Phys. Chem. Chem. Phys.,

PAPER Cite this: Phys. Chem. Chem. Phys., 2014, 16, 13096 Specific rotation of monosaccharides: a global property bringing local information Bruno A. França and Clarissa O. da Silva* Received 26th March 2014, Accepted 15th May 2014 DOI: 10.1039/c4cp01316f www.rsc.org/pccp Carbohydrates generally occur in several conformations that may differ among themselves by energy values that are smaller than the accuracy of the most sophisticated theoretical methods used to determine them. In addition, the preferential orientations of the hydroxyl groups of these molecules cannot be identified by any experimental technique. Therefore, a method that is able to validate the absolute conformations (i.e., consisting of the orientations of the hydroxyl groups) of carbohydrates would be helpful to improve our knowledge about monosaccharides. SR has been used for this purpose, and here, we present a test to measure the specific rotation (SR) ability of a molecule that possesses not only many conformations, but also four adjacent chiral centers. The results show that the final SR value is a weighted average of a global property (obtained for each conformation), and the latter by its turn is influenced by each chiral center in a multi chiral system. By comparing the SR values calculated for the most abundant anomers of xylopyranose with those of the corresponding monochiral analogs obtained by saturation of three different chiral centers each time, the influence of each center on the global property is confirmed. Introduction Even though it is possible to measure the specific rotation (SR or [a] 589 ) of chiral systems in the gas-phase, the large amount of experimental data available in the literature for enantiomorphic molecules refers to SR measurements in solution at certain values of concentration and temperature. Given this situation, as noted by Mukhopadhyay and coworkers, 1 effects such as chiral solvent imprinting, 2,3 perturbation of the solute electronic structure by solvation including association of solvent molecules, 4 solute clustering or assembly, 5 and shifts in the solute conformational distribution may strongly influence the absolute values of the experimentally determined SR. To overcome at least the two latter effects, Polavarapu and coworkers 6 have suggested the comparison of the theoretically calculated SR value with the experimentally determined intrinsic rotation value, 7 the latter being defined as the SR value of a chiral solute under infinitely dilute conditions. With regard to the SR calculations, since quantum mechanical theoretical access to this quantity was made possible, 8 many authors have reported its use to find relative and absolute configurations, 9 to determine the conformational distribution of a chiral and flexible compound, and to study the solvent reordering around chiral solute molecules, just to cite a few examples. However, SR is a very sensitive property, and there are cases where small geometrical distortions at the chiral centers Departamento de Química, Universidade Federal Rural do Rio de Janeiro, Rodovia BR 465, km 47, Seropédica, RJ 23897-000, Brazil. E-mail: clarissa-dq@ufrrj.br may dramatically change the calculated SR value, as reported by Wiberg and coworkers 10 for 3-substituted-1-butenes. Such compounds are able to show a maximum amplitude of approx. 9001 for SR, when geometrical torsions are imposed. Even for rigid molecules at their equilibrium geometries, Stephens and coworkers 11 have reported a RMS deviation of approx. 28.9 for calculated and experimental SR values of molecules with small SR values in a study of 65 compounds, using a TDDFT/GIAO B3LYP/ aug-cc-pvdz//b3lyp/6-31g(d) description. In all of the cases that were theoretically studied above, the chiral molecules present only one chiral center that is atom centered (it is relevant to note that in a more general sense, some achiral systems also have the ability to rotate the plane of plane-polarized incident light 12 ). Despite all of these factors, and mainly due to its ease of experimental access when compared to other physical-chemical methods used to distinguish between enantiomers, SR has been generally used for the determination of enantiomeric ratios in racemic mixtures. The technique can provide a quick (and crude) estimate of a solution s concentration. In this case, SR is assumed to be constant (at a certain T value) in the expression OR = SR/(c l), where OR is the measured optical rotation, c is the solution concentration, and l is the optical length of the light propagating through the solution. In particular, experimental SR values have been used to evaluate the concentration values of carbohydrate solutions for a long time because such molecules are chiral systems that possess not just one but several adjacent chiral centers. Tables containing SR experimental values of carbohydrates in aqueous solution are available in the literature dating back to 1942. 13 13096 Phys. Chem. Chem. Phys., 2014, 16, 13096--13102 This journal is the Owner Societies 2014

