Theoretical Study of the Mutarotation of Erythrose and Threose: Acid Catalysis ⇑ Luis Miguel Azofra , , Ibon Alkorta , José Elguero

Carbohydrate Research 372 (2013) 1–8

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Carbohydrate Research

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Theoretical study of the mutarotation of erythrose and threose: acid catalysis ⇑ Luis Miguel Azofra , , Ibon Alkorta , José Elguero

Instituto de Química Médica (I.Q.M.-C.S.I.C.), Juan de la Cierva, 3, E-28006 Madrid, Spain article info abstract

Article history: The acid catalysis of the mutarotation mechanism in the two aldotetroses, D-erythrose and D-threose, has Received 22 November 2012 been studied at B3LYP/6-311++G(d,p) computational level in gas phase and in solution employing the Received in revised form 18 January 2013 PCM–water model. The open-chain, the furanose and the connecting TS structures have been character- Accepted 21 January 2013 ized. To study the enhancing effect of acid groups on the electrophilicity of the carbonyl carbon atom, four Available online 29 January 2013 + situations have been considered: (i) a classical Lewis acid as BH3; (ii) a classical hard-Pearson acid as Na ; + + + (iii) classical Brønsted acids as H and H3O ; and (iv) a combined strategy using H3O and one bridge-H2O Keywords: molecule as assistant in the proton transfer process. All the acidic groups reduce the activation energy Hemiacetal reaction with exception of the Na+, which can act, in some cases, as inhibitor. It is greatly reduced by the presence DFT-calculations Lewis acid of Brønsted acids (iii) and through the combined strategy (iv). For this last mechanism, the electronic acti- À1 À1 Hard-Pearson acid vation energies are between 12 and 43 kJ mol in vacuum and between 13 and 25 kJ mol in water Brønsted acid solution, through the use of the PCM model. Proton transfer Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction ers, a- and b-, depending on the disposition of the hydroxyl group of the hemiacetal moiety.12 The equilibrium between the different isomers present in the In Figure 2 is reported the reactive process associated with the monosaccharides was observed for the first time by Dubrunfaut mutarotation of a generic D-aldotetrose. The first structure repre- in 18461 when he noticed that the specific rotation of a freshly pre- sented is the non-reactive open-chain one which evolves to a reac- pared cold solution of crystalline glucose decreased from an initial tive structure where the terminal hydroxyl and carbonyl groups value of about 110° to a constant value of 52°. This phenomenon are close and arranged to react. The TS for a reaction without catal- was later called mutarotation2 and its explanation resides in an ysis corresponds to a transition state site characterized by a intramolecular hemiacetal reaction.3,4 The species involved in the four-membered ring with angular strain.13 Two main processes mutarotation process are the open-chain configurations as well are involved in this step: on the one hand, formation of a new C– as the cyclic forms. The cyclic forms can involve five or six bonds, O bond and, on the other hand, a proton transfer from the hydroxyl and are known as furanose and pyranose, respectively.5 Mutarota- group to the carbonyl group to transform it into a new tion has been extensively studied experimentally,6–8 including the hydroxyl group. Depending on the carbonyl face attacked by the 9,10 cases of D-erythrose and D-threose. Experimental studies of hydroxyl group, two furanose forms (a- and b-) are obtained. mutarotation of glucose in acid media indicate that the transfor- Computational studies on the formation of six-membered rings mation barrier is smaller than the one in neutral media.8,11 from open-chain monosaccharides or analogues have been carried 14–17 18 19–21 Aldotetroses, D-erythrose and D-threose, are the simplest carbo- out for glucose, D-xylose, 2-tetrahydropyranol, and deriv- 22 hydrates (see Fig. 1). They are composed of a four carbon atoms atives of L-mannopyranosyl. Furthermore, some of us have studied skeleton with three hydroxyl groups and an aldehyde or hemiace- the hemiacetal formation reaction in D-erythrose and D-threose and tal group. The mutarotation of aldotetroses has only the possibility the catalytic influence of one, two, and three water molecules as of the transformation between the open-chain and the furanose assistants in the proton transfer, as well as simplified models of 12 forms. The only difference between D-erythrose and D-threose is carbohydrates, namely, methanol and 1,2-ethanediol. the configuration of the hydroxyl group attached to C2, R, and S, Related to the study of the mutarotation process, the mecha- respectively. In addition, the cyclic forms present two diasteoisom- nisms of formation of hemiacetals between methanol and formaldehyde have been studied using Conceptual DFT (CDFT).23 The

⇑ Corresponding author. Fax: +34 91 564 48 53. modeling of catalytic strategies was carried out with two objec- E-mail address: [email protected] (L.M. Azofra). tives: (i) to explore the effect of Brønsted acids clustered with http://are.iqm.csic.es the oxygen of the carbonyl group by enhancing the electrophilicity

Open-chain α-furanose β-furanose OH 0 OH 4 O O 4 1 3 O D-erythrose HO 2 1 3 2 OH OH HO OH HO OH OH OH O O O OH OH D-threose HO OH HO OH HO

Figure 1. Open-chain and a- and b-furanose conﬁgurations of D-erythrose and D-threose. Numbering is in agreement with the IUPAC recommendations.

