydrated due to their low charge density [11,12], the Ea magnitude in aqueous GdmClO4 solutions has been considered to be larger than that in aqueous GdmCl solutions. Specifically, Ea(1 M GdmClO4) = −36.0 kJ mol−1, and Ea(2 M GdmClO4) = −41.0 kJ mol−1. All these numbers are listed in the sixth column of Table 1. Even though they do not come from a precise formula or detailed computer simulations, their magnitude should be more-than-qualitatively correct; nevertheless, significant changes to these Ea values might have marked effects on the final results of the present analysis. A last point. According to Eq. (7) and the ⟨σ⟩ estimates listed in the last column of Table 1, 0.36 ≤ fWASA ≤ 0.38. Therefore, I have fixed fWASA = 0.37 for water and all the considered aqueous solutions. 4. Results and discussion The calculated ΔGc[σc = 5 Å] values are listed in the fifth column of Table 1. They are large positive and increase markedly with the volume packing density of the solution. As a consequence, the smallest ΔGc occurs in pure water (i.e., 37.9 kJ mol−1 with ξ3 = 0.383) and the largest in 2 M Gdm2SO4 (i.e., 75.7 kJ mol−1 with ξ3 = 0.546). In comparing the ΔGc magnitude in aqueous solutions, the size of solvent molecules and ions does not play a fundamental role [18,37], because the average effective diameter ⟨σ⟩ is always close to 2.8 Å, the effective size of water molecules, as can be appreciated on looking at the numbers listed in the last column in Table 1. The fundamental role is played by the volume packing density ξ3 whose value reflects the density of such solutions [37,43]. By looking at the second and third columns of Table 1, it is evident that: (a) all the considered salts cause a density increase in view of the strength of ion-water electrostatic interactions; (b) the presence of the sulphate ion causes a marked density increase due to its high charge density and so a marked increase in the ΔGc magnitude. The SPT result that all the considered salts increase the ΔGc magnitude is in line with the experimental fact that all these salts cause an increase of the liquid-vapour surface tension of water, and Gdm2SO4 proves to be the most effective among the guanidinium salts [44]. On the other hand, the Ea estimates are large negative but always smaller in magnitude than the corresponding ΔGc numbers. As a consequence, the ΔGc + Ea values prove to be positive in all cases, but they are small in aqueous GdmClO4 and GdmCl solutions, and large in aqueous Gdm2SO4 solutions (see the numbers listed in the seventh column of Table 1). This is in line with the salting in effect of GdmClO4 and GdmCl, and the salting out effect of Gdm2SO4 experimentally determined by Kumar and co-workers for the solubility of methyl acrylate (see Figure 2 in [13]). It is worth noting that the salting out effect of Gdm2SO4 occurs even though the Ea magnitude in such solutions proves to be the largest among the considered solutions (see Table 1). The salting out effect is due to the ΔGc magnitude, whose marked increase on adding Gdm2SO4 to water is caused by the large density increase [17], that manifests also in the increase of the total number density: 55.3 mol l−1 in water, 56.7 mol l−1 in 1 M Gdm2SO4, and 57.1 mol l−1 in 2 M Gdm2SO4. The ΔGc and Ea values can be used to obtain estimates of the Gibbs energy change δG(HI) associated with the formation of the contactminimum configuration of the two spheres by means of Eqs. (4)–(7). The obtained δG(HI) estimates, listed in the fourth column of Table 2, are positive in aqueous GdmClO4 and GdmCl solutions, but negative in water, and aqueous Gdm2SO4 and Na2SO4 solutions. Clearly, a negative δG(HI) value favours the formation of the contact-minimum configuration of the two spheres, whereas a positive δG(HI) value means that the formation of the contact-minimum configuration is not favoured. It is worth noting that the δG(HI) values are small in comparison to what is expected for ΔGǂ, which would be of the order of several tens of
G. Graziano / Journal of Molecular Liquids 275 (2019) 100–104 Table 2 Estimates, at 25 °C and 1 atm, of the δGc, δEa, and δG(HI) terms, calculated by means of Eqs. (4)–(7) for the contact-minimum configuration of two spherical molecules in all the considered aqueous solutions. In the last two columns, are reported the experimental values, determined by Kumar and co-workers [13], of the second-order rate constant and of the percentage endo yield for the Diels-Alder reaction between cyclopentadiene and methyl acrylate, at 25 °C and 1 atm.