Paper In contrast to the apparent ease of obtaining SR experimental values for carbohydrates, determining the SR theoretical value for such molecules may be a challenging task because it consists of the computation of the relative abundance of each conformation and its individual contribution to the final SR value, obtained as a weighted average in a solution. Even for monosaccharides (the most structurally simple carbohydrates), once they are polyhydroxylated compounds with a huge conformational versatility for the hydroxyl groups, many conformations are possible because the energy differences among them are very small at room temperature. Such a characteristic in principle imposes the necessity to use precise theoretical methods to obtain the energy differences between conformations and, consequently, the individual population values for a monosaccharide. In addition, due to the sensitivity of SR and to the fact that monosaccharides are systems that possess many adjacent chiral centers, the possibility of using a theoretical description to reproduce SR values for monosaccharides in aqueous solution might sound very remote, basically due to the supposition that such a sensitivity could be magnified by the proximity of the adjacent chiral centers. In spite of its sensitiveness, the use of SR has recently been suggested in the literature to validate monosaccharide conformational samplings. 14 16 This procedure has been proven to be effective for glucose, 14 xylose, 15,17 levoglucosan, 18 and other carbo-derivative systems. 16 These findings raise questions about the effects of n vicinal chiral centers in the same molecule, a situation that is by far underrepresented in the literature, likely because this imposes the necessity to study all of the possible 2 n diastereoisomers. However, such a study might shed more light on some aspects of the nature of SR itself, related to its ability to provide local information, despite its global character. It would be important to study these characteristics of the SR not only to improve our knowledge about its intrinsic nature in general but also to evaluate its ability to validate carbohydrate conformations. In a recent paper, we have demonstrated that the difference in SR values among different conformations is larger than the difference due to changes in the description level, 15 which is a prerequisite for a property that is to be used in a validation procedure. In the previous study, we chose only the most stable xylopyranose conformers in their equilibrium geometries. It was of interest to determine if a unique SR individual value is possible for each defined hydroxyl group orientation, i.e., if there is a univocal correspondence between an individual SR value of a particular conformation and the orientation of each one of its hydroxyl groups. We undertook this investigation as a necessary second test before accepting SR as a validation property for monosaccharide conformational samplings, due to the doubts already raised with regard to its local or global character for systems with two chiral centers. 19 Therefore, in this work, we will investigate how geometrical distortions introduced in the most stable xylose-solvated conformations influence their individual SR values. We hope that this analysis will make possible the evaluation of the ability of the global SR value for a particular conformation to reflect the different orientations of the hydroxyl groups that are bonded to the chiral centers. Due to its very high sensitivity, in the next sections, we will study SR for a system with several and adjacent chiral centers, and we will quantify how different the SR global values are for conformations that differ among themselves in the orientation of one hydroxyl group each time. Methodology PCCP Initially, the two most stable conformers found for each anomer of xylopyranose in aqueous solution (15a and 20b, keeping the nomenclature of the original paper) were selected for the study of how individual SR values change with geometrical distortions of the hydroxyl groups bonded to each chiral center. Such distortions are defined by the values of the dihedral angles j1, j2, j3, and j4. The starting geometries of each anomer have the original values that are reported in Fig. 1. The solvation was considered using the Integral Equation Formalism of the Polarizable Continuum Model (PCM): 20 the solute is introduced into a cavity with a molecular shape that is opened in a continuum dielectric and formed by interlocking spheres centered on atoms or groups of atoms. The radii of the spheres are 2.40 Å for CH and CH 2 groups, 1.80 Å for an O atom, and 1.44 Å for a H atom bonded to the oxygen atom of a hydroxyl group. 21 In this PCM version, we computed the solvation energy (G solv ) as a summation of the electrostatic (G elect ) and nonelectrostatic (G non-elect ) components. This latter component is obtained via the computation of the dispersion, repulsion, and cavitation terms. 