12414
J. Phys. Chem. B 2008, 112, 12414–12419
Influence of the Solvent Description on the Predicted Mechanism of SN2 Reactions Monika Wujec,† Agata Siwek,† Joanna Dzierzawska,‡ Michal Rostkowski,‡ Rafal Kaminski,‡ and Piotr Paneth*,‡ Department of Organic Chemistry, Faculty of Pharmacy, Medical UniVersity, Staszica 6, 20-081 Lublin, Poland, and Institute of Applied Radiation Chemistry, Technical UniVersity, Zeromskiego 116, 90-924, Lodz, Poland ReceiVed: April 24, 2008; ReVised Manuscript ReceiVed: July 8, 2008
The influence of the implicit solvent model on transition state structures of two SN2 reactions of biochemical importance is presented. In the considered methyl transfer reaction, we show experimentally that the rate constant in blood serum is about 60% slower than in the aqueous solution and that the implicit solvent model with slightly modified parameters for water captures correctly the energetics of this reaction. With the example of the reaction between 4-methyl-1,2,4-triazol-3-thione and ethyl bromoacetate, we show that relative stabilities of the conformationally different transition states depend upon the solvent inclusion strategy. 1. Introduction Molecular modeling of reactions of pharmacological importance in condensed phases, such as aqueous and cellular solutions, requires inclusion of the environment. However, quantum description of the reacting molecules and the environment is prohibitively expensive. Therefore, nowadays two simplified approaches are used. In the first one, the system is divided into two parts. The smaller part, which usually includes reacting species and sometimes a few solvent molecules, is treated at the quantum level. The other part that comprises (remaining) solvent molecules is described by a force field. This approach, called QM/MM, is a compromise between the speed and accuracy of calculations. Although it is quite successful for the enzymatic environment, it suffers from several factors, such as slow convergence, arbitrary division into parts, overpolarization at the border of division into parts, and dependence on the size of the quantum part.1,2 In the alternative approach, the solvent is treated as a dielectric continuum in which the reacting species are embedded. These so-called continuum (or implicit) solvent models are not too demanding in terms of computational resources and therefore are frequently used in calculations of chemical and biochemical reactions. There is a wealth of data regarding performance of both implicit and explicit solvent models which is growing steeply nearly on a daily basis. Thus, we point out only the two most recent publications3 that set up a benchmarking set of molecules of pharmacological relevance and from which the older literature can be traced back. Continuum solvent models may fail when the explicit interactions between the solute and the solvent are of importance. For example, the oxygen vapor pressure isotope effect (18O VPIE) of water calculated using an implicit solvent model is equal to 0.9957, opposite to the experimental value of 1.0091 ( 0.0002.4 This is because low frequency vibrations originating from hydrogen bonds are not included in these models. On the other hand, inclusion of only one explicit water molecule yields the isotope effect in the right direction, 1.0035, while inclusion * Corresponding author. Phone: +48 42 631 3199. Fax: +48 42 636 5008. E-mail:
[email protected]. † Medical University. ‡ Technical University.
of four water molecules at positions taken from the TIP3P model5 yields 18O VPIE equal to 1.0081 in excellent agreement with the experiment. This example signifies that implicit solvent models should be used cautiously. Even when energetics of the explicit solute-solvent interactions may be approximated by an implicit model, some parameters, such as activation barriers and/or transition state structures of chemical or biochemical reactions, may be affected by the choice of the solvent model. Herein, we explore this point on the example of two SN2 reactions of biological importance. The first example is the reaction between the trimethylsulfonium cation and trimethylamine illustrated in Figure 1. This SN2 reaction is considered a good model for the in vivo methyl group transfer from S-adenosylomethionine that is important in all metabolic processes.6 Methyl transfer reactions play the key role in many biological processes7 and their mechanisms are still the subject of much experimental and theoretical study.8 Enzymatic methylation of hydroxyl and carboxyl moieties is catalyzed by O-methyltransferases.9 For example, catechol O-methyltransferase (COMT) is a ubiquitous enzyme that catalyzes the transfer of the activated methyl group of Sadenosyl-L-methionine (AdoMet) to an oxygen atom of catechol.10 The stereochemical course of the reaction has shown that the methyl transfer proceeds through a direct nucleophilic attack by one of the hydroxyl groups of catechol on the methyl carbon of AdoMet in a tight SN2-like transition state.11 COMT plays a central role in the metabolic inactivation of neurotransmitters and neuroactive xenobiotics, accepting a wide variety of substrates containing a vicinal dihydroxyphenyl moiety. The second example is the reaction of a triazole with ethyl bromoacetate. In the last few decades, 1,2,4-triazoles have received much attention due to their biological importance. Two main types of their activity are antimicrobial12 and on the central nervous system.13 Moreover, sulfur-containing heterocycles represent an important group of compounds that are promising for use in practical applications. Among these heterocycles, the mercapto/thione-substituted 1,2,4-triazole systems have been well studied, and so far a variety of biological activities have been reported for a large number of their derivatives, such as antimicrobial,14 antitubercular,15 anticancer,16 antinociceptive,17 and anti-inflammatory18 properties.