O OH OH O H C O OH OH * OH HO O O HO OH OH OH OH

Non-reactive Reactive open-chain open-chain TS Furanose

Figure 2. Equilibrium process of mutarotation in a D-aldotetrose. One intramolecular hemiacetal reaction is involved. The asterisk in the furanose structure indicates the anomeric carbon atom. on the carbon atom of formaldehyde; and (ii) to explore the effect Atoms in Molecules (AIM)31,32 methodology with the MORPHY33–35 of this kind of charge extractors and combine with the assistance in and the AIM2000 programs.36 On the basis of this methodology, all the proton transfer through the use of water molecules.4 One of the the interactions (covalent and weak interactions) were characterized main conclusions of this study was that the energy barriers de- by the presence of a bond critical point (BCP) and the corresponding crease in all these cases, specially, when both strategies are used bond path linking the two interacting nuclear attractors. The values at the same system. Thus, the activation barriers in the reactions of the electron density and its Laplacian at the BCP allow to classify between methanol and formaldehyde were 141.3 kJ molÀ1 with the contacts as covalent or non-covalent.31,37,38 the isolated monomers, 74.7 kJ molÀ1 with the use of one bridge- À1 H2O molecule, 99.9 kJ mol with the use of the acidic group 3. Results and discussion + À1 H3O , and finally and optimally, 25.0 kJ mol with both. Here we investigate the hemiacetal formation reaction in D-ery- This section has been divided into five parts. In the first one, the throse and D-threose influenced by different acid groups: (i) a clas- stationary points (minima and TS) of the uncatalyzed reaction rep- + sical Lewis acid as BH3; (ii) a classical hard-Pearson acid as Na ; resented in Figure 2 will be discussed. The catalytic ability of a Le- + + + + and (iii) classical Brønsted acids as H and H3O . Finally, the ap- wis acid, BH3, a hard-Pearson acid, Na , and the Brønsted acids, H + + proach (iv) corresponding to a combined strategy using H3O and and H3O , will be examined in the second, third, and four parts, one bridge-H2O molecule as assistant in the proton transfer, has respectively. The last part will be devoted the simultaneous action + been take into account based on the excellent results obtained of H3O and a water molecule assisting the proton transfer process. previously. In order to establish a common reference for all the reactions, the open-chain monosaccharide species will be considered as reac- 2. Computational methods tants and their relative energies will be defined as 0.0 kJ molÀ1.

The geometries used in this study have been selected from a sys- 3.1. Isolated carbohydrates: uncatalyzed process tematic conformational search of the open-chain and furanose con- 24 figurations of the aldotetroses D-erythrose and D-threose. All the The geometries of the open-chain and furanose structures have geometries have been fully optimized with the hybrid Becke,25 been selected based on a previous and systematic conformational three-parameter, Lee–Yang–Parr26 density functional (B3LYP), and search at DFT level24 and they have been used here as reactants Pople’s basis set 6-311++G(d,p).27 Initially, all the systems were con- or products. Also, in the following sections, they have been used sidered in vacuum environment, and subsequently, the solvent ef- in the construction of the reactive forms. The most stable open- fect was taken into account by optimizing the systems through chain conformation, which shows a dihedral angle (compactness) 28 the use of the Polarizable Continuum Model (PCM) using the stan- of the carbon chain of À52.0° and À171.9° for the D-erythrose dard water parameter and including the solute–solvent dispersion and D-threose, has been used as energetic reference in all the reac- interaction energy, the solute–solvent repulsion interaction energy tions studied. and the solute cavitation energy. The transition states (TS) have been The ring configuration analysis in the cyclic forms was carried located employing the Synchronous Transit-Guided Quasi-Newton out within the Cremer–Pople methodology39 and the values ob- (SQTN)29 Methods (QST2 and QST3). In all the cases, vibrational fre- tained overlaid on the Altona–Sundaralingam wheel.40 In Table 1 quencies were calculated to confirm that the structures obtained can be found the values of the P parameter, which characterizes corresponded to energetic minima or true TS. The interaction energy numerically the ring configuration, and of the Q parameter, which has been evaluated as the difference between the energy of the com- is the total puckering amplitude and indicates how much a config- plexes and the sum of the isolated monomers. uration is away from the average planar disposition. All the DFT-calculations were carried out with the GAUSSIAN09 The activation and reaction (electronic and free Gibbs) barriers program.30 The electron density of the systems was analyzed within obtained for the transformation of the open-chain into the L. M. Azofra et al. / Carbohydrate Research 372 (2013) 1–8 3