22 The calculations were all performed with the Gaussian03 23 computational code. The SR values were calculated using B3LYP/6-311++G(2d,2p), on geometries that were previously obtained, as suggested in the literature for rigid systems. 24 These values were obtained for conformers in PCM following the TD-DFT/GIAO approach, as described previously. 25 The results are reported as specific rotation values (SR or [a] D ) calculated at the sodium D line frequency. Since for the systems under study (polyhydroxylated compounds in a high dielectric protic medium at thermodynamical equilibrium conditions), the main component of the solvation energy is electrostatic, as well as the main component of the solute solvent hydrogen bond (if its quantitative decomposition is considered 26,27 ) we will not consider further refinements. 18,28 Geometrical distortions were imposed on all four hydroxyl groups, one at a time, in a scanning procedure where the corresponding j angle to be investigated assumed all possible Fig. 1 Most stable conformations found for a and b xylopyranose anomers and the corresponding dihedral angles, j1 = H1 O1 C1 O5, j2 = H2 O2 C2 C1, j3 = H3 O3 C3 C4, and j4 = H4 O4 C4 C5, which define their hydroxyl group orientations. This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16, 13096--13102 13097

values from 01 to 3601, in steps of 201. During this procedure, the dihedral angle values of all other hydroxyl groups remained unchanged for the corresponding anomer. We can see that the most abundant conformer of each anomer has the hydroxyl groups bonded to all chiral centers, except the anomeric one, oriented in an anti-clockwise direction. This is a clear manifestation of the cooperativity effect. 29 The corresponding potential energy surfaces were not calculated because the most stable conformations for each anomer were already identified previously, and exactly the most abundant ones are used here to provide an estimate of how much SR is affected by small geometrical distortions around the most common values of the dihedral angles that define the hydroxyl group orientation. It is necessary to evaluate if such small geometrical distortions may cause very large changes in SR, as those observed in other systems. 10,30 No geometrical optimization was performed. The SR value was calculated for each geometry that was obtained in the scanning procedure for the dihedral angles. The SR values were calculated at the B3LYP/6-311++G(2d,2p) level. To investigate how the presence of vicinal chiral groups affects the individual SR values of each conformation, the hydroxyl groups that were not being scanned were replaced by hydrogen atoms. This generated monochiral hydroxylated compounds in which the only hydroxyl group that was preserved in the molecule was bounded to the only chiral center that remained in the molecule. Such a procedure generated five analogs that were identified by the number of the carbon atom kept as the chiral center: a-c1, b-c1, C2, C3, and C4. Only the two first ones preserve the anomerization center. C2, C3, and C4 are equal for a and b anomers because the chirality of the anomeric center was eliminated by saturation, and the orientation of all other chiral centers is very similar for both anomers, as already noted and shown in Fig. 1. The saturated analogs are reported in Fig. 2 below. Such structures were obtained after geometrical optimization was performed using the density functional B3LYP and the 6-31+G(d,p) basis-set functions. The scanning of the dihedral angles that define the orientation of each hydroxyl group was performed as has already been described for the xylopyranose anomers. Fig. 2 Saturated analogs obtained from the two most stable anomers of xylopyranose. Results and discussion Paper From Fig. 3, we can see that the SR values of different anomers have different magnitudes. The SR values of b anomers are always smaller than those of a anomers, even when geometrical distortions are imposed on the hydroxyl groups of all the chiral centers (one at a time). This observation could be thought of as concerning only the SR curves for these two anomers, but when the whole set of the most stable xylopyranose conformations are taken into account, 15 we see that among all of the conformations of the a anomers, the lowest individual SR value is +83.2 deg dm 1 cm 3 g 1 (for conformation 2a), while the highest SR value for b (29b) is +43.2 deg dm 1 cm 3 g 1. Similar observations are also possible when the most stable glucose conformations and their corresponding SR individual contributions are considered. 14 In Fig. 3, we see that in all cases, the maximum amplitudes for SR variation are approximately 100 deg dm 1 cm 3 g 1,when geometrical distortions are imposed on each hydroxyl group bonded to the chiral centers of the molecule, one at a time. No large variations are observed for the SR values, as has been previously reported for 3-chloro-1-butene 10 and 2-chloro butane. 