10.1021/jp8035956 CCC: $40.75 2008 American Chemical Society Published on Web 09/09/2008
Solvent Description of SN2 Reactions
J. Phys. Chem. B, Vol. 112, No. 39, 2008 12415
Figure 1. SN2 reaction between the trimethylsulfonium cation and trimethylamine.
Figure 2. SN2 reaction between 4-methyl-1,2,4-triazol-3-thione and ethyl bromoacetate.
TABLE 1: Experimental Rate Constants for the Reaction between the Trimethylsulfonium Cation and Trimethylamine in Water and Serum at 60 °C water + 10% D2O serum + 5% D2O serum + 10% D2O
Figure 3. Time-dependence of concentrations. a and b are initial concentrations of trimethylamine and trimethylsulfonium nitrate, respectively, and x is the fraction of reaction calculated from integration of NMR signals corresponding to trimethylsulfonium and tetramethylammonium cations.
In addition to these important biological applications, mercapto/thione-1,2,4-triazoles are also of great utility in preparative organic chemistry in the synthesis of fused mercapto/thione1,2,4-triazole heterocycles and S-/N-substituted 1,2,4-triazoles. The chemistry of substitution of these compounds is quite variable depending on reagents and the conditions used. Aminomethylation and hydroxymethylation reactions occur at the nitrogen atom, while alkyl/aryl, acid, ester, amine, and glycoside halides react at the sulfur atom.19 Recently, we have shown20 that 4-methyl-1,2,4-triazol-3-thione reacts with formaldehyde via a cyclic transition state to form N1-hydroxymethyl4-methyl-1,2,4-triazol-3-thione. The predominant thione tautomer21 of this triazole, on the other hand, gives the same product under acidic conditions but with intervention of the triazole anion.22 Yet, with ethyl bromoacetate in acetone, the same thione tautomer reacts via the SN2 mechanism as illustrated in Figure 2.
rate constant
standard error
0.00161 0.00092 0.00101
0.00002 0.00003 0.00001
measuring rates of this reaction in pure water and in blood serum. Kinetics measurements were carried out at 60 °C by monitoring NMR signals of the trimethylsulfonium cation. A fraction of 5 or 10% of D2O was added to each sample. The time dependence of concentrations was fitted to the secondorder rate equation. The results are presented in Figure 3. The observed rate constants obtained from slopes of lines shown in Figure 3 for the aqueous solution with 10% D2O and for serum with 5 and 10% of D2O are collected in Table 1. From these three experimental values, the individual rate constants for the reactions in pure H2O, D2O, and serum were evaluated, which in turn allowed us to calculate the difference in Gibbs free energies of activation in aqueous solution and in serum. This difference is given by eq 1. Substitution of the corresponding rate constants to eq 1 yields the experimental difference of 0.39 kcal/mol. ‡ ∆∆G‡ ) ∆G‡serum - ∆GH2O ) RT ln(kH2O ⁄ kserum)
(1)
We have modeled the reaction given in Figure 1 using the PCM model.23 The full PCM model, including nonelectrostatic
2. Results and Discussion The reaction between the trimethylsulfonium cation and trimethylamine illustrates the problem that emerges when reactivity in biological environment is considered. Typically, if a continuum solvent model is employed to model processes in a cell, the parameters for aqueous solution are used. We have tested experimentally the validity of this approximation by
Figure 4. Transition state structure obtained at the PCM/B3LYP/631+G(d,p) level of theory for the reaction between the trimethylsulfonium cation and trimethylamine.