Table 1 tion energies are negative only for the transformation process for P parameter, in °, and Q parameter, in Å, in the absolute minimum energy structures D-erythrose in PCM–water and in gas phase for the a-path. The for the furanoses configurations of the D-erythrose and D-threose used in the reaction reduction of the electronic activation energies in PCM–water with study, obtained at the B3LYP/6-311++G(d,p) computational level respect to vacuum is up to 33 kJ molÀ1. Molecule PQConf.a In the reactions with BH3, the solvation energies for the station- 2 2 a-D-Erythrofuranose 171.7 0.368 T3 ary points present a good linear correlation (R = 0.94) with the di- 4 b-D-Erythrofuranose 236.4 0.411 E pole moment of the systems in vacuum. However, all attempts to 2 a-D-Threofuranose 166.6 0.368 E find similar relationships in the rest of the reactions studied here b-D-Threofuranose 31.9 0.355 E2 show poor correlations. a x x Where Ty: twist ring configuration, x refers to exo and y to endo faces; and Eis The five stationary points (three minima and two TS) in gas envelope on the exo face and Ey on the endo face. phase for the mutarotation process of the isolated D-threose mole-

cule (open-chain and furanose forms) catalyzed by BH3 are repre- sented in Figure 4. furanose forms are shown in Table 2. It can be observed that the The complexation of the open-chain forms with BH results in electronic activation energies range between 159 and 3 small changes in the geometry of the sugars when compared to 192 kJ molÀ1. The inclusion of the solvent effect by PCM–water re- À1 the isolated ones as indicated by very similar values of compact- duces them up to 15 kJ mol . Practically, in all the cases of the D- ness, À52.6° and À172.3° for D-erythrose and D-threose respec- erythrose, the cyclic forms are more stable than the linear ones, tively. In the cyclic forms, small changes are observed in the with the exception of the a-D-erythrofuranose in gas phase which 2 2 configuration of the a-D-erythrofuranose ( T3 to E), a-D-threofura- has a small non-spontaneous value for the electronic reaction en- 2 À1 nose ( EtoE3) and no change in the b-D-threofuranose. In contrast, ergy of 2.2 kJ mol . In the case of the D-threose the open-chain 4 the b-D-erythrofuranose evolves from a E exo to an E endo confor- forms are always more stable than the furanose ones. The elec- 2 mation which corresponds to a change of six units in the Altona– tronic activation barrier for the b-D-erythrofuranose in gas phase Sundaralingam wheel. In the TS structures, the presence of a is significantly higher than the rest, between 13 and 21 kJ molÀ1. four-membered ring in the transition state is found again. The elec- This also happens in PCM–water, with differences between 4 and tronic activation energy in gas phase for the b-TS in D-erythrose is 17 kJ molÀ1. These quantities are directly associated with the long between 17 and 23 kJ molÀ1 higher than in the rest of the cases due C1–O5 distance of the b-TS in D-erythrose. In the gas phase and in to the fact that the C1–O5 distance is longer. With the use of the PCM–water, the distances attain 1.776 and 1.645 Å, respectively, PCM–water, this difference disappears: now, the C1–O5 distance which are 0.145 and 0.060 Å longer than the average distance in is in a range of 1.502 and 1.505 Å for all cases. The presence of the other TS structures. the BH on the carbonyl oxygen atoms increases the C1–O1 dis- The values obtained for the Gibbs free activation and reaction 3 tance with respect to the isolated mechanisms by an average of energies at 298 K (Table 2), are very similar to those obtained for 0.054 Å. the electronic energies, following the same patterns. The five stationary points (three minima and two TS) in gas 3.3. Catalysis with a hard-Pearson acid, Na+ phase for the mutarotation process of the isolated D-erythrose molecule (open-chain and furanose forms) are gathered in Figure 3. The effect of the interaction of Na+ with the aldotetroses on the Along the reaction path, the C1–O1 double bond as well as the elec- reaction profile is different to the rest of the acidic agents studied tron density in the O5–H5 covalent bond are weakened. Instead, in the present work. Initially, the Na+ cation is placed interacting two new interactions begin to appear: O1ÁÁÁH5 and C1ÁÁÁO5. In with the carbonyl oxygen atom but it moves to interact with the the TS structures, a four-membered ring in the reaction site is pres- maximum possible number of oxygen atom lone pairs. Due to ent which is highly unstable and angularly stressed.13 Along the the structures of the reactants, TS and products, the Na+ is usually reaction, the C1 anomeric carbon atom becomes stereogenic. positioned at the vertex of a pyramid (Fig. 5). The presence of Na+ results in a reduction of the electronic reac- 3.2. Catalysis with Lewis acid, BH 3 tion barriers between 19 and 24 kJ molÀ1 in all the reactions occur- ring in gas phase (Table 4) with exception of the b-path for In this section we will discuss the effect produced by the com- D-erythrose with the largest increment found in this work, plexation of the Lewis acid BH on the carbonyl group: this will 3 51 kJ molÀ1, and also the highest electronic activation energy com- produce a change in the electron density of the carbon atom C1 puted here, 242.7 kJ molÀ1. This unusually high value is due to the resulting in an increase of its local electrophilicity. In Table 3 are direct interaction of the Na+ with the hydroxyl group involved in gathered the activation and reaction (electronic and free Gibbs) the reaction (see Fig. 5). This fact occurs only in this reaction. barriers for the studied processes. As can be seen, the presence of The application of the PCM–water model decreases the electronic BH reduces the electronic activation energies between 28 and 3 activation barriers in all the cases between 0.2 and 8 kJ molÀ1 with 46 kJ molÀ1 with respect to the process of the isolated reactants. the exception of the b-path for D-erythrose with a large reduction These values are significantly lower, but still the TS barriers ob- of 77 kJ molÀ1. The electronic reaction energies show spontaneous tained are too high. It is important to note that the electronic reac- values in all the cases, they being between À7 and À25 kJ molÀ1,