H2O 1 M GdmCl 2 M GdmCl 1 M Gdm2SO4 2 M Gdm2SO4 1 M GdmClO4 2 M GdmClO4 1 M Na2SO4
δGc kJ mol−1
δEa kJ mol−1
δG(HI) kJ mol−1
k2⋅104 M−1 s−1
endo %
−14.0 −14.7 −15.5 −19.8 −28.0 −15.0 −16.0 −15.8
13.7 15.1 16.9 18.6 23.1 16.0 18.2 14.2
−0.7 0.4 1.4 −1.2 −4.9 1.0 2.2 −1.6
25.0 17.0 11.0 33.1 39.3 10.5 4.1 37.3
67 58 53 75 82 52 -79
103
between the transition state of Diels-Alder reactions and the contactminimum configuration of pairwise HI. It was proposed, mainly on the basis of molecular dynamics results [47], that the stabilizing effect of Gdm2SO4 towards the native state of globular proteins is due to the formation of ion-pairs in water that lead to the formation of nanoscale aggregates, rendering the Gdm + ions not available to directly interact with the protein surface. However, a detailed conductance study concluded that the observed ion association is rather weak and cannot explain the different behaviour of Gdm2SO4 with respect to the other guanidinium salts towards the native state of globular proteins [48]. This conclusion is in line with that emerged earlier from my theoretical approach [17]. As a consequence, the formation of ion-pairs cannot be invoked to rationalize the special behaviour of Gdm2SO4 towards the kinetics of Diels-Alder reactions. 5. Conclusion
kJ mol−1 [45,46]. Most of the ΔGǂ magnitude depends upon the rearrangement of chemical bonds during the formation of the transition state. This rearrangement of π-electrons should be little affected by changes in the solvent medium and should represent a common ground for a given Diels-Alder reaction. The δG(HI) values represent a small perturbation to this common ground, but important to increase or decrease the rate constant. Importantly, the calculated δG(HI) values prove to be correlated with the experimental values of both the second order rate constant k2 and the percentage endo yield of the Diels-Alder reaction of cyclopentadiene with methyl acrylate. The latter numbers, determined by Kumar and co-workers at 25 °C and 1 atm [13], are listed in the last two columns of Table 2. A plot of the correlation between the experimental k2 values and the present δG(HI) estimates is shown in Fig. 1. The correlation is reasonably good, indicating the reliability of the present approach, even though it is stretched very far from its range of applicability. As already underscored in the Theoretical approach section, this is solely a correlation because there is no straightforward formula to pass from δG(HI) to the k2 values. In general, Diels-Alder reactions are characterized by negative activation volumes [21], indicating that the transition state occupies less volume in solution than the two separated reactants. The activation volumes determined by Kumar and co-workers for the Diels-Alder reaction between cyclopentadiene and methyl acrylate at 25 °C proved to be negative and to follow the same rank order of the k2 values (see Table 5 in [13]). The present approach is in line with experimental data on activation volumes, as expected due to the geometric similarity
By assuming that the transition state of Diels-Alder reactions can be described as the contact-minimum configuration of pairwise HI, it has been possible to find a robust correlation between the δG(HI) estimates and the experimental k2 values for the reaction between cyclopentadiene and methyl acrylate. The enhancement of rate constant caused by Gdm2SO4 is due to the large density increase caused by its addition to water (i.e., the strong electrostrictive power of sulphate ions), that renders very large the Gibbs energy cost of cavity creation. Indeed, the WASA decrease associated with the formation of the contact-minimum configuration leads to a decrease in the Gibbs energy cost of cavity creation with respect to the situation of the two molecules far apart from each other. This corresponds to a gain in translational entropy of ions and water molecules (for the increase in the accessible configurational space) that is larger the greater the density or better the number density of the aqueous solution. This entropy gain in the case of Gdm2SO4 overwhelms the energy decrease associated with the loss of several attractive interactions between the Gdm + ions and the nonpolar solute molecules. Acknowledgements I would like to thank the two reviewers for their useful comments on the original version of the manuscript. The present work has been supported by the fund for research activity of the Università del Sannio. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
Fig. 1. Plot of the second order rate constant k2 values for the Diels-Alder reaction between cyclopentadiene and methyl acrylate, at 25 °C and 1 atm, in water and different aqueous salt solutions [13] versus the δG(HI) estimates obtained in the present study. See Table 2 for the precise numbers.
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