12416 J. Phys. Chem. B, Vol. 112, No. 39, 2008
Wujec et al.
TABLE 2: Most Important Bond Distances (in Å) and Valence Angles (in °) of the PCM/B3LYP/6-31+G(d,p) Optimized Transition State and Reactants parameters for water coordinate/property N C N S
a
C S C C
S Ha Gsolb ∆G+c ν+d µe
modified water parameters
reactants
transition state
reactants
transition state
3.2452 1.8245 177.83 108.28 -692.236827 9.566
2.1637 2.2706 179.68 92.94 -692.217929 11.86 490.6i 1.439
3.2572 1.8243 177.15 108.28 -692.249057 9.615
2.1637 2.2706 179.68 92.94 -692.229550 12.24 490.8i 1.440
Average over three hydrogen atoms of the central methyl group. b In atomic units. c In kcal/mol. d In cm-1. e In D.
Figure 5. Transition state structures TSgg (left) and TSgt (right) of the reaction between 4-methyl-1,2,4-triazol-3-thione and ethyl bromoacetate obtained at the DFT level in the gas phase.
contribution has been used. Two parameters have been modified from values used for aqueous solution to account for the differences in the rate constants in water and in blood serum. The first one is the macroscopic dielectric constants. For the blood serum, its value has been calculated to be equal to ε ) 89.45 based on the content of the used material following the formula given in the literature.24 The actual value of the dielectric constant, however, proved to have a negligible effect on the calculated activation Gibbs free energy. To reproduce experimentally the determined difference of 0.39 kcal/mol, we have changed the solvent radius from the value of 1.385 Å used for water to the value of 1.29 Å. This value allows us to reproduce computationally the difference in the activation parameters. The dependence of the energetics on the hard sphere radius of the solvent is documented in the literature.3b
It is interesting to learn if the resulting difference in parameters for water and serum yields noticeable changes in geometries. The optimized structure of the transition state in water is illustrated by Figure 4. Table 2 lists major geometrical features of the corresponding reactants and transition states in both media. As can be seen, changes are negligible. To make them visible, we have listed bond lengths with three digits and bond angles and energies with two digits after the decimal point. In conclusion, experiments show that the activation parameters are different for the reaction carried out in bovine blood serum and in aqueous solution and that the implicit solvent model can be modified to account for these changes. In the case of the PCM model, the appropriate results can be obtained by changing the dielectric constant and the solvent radius, the latter parameter playing the major role. Calibration of this latter
Solvent Description of SN2 Reactions
J. Phys. Chem. B, Vol. 112, No. 39, 2008 12417
TABLE 3: Bond Distances (in Å) and Valence and Dihedral Angles (in °) of Transition State Structures coordinate/property Ca S C N Br C C C C O S S Ca S
S C Br H H(N) Hb C Oc O C C C S C
Br Hb C C
C Oc Gsold ∆G+e ν+f µh
R
TSgg
TSgt
TSag
TSta
1.691 1.976 1.011 1.084 1.512 1.220 1.336 1.459 -3558.637636 9.18
1.715 2.154 2.727 1.012 1.079 1.498 1.213 1.361 1.452 169.1 98.9 59.0 87.2 -3558.618442 12.0 247.7i 17.95
1.714 2.290 2.600 1.030 2.615 1.073 1.495 1.214 1.343 1.451 148.4 90.6 178.3 88.9 -3558.609556 17.6 351.7i 15.74
1.716 2.404 2.510 1.013 1.076 1.491 1.221 1.341 1.458 172.8 89.8 64.9 90.0 -3558.613417 15.2 421.6i 15.98
1.711 2.403 2.506 1.010 4.174 1.077 1.495 1.221 1.336 1.459 176.7 91.7 178.3 86.1 -3558.614608 14.5 421.6i 17.21
a Carbon atom of the triazole ring. b Average over three hydrogen atoms of the central methyl group. c Carbonyl oxygen atom. d In atomic units. e In kcal/mol. f In cm-1. h In D.