30 Additionally, we see that the SR global value is dependent on the orientation of each hydroxyl group of the molecule. In fact, the geometrical distortions on C2, defined by the values of j2 in the a anomer, keep the SR value practically unchanged only in the range from 401 to 901. Although the variations observed in the SR values are not as large as those observed for other systems (which could preclude its usage as a validation property for conformational samplings on monosaccharide potential energy surfaces), they are intense enough to distinguish between different conformations. This happens because SR values are quite distinct when the j1, j2, j3, and j4 angles are close to their most common values found in monosaccharides, i.e., 601, 1801, and 601 (or 3001), as observed from Table 1. The data in Table 1 show that the global SR values differ appreciably among themselves, depending on the orientation of each hydroxyl group, when all others (defined by the dihedral angles that are not being scanned) remain in the original orientation found in the corresponding anomer. This is true for both anomers, and the smallest differences, always found for 601 and 3001 of j2 and j4, are italicized. These small differences are unlikely to cause indistinguishability of the SR values because the energy of such conformations will be very different (in any case, they are both stationary points on the potential energy surface), as is generally the case when only one dihedral of the compound is changed. This observation is easily checked by inspection of the whole set of xylopyranose conformations that are found to be abundant in aqueous solution at room temperature. 15 In this set, no pairs of conformations are found that differ from each other by only one hydroxyl group orientation on C2 or C4. Compared to systems where SR was investigated from geometrical distortions, these hydroxylated molecules have four adjacent chiral centers, and perhaps such a characteristic may be responsible for this unexpected behavior, i.e., the presence of 13098 Phys. Chem. Chem. Phys., 2014, 16, 13096--13102 This journal is the Owner Societies 2014

Paper PCCP Fig. 3 SR values of the two most abundant xylopyranose anomers (15a and 20b), for different hydroxyl group orientations defined by the corresponding dihedral angles j1, j2, j3, or j4. See Fig. 1 for dihedral angle definition. The SR values defined by the j values at equilibrium geometries for the most stable anomers are circled. Table 1 SR values (in deg dm 1 cm 3 g 1 ) calculated when jx (X =1,2,3, or 4) assumes the three most common values for a staggered conformation of the H atom of the hydroxyl group Anomer jx X =1 X =2 X =3 X =4 15a 601 160 150 205 120 1801 90 85 150 150 3001 65 140 170 115 20b 601 15 20 35 55 1801 40 80 20 20 3001 50 30 0 65 several vicinal chiral centers restricted the amplitude of the SR variation instead of enlarging it, as could be initially supposed due to the simple idea previously mentioned. To investigate how vicinal chiral centers influence the SR value of the whole molecule, four analogs were built, replacing all but one hydroxyl group with hydrogen atoms. Such a procedure eliminates the chirality of the corresponding centers where saturation took place, as has been explained in the Methodology section. The SR was calculated for all of those systems in which geometrical distortions were imposed on the only chiral center that was preserved. The results are reported in Fig. 4. The identification labels of the scanned dihedral angle are preserved. From Fig. 4, we see that even in the saturated xylopyranose analogs, the amplitudes of variation of the SR values are similar to, but slightly larger than, those observed for the monosaccharides. Therefore, it is not the presence of adjacent chiral centers that diminishes the amplitude of the SR variation to values of almost 8 or at least 2 times smaller than those found for 3-chloro-1-butene 10 and 2-chloro butane, 30 respectively. However, it is clear from Fig. 4 that vicinal chiral centers have a strong influence on the absolute SR values of the conformers for the chiral centers C2, C3, and C4. The SR values of the xylopyranose anomers are represented by the solid lines in the graphs. These values are always very far from the SR values (dashed lines) of the analogs that are created by saturation of all other chiral centers except for the one that is scanned. In general, such a vicinal influence is more intense on a than on b anomers because the distances between the This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16, 13096--13102 13099

