ARTICLES
2. Maki, B. E., Patterson, E. V., Cramer, C. J. & Scheidt, K. A. Impact of solvent
polarity on N-heterocyclic carbene-catalyzed b-protonations of homoenolate
equivalents. Org. Lett. 11, 3942–3945 (2009).
3. Carlson, R. Designs for explorative experiments in organic synthetic chemistry.
Chemom. Intell. Lab. Syst. 73, 151–166 (2004).
Methods
Experimental methods. To determine the reaction rate constants, four experiments
at 298 K with different initial concentrations were carried out for each deuterated
solvent, using trimethoxybenzene as an internal standard. NMR spectra were
recorded on a Bruker AV500 (1H 500 MHz). To ensure that the data collected were
quantitative, T1-relaxation times were determined and the time between
radiofrequency pulses was set to be greater than five times the longest T1 value. The
use of four runs ensures that the values obtained for the measured rate constants are
statistically significant and leads to very tight confidence intervals on the regressed
rate constants (2–3 orders of magnitude smaller than the rate constants). In each
experiment, sufficient time was allowed to reach a conversion of at least 50%. As
many peaks as available from the 1H NMR spectra were used to extract the
experimental rate constant. In all cases this included at least two of the four phenacyl
bromide peaks (three aromatic peaks and one CH2 peak), at least one of the three
pyridine peaks and as many of the seven product peaks available as possible (except
in THF and toluene, where the product was insoluble and thus could not be followed
by liquid-state NMR spectroscopy). Molar concentrations for the two reactants and,
when feasible, for the product were obtained from the measured peaks and internal
standard concentrations. The molar concentrations were then used to determine the
rate constants, based on second-order kinetics, that is
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4. Gani, R., Jimenez-Gonzalez, C. & Constable, D. J. C. Method for selection of
solvents for promotion of organic reactions. Comput. Chem. Eng. 29,
1661–1676 (2005).
5. Otto, R. et al. Single solvent molecules can affect the dynamics of substitution
reactions. Nature Chem. 4, 534–538 (2012).
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6. Jimenez-Gonzalez, C. et al. Key green engineering research areas for sustainable
manufacturing: a perspective from pharmaceutical and fine chemicals
manufacturers. Org. Process Res. Dev. 15, 900–911 (2011).
7. Achenie, L. E. K., Gani, R. & Venkatasubramanian, V. (eds) Computer Aided
Molecular Design: Theory and Practice (Elsevier, 2003).
8. Giovanoglou, A., Barlatier, J., Adjiman, C. S., Pistikopoulos, E. N. &
Cordiner, J. L. Optimal solvent design for batch separation based on
economic performance. AIChE J. 49, 3095–3109 (2003).
9. Fredenslund, A., Jones, R. L. & Prausnitz, J. M. Group-contribution estimation
of activity-coefficients in nonideal liquid mixtures. AIChE J. 21,
1086–1099 (1975).
d[1]
´
10. Folic, M., Adjiman, C. S. & Pistikopoulos, E. N. Design of solvents for optimal
= −k[1][2]
dt
reaction rate constants. AIChE J. 53, 1240–1256 (2007).
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11. Folic, M., Adjiman, C. S. & Pistikopoulos, E. N. Computer-aided solvent design
d[2]
= −k[1][2]
for reactions: Maximizing product formation. Ind. Eng. Chem. Res. 47,
5190–5202 (2008).
12. Carlson, R. & Carlson, J. E. Design and Optimization in Organic Synthesis
(Elsevier, 2005).
dt
d[3]
= k[1][2]
dt
13. Koppel, I. A. & Palm, V. A. in Advances in Linear Free Energy Relationships (eds
Chapman, N. B. & Shorter, J.) Ch. 5 (Plenum Press, 1972).
14. Kamlet, M. J., Abboud, J. L. & Taft, R. W. The solvatochromic comparison
method. 6. The p* scale of solvent polarities. J. Am. Chem. Soc. 99,
6027–6038 (1977).
15. Taft, R. W., Pienta, N. J., Kamlet, M. J. & Arnett, E. M. Linear solvation energy
relationships. 7. Correlations between the solvent-donicity and acceptor-number
scales and the solvatochromic parameters, p*, a, and b. J. Org. Chem. 46,
661–667 (1981).
16. Taft, R. W., Abboud, J. L. M. & Kamlet, M. J. Linear solvation energy
relationships. 12. The dd term in the solvatochromic equations. J. Am.
Chem. Soc. 103, 1080–1086 (1981).
17. Kamlet, M. J., Abboud, J-L. M., Abraham, M. H. & Taft, R. W. Linear solvation
energy relationships. 23. A comprehensive collection of the solvatochromic
parameters, p*, a and b, and some methods for simplifying the generalized
solvatochromic equation. J. Org. Chem. 48, 2877–2887 (1983).
18. Taft, R. W., Abboud, J-L. M., Kamlet, M. J. & Abraham, M. H. Linear solvation
energy relations. J. Solution Chem. 14, 153–186 (1985).
where t is time, k (dm3 mol21 s21) is the rate constant and [i] denotes the
concentration of species i, where i ¼ 1, 2 and 3 here. As an example, the initial
concentrations used for 1 and 2 for the reaction in nitromethane-d3 are shown in
Supplementary Table 2. The initial product concentration was always set to 0. The
estimates of the rate constant were obtained by applying nonlinear least-squares
quality of fit was achieved in all cases, as illustrated in Supplementary Figs S1–S3.