parameter on more reactions is required to construct a reliable model of blood serum. The results of calculations indicate, however, that in this particular case the changes in the geometries of the corresponding transition states as well as reactants are insignificant. This makes results obtained with the PCM model with parameters for water useful in studies aimed at geometries (but not the energetics), such as, for example, modeling of transition state structure for drug design purposes.25 The following example shows that this is not always the case. The second example illustrates another approach to the use of implicit solvent models. Namely, optimization of a system is carried out in the gas phase, and then the energy is calculated for this geometry using an implicit solvent model.26 This approach neglects changes of geometry that are induced by solvation. We have tested the validity of this approach on the example of the reaction shown in Figure 2 that has been studied experimentally in our laboratory.27 First, gas phase geometries of reactants and transition states were optimized in the gas phase at the DFT level that proved adequate in mechanistic studies of reactions involving 1,2,4-triazoles.20,22 The transition state structures optimized in the gas phase are identified by the trailing subscript g. Calculations carried out using different relative orientation of the reactants lead to two structures illustrated in Figure 5. This relative orientation of the triazole ring and the carboxylic moiety of the ester are best described by the C-S-C-C dihedral angle, which is close to 60° in one structure and about 180° in the other. We have, therefore, labeled these structures with the second trailing subscript g or t corresponding to gauche or trans orientation, respectively. Basic properties of these transition state structures are given in the third and fourth columns of Table 3. For both of these structures, energies with the PCM solvent model were then calculated using parameters for acetone. In comparison with energies of the complex of reactants R optimized with the PCM model, these energies allowed for calculations of Gibbs free energy of activation. As can be seen, these calculations point to the TSgg structure as significantly more stable. Subsequently, both gas phase transition state structures have been reoptimized using the same PCM model. The optimized structures are labeled with the trailing subscript a, and their basic parameters are presented in the last two columns of Table
3. The most striking result of these calculations is the change of relative energies of the transition states g or t and corresponding change in the Gibbs free energy of activation. Full optimization of the transition state structure in the presence of the solvent model points to the TSta structure as more stable by 0.7 kcal/mol. This signifies that the approach in which changes to geometry that result from the presence of the solvent are neglected can lead to wrong results. In terms of chemistry, this is a very interesting structure because it does not allow for an easy typical classification of the transition state structure.28 It can be regarded as “exploded” since both C-S and C-Br bonds are very long. From the point of view of the methyl group that is being transferred, it could be considered symmetrical with a slight shift toward the “early” structure since the average value of the S-C-H valence angles is close but slightly larger than 90°. On the other hand, the forming C-S bond is very long, e.g., significantly longer than in the transition state for the reaction illustrated in Figure 1. This makes this transition state very early. As can be seen, and as we have pointed out earlier,29 traditional qualitative/intuitive classifications are intrinsically contradictory when compared to quantum mechanical results. In the