Paper Fig. 4 SR values of a-andb-c1, C2, C3, and C4 analogs (dashed lines) of 15a and 20b xylopyranose conformations, obtained while the corresponding dihedral angle j of the only remaining hydroxyl group is scanned. The SR values obtained during the scanning of the corresponding chiral center for both anomers are reported (solid lines) for comparison. The SR values defined by the j values at equilibrium geometries for the most stable anomers are circled. solid and the dashed lines are larger for a than for b anomers. The situation is different only for the C1 chiral center. In fact, the situation seems to be exactly the opposite: all of the remaining chiral centers seem to not affect the SR global value very much. The saturated analog has SR values that are similar to those of the anomers studied, in particular when the j1 value is in the range found in the equilibrium geometry for both xylopyranose anomers. To check this observation, which could prevent the use of SR as a property to validate monosaccharide conformational samplings, we used the same procedure to investigate two other xylopyranose anomers that have j2, j3, and j4 angles that are different from the corresponding dihedral angles in the 15a and 20b anomers. This situation needs to be investigated because this study is based on how the rotation of only one hydroxyl group affects the SR of the conformers, while all other hydroxyl groups of the molecule remain unchanged. In other words, the results that we obtain for SR changes upon rotation of the hydroxyl group that is bonded to the chiral center are valid as long as all of the other hydroxyl groups are kept fixed in their original position. The two new anomers that we considered are reported in Fig. 5, where the dihedral angle values that define the orientation of each hydroxyl group are shown. In Fig. 6, the behavior of SR is completely different from that observed in Fig. 4 C1. The saturated analogues now have SR values different from those of the 4a and 16b conformations, particularly in the regions of j1 = 601, 1801, and 3001. It is clear that the existence of other chiral centers vicinal to the chiral anomeric carbon contributes to the global SR value of Fig. 5 Conformations found for xylopyranose that differ from those of the most abundant anomers (15a and 20b) by the orientation of the hydroxyl group bonded to C2, C3, and C4 chiral centers (4a and 16b). these conformations. The SR values are all shifted upward in both anomers by saturation of all of the chiral centers except C1, and for the a anomer, the maximum amplitude value is also slightly increased. Conclusions This study evaluated the viability of using SR to validate monosaccharide conformations that are theoretically sampled. There is no experimental technique that is able to distinguish between orientation preferences for the hydroxyl group. SR may be able to help in this case. Our results suggest that even though SR is a global property, it is able to provide local information about the orientation of each hydroxyl group for xylopyranose conformations that are abundant in aqueous solution. The differences between SR values for conformations exhibiting the most common dihedral angles for the hydroxyl 13100 Phys. Chem. Chem. Phys., 2014, 16, 13096--13102 This journal is the Owner Societies 2014

Paper PCCP Fig. 6 SR values for the conformations found by scanning the j1 angle of 4a and 16b, compared to those of the a-c1 and b-c1 analogues. The SR values defined by the j values for equilibrium geometries of the xylopyranose stable anomers are circled. groups are neither too large nor too small. Both extreme cases would preclude its use as a validation property. In the former case, even small geometrical perturbations would result in very large SR deviations. In the latter case, SR would not be able to distinguish between different conformations. Indeed, what was observed was that (1) the maximum amplitude of the SR variations was approximately 100 deg dm 1 cm 3 g 1 for geometrical torsions of the C OH bonds of the four hydroxyl groups of the most stable anomers of xylopyranose; (2) the presence of several adjacent chiral centers is not the reason for this value being smaller than expected 10,30 because the saturated xylopyranose analogues that preserved only one of the four chiral centers have similar values for SR amplitude variations; (3) such saturated xylopyranose analogues that preserved only one of the four chiral centers have SR global values that are different from those of the corresponding xylopyranose conformations that were derived by saturation, particularly in the regions of jx (X =1,2,3,and4)= 601, 1801, and 3001. This finding shows that the elimination of chiral centers changes the SR global value or, in other words, that each chiral center provides a local contribution to the SR global value; (4) for the jx values of interest, there is a univocal correspondence between the SR global value and the orientation of each hydroxyl group for the xylopyranose conformations that are investigated here. Similar studies were performed for both anomers as openchain structures, i.e., those that would take part in the xylose mutarotation reaction. The results were not appreciably different from those reported here. This finding suggests that the presence of the cycle does not influence the amplitude variation of the