Computational methods. The overall approach to computing reaction rate
constants in the liquid phase from a basic description of the solvent in terms of its
composition in atom groups is illustrated in Supplementary Fig. S4. The rate
constant kQM was computed using transition-state theory, according to the following
equation, which applies to the second-order Menschutkin reaction:
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
o,IG
q
(AB)‡
kBT
h
1
co,L
−D‡Eel
−D‡DGo,solv
kQM = k
exp
exp
qoA,IGqoB,IG
RT
RT
19. Bini, R., Chiappe, C., Mestre, V. L., Pomelli, C. S. & Welton, T. A rationalization
of the solvent effect on the Diels–Alder reaction in ionic liquids using
multiparameter linear solvation energy relationships. Org. Biomol. Chem. 6,
2522–2529 (2008).
where k is the transmission coefficient, calculated according to the Wigner
tunnelling correction factor, kB is the Boltzmann constant, T is the temperature, h is
the Planck constant, co,L is the standard-state liquid-phase concentration (here,
1 mol dm23), qoi ,IG is the ideal gas partition function (excluding the electronic
energy, as is standard practice) for component i, where i ¼ A (reactant A), B
(reactant B) or (AB)‡ (transition state), R is the gas constant, Eel is the gas phase
electronic energy, DGo,solv is the standard-state free energy of solvation and D‡
indicates that an activation energy barrier is being calculated, that is
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20. Gani, R., Gomez, P. A., Folic, M., Jimenez-Gonzalez, C. & Constable, D. J. C.
Solvents in organic synthesis: replacement and multi-step reaction systems.
Comput. Chem. Eng. 32, 2420–2444 (2008).
21. Stanescu, I. & Achenie, L. E. K. A theoretical study of solvent effects on
Kolbe–Schmitt reaction kinetics. Chem. Eng. Sci. 61, 6199–6212 (2006).
el
¨
D‡Eel = E
− EAel − EBel
22. Menschutkin, N. A. Uber die Affinita¨tskoeffizienten der Alkylhaloide und der
(AB)‡
Amine. Z. Physik. Chem. 6, 41–57 (1890).
D‡DGo,solv = DG
− DGoA,solv − DGBo,solv
o,solv
(AB)‡
23. Abraham, M. H. & Grellier, P. L. Substitution at saturated carbon. Part XX. The
effect of 39 solvents on the free energy of Et3N, EtI, and the Et3N–EtI transition
state. Comparison with solvent effects on the equilibria Et3N þ EtI ↔ Et4NþI2
and Et3N þ EtI ↔ Et4Nþ þ I2. J. Chem. Soc. Perkin Trans. 2 1735–1741 (1976).
The gas-phase minimum-energy structures for the reactants, the gas-phase
transition-state structures and the gas-phase partition functions were computed with
Gaussian 09 (ref. 50) using the B3LYP/6-31 þ G(d) functional. For the calculation of
the free energies of solvation, the structures were re-optimized using the same
functional, the SMD continuum solvation model37 and intrinsic Coulomb radii.
Gas-phase vibrational frequencies were used. The bulk solvent properties required in
the SMD model were obtained using GC methods41. All structures obtained are
reported in the Supplementary Information, together with further details of the
computational methodology and justification of the choices made.
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24. Lassau, C. & Jungers, J. L’influence du solvant sur la reaction chimique. La
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quaternation des amines tertiaires par l’iodure de methyle. Bull. Soc.
Chim. Fr. 7, 2678–2685 (1968).
25. Castejon, H. & Wiberg, K. B. Solvent effects on methyl transfer reactions. 1. The
Menshutkin reaction. J. Am. Chem. Soc. 121, 2139–2146 (1999).
26. Acevedo, O. & Jorgensen, W. L. Exploring solvent effects upon the Menshutkin
reaction using a polarizable force field. J. Phys. Chem. B 114, 8425–8430 (2010).
27. Chuang, Y-Y., Cramer, C. J. & Truhlar, D. G. The interface of electronic structure
and dynamics for reactions in solution. Int. J. Quantum Chem. 70,
887–896 (1998).
The MILPs were solved by the CPLEX solver, accessed via the GAMS software
28. Su, P., Wu, W., Kelly, C. P., Cramer, C. J. & Truhlar, D. G. VBSM: a solvation
model based on valence bond theory. J. Phys. Chem. A 112, 12761–12768 (2008).
29. Pearson, R. G., Langer, S. H., Williams, F. V. & McGuire, W. J. Mechanism of the
reaction of a-haloketones with weakly basic nucleophilic reagents. J. Am. Chem.
Soc. 74, 5130–5132 (1952).
Received 17 June 2013; accepted 12 August 2013;
published online 22 September 2013
References
30. Barnard, P. W. C. & Smith, B. V. The Menschutkin reaction – a group
experiment in a kinetic study. J. Chem. Educ. 58, 282–285 (1981).
1. Reichardt, C. & Welton, T. Solvents and Solvent Effects in Organic Chemistry
(Wiley-VCH, 2011).
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