conclusions that emerge from the calculations carried out for the reaction illustrated in Figure 2, we have shown that substantially different transition state structures of relatively close energies in the gas phase can be identified for this reaction. The presence of conformationally different transition state structures is also worth noticing, as typically it is assumed that reactions of simple molecules proceed via a single transition state and the conformational space is usually taken into account only when enzymatic reactions are considered.30 Most importantly, the relative stability of these transition states is miscalculated when the solvation effects are neglected during optimization. In summary, presented studies lead to the conclusion that implicit solvent models, which are attractive alternatives to the expensive, explicit treatment of the solvent molecules, can be successfully applied to SN2 reactions. Although we have studied only one reaction, it seems that if small energetic differences are not of importance implicit solvent models for aqueous solution may be used to describe blood serum environment since geometric features are practically not
12418 J. Phys. Chem. B, Vol. 112, No. 39, 2008 perturbed. This conclusion and the extension of the aqueous model to grasp all features of the serum environment require further studies of a large number of other types of reactions to yield adequate parameters. Our studies also point out that the frequently used, and recommended from the energetic point of view,3a strategy of using the gas phase to optimize structures in predicting solvation effects, although economically attractive, should be used with great care and omitted if possible since the conformation of the reactants and transition states may change from the gas phase to solution. 3. Experimental Protocols 3.1. Materials. Trimethylsulfonium nitrate was obtained from trimethylsulfonium iodide, purchased from Fluka (>98%) using silver nitrate (POCh; pure p.a.) and was purified by crystallization from anhydrous ethanol (POCh; 99.8%,) and acetone (Chempur, 99.5%). The melting point of the product was 134-134.5 °C. Water was purified using the Nanopure system from Millipore. The remaining reagents, trimethylamine (45% aqueous solution, Merck), deuterium oxide (Dr. Glaser AG, Basel, 99.9% D), and bovine serum purchased from SigmaAldrich (B-9433) were used without further purification. Serum thermal stability was tested by prolonged heating at 40, 60, 70, 80, and 90 °C. Nephelometrical measurements with a Carl Zeiss Jena diffuser showed no turbid formation up to 60 °C within the time corresponding to experiment duration. 3.2. Kinetic Measurements. Solutions of reactants, trimethylsulfonium nitrate (0.093 mol/dm3) and trimethylamine (0.256 mol/dm3), in blood serum or water were prepared, and 5 or 10% (v/v) of D2O were sealed in NMR tubes termostatted at 59.8 °C. At time interval, NMR proton spectra were recorded. Chemical shifts of reactants in 1H NMR spectra obtained with Bruker DPX 250 Avance were 3.11 ppm (12H, s) for tetramethylammonium cation, 2.84 ppm (9H, s) for trimethylsulfonium cation, 2.15 ppm (9H, s) for trimethylamine, and 2.04 ppm (6H, s) for dimethyl sulfide. Rate constants were determined from the slopes of the time dependence of concentrations corresponding to the second-order reaction as illustrated by Figure 3. 