SR for these compounds. This was a preliminary work that studied the extreme situations, where the SR global values of xylopyranose anomers that were identified as most abundant (which possess four adjacent chiral centers each) are compared with those of molecular analogues that contain only one chiral center. There are other possibilities, such as studying the changes in SR global values of analogues when the number of chiral centers is systematically increased from 1 to 4. Other investigations are also possible for chiral systems that are atom centered and with more than one chiral center. This is a situation that has almost no reports in the literature. Finally, we have found that all a anomers have SR individual values larger than those of b anomers. In this work we have demonstrated that it is true even when the hydroxyl groups are not in their most stable orientations. From these findings, a comparison with mannose aqueous solution may be very suggestive, since it possesses a SR experimental value (SR = +14.4 deg dm 1 cm 3 g 1 ) 13 smaller than that of glucose aqueous solution (SR = +52.7 deg dm 1 cm 3 g 1 ), 13 but a higher a : b anomeric relative abundance (mannose = 65 : 35 and glucose = 62 : 38). 31 Perhaps a detailed theoretical study of SR of such conformers accompanied by their SR individual values may shed some light on the solvation aspects of monosaccharides. 32 Nevertheless, our results reinforce the supposition that SR can be used in the validation of monosaccharide conformational samplings, and perhaps in a near future, it may also help to unravel solvation aspects of monosaccharide aqueous solution. Acknowledgements The authors thank CNPq and FAPERJ for financial support for this work. References 1 P. Mukhopadhyay, P. Wipf and D. N. Beratan, Acc. Chem. Res., 2009, 42, 809 819. 2 P. Mukhopadhyay, G. Zuber, P. Wipf and D. N. Beratan, Angew. Chem., Int. Ed., 2007, 46, 6450 6452. 3 F. Lipparini, F. Egidi, C. Cappelli and V. Barone, J. Chem. Theory Comput., 2013, 9, 1880 1884. 4 P. Mukhopadhyay, G. Zuber, M. R. Goldsmith, P. Wipf and D. N. Beratan, ChemPhysChem, 2006, 7, 2483 2486. 5 M. R. Goldsmith, N. Jayasuriya, D. N. Beratan and P. Wipf, J. Am. Chem. Soc., 2003, 125, 15696 15697. 6 P. L. Polavarapu, A. Petrovic and F. Wang, Chirality, 2003, 15, S143 S149. 7 H. G. Curme and W. Heller, in Techniques of chemistry, Physical methods of chemistry, Part IIIc, Polarimetry, ed. A. Weissberger and B. W. Rossiter, Wiley-Interscience, New York, 1972, vol. 1, pp. 51 182. 8 P. L. Polavarapu, Mol. Phys., 1997, 91, 551 554. 9 E. D. Hedegård, F. Jensen and J. Kongsted, J. Chem. Theory Comput., 2012, 8, 4425 4433. This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16, 13096--13102 13101

10 K. B. Wiberg, P. H. Vaccaro and J. R. Cheeseman, J. Am. Chem. Soc., 2003, 125, 1888 1896. 11 P. J. Stephens, D. M. McCann, J. R. Cheeseman and M. J. Frisch, Chirality, 2005, 17, S52 S64. 12 K. Claborn, C. Isborn, W. Kaminsky and B. Kahr, Angew. Chem., Int. Ed., 2008, 47, 5706 5717. 13 F. J. Bates, Polarimetry, Saccharimetry and the Sugars, NBS Circular C440, U.S. Government Printing Office, Washington, D.C., 1942. 14 C. O. da Silva, B. Mennucci and T. Vreven, J. Org. Chem., 2004, 69, 8161 8164. 15 R. R. Andrade and C. O. da Silva, Carbohydr. Res., 2012, 350, 62 70. 16 J. Kaminský, I. Raich, K. Tomčáková and P. Bouř, J. Comput. Chem., 2010, 31, 2213 2224. 17 R. R. Andrade and C. O. da Silva, Mini-Rev. Org. Chem., 2011, 8, 239 248. 18 A. V. Orlova, R. R. Andrade, C. O. da Silva, A. I. Zinin and L. O. Kononov, ChemPhysChem, 2014, 15, 195 207. 19 C. O. da Silva and B. Mennucci, J. Chem. Theory Comput., 2007, 3, 62 70. 20 B. Mennucci, E. Cancès and J. Tomasi, J. Chem. Phys., 1997, 107, 3032 3037. 21 A. Bondi, J. Phys. Chem., 1964, 68, 441 451. 22 Continuum Solvation Models in Chemical Physics: From Theory to Applications, ed. B. Mennucci and R. Cammi, Wiley & Sons, 2007. 23 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, Paper M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez and J. A. Pople, Gaussian 03, Revision C.01, Gaussian, Inc., Wallingford, CT, 2004. 24 P. J. Stephens, F. J. Devlin, J. R. Cheeseman and M. J. Frisch, J. Phys. Chem. A, 2001, 105, 5356 5371. 25 B. Mennucci, J. Tomasi, R. Cammi, J. R. Cheeseman, M. J. Frisch, F. J. Devlin, S. Gabriel and P. J. Stephens, J. Phys. Chem. A, 2002, 106, 6102 6113. 26 S. J. Grabowski, Chem. Rev., 2011, 111, 2597 2625. 27 Y. Mo, J. Gao and S. D. Peyerimhoff, J. Chem. Phys., 2000, 112, 5530 5538. 28 F. Egidi and V. Barone, J. Chem. Theory Comput., 2012, 8, 585 597. 29 R. A. Klein, J. Am. Chem. Soc., 2002, 124, 13931 13937. 30 K. B. Wiberg, Y.-G. Wang, P. H. Vaccaro, J. R. Cheeseman and M. R. Luderer, J. Phys. Chem. A, 2005, 109, 3405 3410. 31 K. Matsuo and K. Gekko, Carbohydr. Res., 2004, 339, 591 597. 32 N. Mayorkas, S. Rudić, B. G. Davis and J. P. Simons, Chem. Sci., 2011, 2, 1128 1134. 13102 Phys. Chem. Chem. Phys., 2014, 16, 13096--13102 This journal is the Owner Societies 2014