3.3. Properties Determination. Refraction was measured using an Abbe Refraktometer Model G. The density of blood serum was found equal to 1015.88 g/L. Macroscopic surface tension was determined stalagmometrically. The average from three separate measurements equals 122.093 dyn/cm. 3.4. Theoretical Calculations. Calculations of 18O VPIE were carried out at the HF level of theory using the standard 6-31G(d) basis set.31 The polarizable continuum solvent model (PCM)23 with parameters for water was used. Isotope effects were calculated using Isoeff.32 The same solvent model was used in calculations of reactions shown in Figures 2 and 3, while the theory level was upgraded to the DFT level by employing a B3LYP functional33 with the 6-31+G(d,p) basis set.34 All gas phase and PCM calculations were carried out using the Gaussian package35 with default convergence criteria. Vibrational analysis was performed for the optimized structures to confirm that they represent stationary points on the potential energy surfaces (3n-6 real normal modes of vibration for the reactant and exactly one imaginary frequency for the transition state) and to calculate gas phase Gibbs free energies. Acknowledgment. This work was supported by the Technical University funds I-19/010/2008. Computer time was provided by the Polish supercomputing facilities at PSNC (Poznan), ICM (Warsaw), and Cyfronet (Cracow).
Wujec et al. References and Notes (1) Lundberg, M.; Morokuma, K. J. Phys. Chem. B 2007, 111, 9380. (2) Zheng, G.; Witek, H. A.; Bobadova-Parvanova, P.; Irle, S.; Musaev, D. G.; Prabhakar, R.; Morokuma, K.; Lundberg, M.; Elstner, M.; Ko¨hler, C.; Frauenheim, T. J. Chem. Theory Comput. 2007, 3, 1349. (3) (a) Nicholls, A.; Mobley, D. L.; Guthrie, J. P.; Chodera, J. D.; Bayly, C. I.; Cooper, M. D.; Pande, V. S. J. Med. Chem. 2008, 51, 769. (b) Chamberlin, A. C.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 2008, 112, 8651. (4) Jancso, G.; Van Hook, A. Chem. ReV. 1974, 74, 689. (5) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (6) (a) Castejon, H.; Wiberg, K. B.; Sklenak, S.; Hinz, W. J. Am. Chem. Soc. 2001, 123, 6092. (b) Ruggiero, G. D.; Williams, I. H. J. Am. Chem. Soc. 2004, 126, 8634. (c) Mannisto, P. T.; Kaakkola, S. Pharmacol. ReV. 1999, 51, 593. (d) Effmert, U.; Saschenbrecker, S.; Ross, J.; Negre, F.; Fraser, C. M.; Noel, J. P.; Dudareva, N.; Piechulla, B. Phytochem. 2005, 66, 1211. (7) Waddell, T. G.; Eilders, L. L.; Patel, B. P.; Sims, M. Orig. Life EVol. Biosph. 2000, 30, 539. (8) Moliner, V.; Williams, I. H. J. Am. Chem. Soc. 2000, 122, 10895. (9) Ko, S.; Eliot, A. C.; Kirsch, J. F. Arch. Biochem. Biophys. 2004, 421, 85. (10) Ruggiero, G. D.; Williams, I. H.; Roca, M.; Moliner, V.; Tun˜o´n, I. J. Am. Chem. Soc. 2004, 126, 8634. (11) Ma¨nnisto¨, P. T.; Kaakkola, S. Pharmacol. ReV. 1999, 51, 593. (12) (a) Richardson, K.; Barmmer, K. W.; Marriott, M. S.; Troke, P. F. Antimicrob. Agents Chemother. 1985, 27, 832. (b) Maesaki, S.; Iwakawa, J.; Higashiyama, Y.; Miyazaki, Y.; Yanagihara, K.; Tomono, K.; Tashiro, K.; Kohno, S. J. Infect. Chemother. 2000, 6, 101. (c) Perea, S.; Fothergill, A. W.; Sutton, D. A.; Rinaldi, M. G. J. Clin. Microbiol. 2001, 39, 385. (13) Brunton, L. L.; Lazo, J. S.; Parker, K. L. The Pharmacological Basis of Therapeutics; McGraw-Hill Med. Pub. Div.: New York, 2006. (14) (a) Chu, C. H.; Hui, X. P.; Zhang, Y.; Zhang, Z. Y.; Li, Z. C.; Liao, R. A. J. Chin. Chem. Soc. 2001, 48, 121. (b) Hui, X. P.; Zhang, L. M.; Zhang, Z. Y.; Wang, Q.; Wang, F. J. Chin. Chem. Soc. 2000, 47, 535. (c) ¨ tuk, G. Il Farmaco 2001, 56, 947. (d) Burch, Ulusoy, N.; Gu¨rsoy, A.; O H. A.; Smith, W. O. J. Med. Chem. 1966, 9, 405. (e) Foroumadi, A.; Mansouri, S.; Kiani, Z.; Rahmani, A. Eur. J. Med. Chem. 2003, 38, 851. (f) Ram, V. J.; Mishra, L.; Pandey, N. H.; Kushwaha, D. S.; Pieters, L. A. C.; Vlietinck, A. J. J. Heterocycl. Chem. 1990, 27, 351. (g) Ergenc, N.; Ilhan, ¨ tu¨k, G. Pharmazie 1992, 47, 59. (h) Kalyoncuog˘lu, N.; Rollas, S.; E.; O ¨ . Pharmazie 1992, 47, 796. (i) Rollas, Su¨r-Altiner, D.; Yegenog˘lu, Y.; Ang˘, O ¨ . Pharmazie S.; Kalyoncuog˘lu, N.; Su¨r-Altiner, D.; Yegenog˘lu, Y.; Ang˘, O 1993, 48, 308. (15) (a) Shiradkar, M.; Kumar, G. V. S.; Dasari, V.; Tatikonda, S.; Akula, K. C.; Shah, R. Eur. J. Med. Chem. 2007, 42, 807. (b) Rudnicka, W.; Foks, H.; Janowiec, M.; Zwolska-Kwiek, Z. Acta Polon. Pharm. 1986, 43, 523. (c) Mir, I.; Siddiqui, M. T.; Comrie, A. Tetrahedron 1970, 26, 5235. (16) (a) Holla, B. S.; Veerendra, B.; Shivananda, M. K.; Poojary, B. Eur. J. Med. Chem. 2003, 38, 759. (b) Duran, A.; Dogan, H. N.; Rollas, S. Farmaco 2002, 57, 559. (17) Siwek, A.; Wujec, M.; Jagiełło-Wójtowicz, E.; Chodkowska, A.; Kleinrok, A.; Paneth, P.; Dobosz, M. Cent. Eur. J. Chem 2008, 6, 47. (18) Palaska, E.; S¸ahin, G.; Kelicen, P.; Durlu, N. T.; Altinok, G. Il Farmaco 2002, 57, 101. (19) Shtefan, E. D.; Vvedenskii, V. Yu. Russ. Chem. ReV. 1996, 65, 307. (20) Wujec, M.; Paneth, P. J. Phys. Org. Chem. 2007, 20, 1043. (21) Siwek, A.; Wujec, M.; Wawrzycka-Gorczyca, I.; Dobosz, M.; Paneth, P. Heteroat. Chem. 2008, 19, 337. (22) Wujec, M.; Paneth, P. J. Phys. Org. Chem. 2008, 20, 345. (23) Miertus, S.; Scrocco, E.; Tomasi, J. J. Chem. Phys. 1981, 55, 117. (24) (a) Moser, P. G.; Squire, P. G.; O’Konski, C. T. J. Phys. Chem. 1966, 70, 744. (b) Oncley, J. L. Biophys. Chem. 2003, 100, 151. (c) Oncley, J. L. J. Am. Chem. Soc. 1938, 60, 1115. (d) Oncley, J. L., Ferry, J. D. J. Am. Chem. Soc. 1938, 60, 1123. (25) (a) Singh, V.; Evans, G. B.; Lenz, D. H.; Mason, J. M.; Clinch, K.; Mee, S.; Painter, F. G.; Tyler, P. C.; Furneaux, R. H.; Lee, J. E.; Howell, P. L.; Schramm, V. L. J. Biol. Chem. 2005, 280, 18265. (b) Kwiecien´, R. A.; Lewandowicz, A.; Paneth, P. Substrate-Enzyme Interactions from Modeling and Isotope Effects. In Sokalski, A., Ed. Challenges and AdVances in Computational Chemistry and Physics of Molecular Materials with Specific Interactins; Leszczyn´ski, J., Ed.; 2007; Vol. 4, Chapter 7, pp 341364, and references therein. (c) Lee, J. E.; Singh, V.; Evans, G. B.; Tyler, P. C.; Furneaux, R. H.; Cornell, K. A.; Riscoe, M. K.; Schramm, V. L.; Howell, P. L. J. Biol. Chem. 2005, 280, 18274. (d) Lewandowicz, A.; Shi, W.; Evans, G. B.; Tyler, P. C.; Furneaux, R. H.; Basso, L. A.; Santos, D. S.; Almo, S. C.; Schramm, V. L. Biochemistry 2003, 42, 6057. (26) Vargiu, A. V.; Robertazzi, A.; Magistrato, A.; Ruggerone, P.; Carloni, P. J. Phys. Chem. B 2008, 112, 4401.
Solvent Description of SN2 Reactions (27) Maliszewska-Guz, A.; Wujec, M.; Pitucha, M.; Dobosz, M.; Chodkowska, A.; Jagiełło-Wójtowicz, E.; Mazur, L.; Kozioł, A. Collect. Czech. Chem. Commun. 2005, 70, 51. (28) Fang, Y.-r.; Gao, Y.; Ryberg, P.; Eriksson, J.; Kołodziejska-Huben, M.; Dybała-Defratyka, A.; Danielsson, A.; Paneth, P.; Matsson, O.; Westaway, K. C. Chem. Eur. J. 2003, 9, 2696. (29) (a) Matsson, O.; Dybała-Defratyka, A.; Rostkowski, R.; Paneth, P.; Westaway, K. C. J. Org. Chem. 2005, 70, 4022. (b) Dybała-Defratyka, A.; Rostkowski, M.; Matsson, O.; Westaway, K. C.; Paneth, P. J. Org. Chem. 2004, 69, 4900. (30) Dybała-Defratyka, A.; Paneth, P.; Truhlar, D. G. Quantum Catalysis in Enzymes In Quantum Tunneling in Enzyme Catalyzed Reactions; Scrutton, N., Allemann R., Eds.; RSC Publishing: Cambridge, UK; Chapter 3, in press. (31) (a) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. (b) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (c) Hariharan, P. C.; Pople, J. A. Mol. Phys. 1974, 27, 209. (d) Rassolov, V. A.; Pople, J. A.; Ratner, M. A.; Windus, T. L. J. Chem. Phys. 1998, 109, 1223. (e) Rassolov, V. A.; Ratner, M. A.; Pople, J. A.; Redfern, P. C.; Curtiss, L. A. J. Comput. Chem. 2001, 22, 976. (32) Anisimov, V.; Paneth, P. J. Math. Chem. 1999, 26, 75. (33) (a) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (b) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (c) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785.
J. Phys. Chem. B, Vol. 112, No. 39, 2008 12419 (34) (a) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. (b) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. (35) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y., Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, reVision D.01; Gaussian Inc.: Wallingford CT, 2004.
JP8035956