Table 2 À1 Electronic activation (Eac) and reaction (ER) energies and Gibbs free activation (DGac) and reaction (DGR) energies at 298 K in kJ mol for the uncatalyzed process in vacuum and PCM–water at the B3LYP/6-311++G(d,p) computational level

Molecule Env. Eac a- Eac b- DGac a- DGac b- ER a- ER b- DGR a- DGR b-

D-Erythrose Vacuum 171.0 191.6 169.5 184.9 À7.3 2.2 4.9 12.9

D-Erythrose PCM 159.9 176.9 161.9 172.0 À11.1 À2.7 À1.3 5.1

D-Threose Vacuum 175.9 178.4 172.5 173.2 4.9 1.6 13.9 9.4

D-Threose PCM 167.1 173.2 165.2 168.6 1.3 2.9 11.7 9.7 4 L. M. Azofra et al. / Carbohydrate Research 372 (2013) 1–8

α-TS α C1O1: 1.327 C1O5: 1.595 -D-erythrofuranose O5H5: 1.164 O1H5: 1.376

Open-chain D-erythrose

β-TS β-D-erythrofuranose C1O1: 1.307 C1O5: 1.776 O5H5: 1.215 O1H5: 1.268

Figure 3. All ﬁve stationary points (minima and TS) located in gas phase for the mutarotation process of the isolated D-erythrose molecule (open-chain and furanose forms). The atoms involved in the reaction site are indicated in all the cases. The main distances of the reaction site (for both TS) are also shown, in Å. The asterisk in the products indicates the anomeric carbon atom whose local environment marks whether a monosaccharide is a-orb-.

Table 3 À1 Electronic activation (Eac) and reaction (ER) energies and Gibbs free activation (DGac) and reaction (DGR) energies at 298 K in kJ mol for the process catalyzed by BH3 in vacuum and PCM–water at the B3LYP/6-311++G(d,p) computational level

Molecule Env. Eac a- Eac b- DGac a- DGac b- ER a- ER b- DGR a- DGR b-

D-Erythrose Vacuum 141.0 163.9 142.6 159.9 À5.4 1.0 6.5 11.0

D-Erythrose PCM 130.5 130.9 131.7 127.3 À10.9 À1.3 3.6 10.1

D-Threose Vacuum 144.3 146.8 141.1 143.2 8.9 24.0 15.3 30.1

D-Threose PCM 132.2 135.5 129.4 132.3 8.7 17.1 14.9 25.3

+ À1 with the exception of the b-D-erythrofuranose in gas phase, in for H3O between 76 and 105 kJ mol . In both cases the TS for À1 which an electronic reaction energy of 13.3 kJ mol has been D-threose are energetically more reduced than for D-erythrose, this found. difference being more important for the processes catalyzed by H+. + The complexation with Na only changes slightly the compact- For example, the barrier of the a-TS in gas phase for D-threose is À1 ness of the open-chain form of the D-erythrose (À63.8°) while in 58.5 kJ mol while in D-erythrose, this amount is approximately À1 the case of D-threose there is an inversion of the dihedral angle the double, 105.7 kJ mol . The only exception happens with the of the carbon chain (169.2°). In the cyclic forms, the changes in a-path and the b-path for D-threose in PCM–water in which the + the ring conﬁguration are small for the a-D-erythrofuranose (from H3O catalyst exhibits an electronic activation energy of 2 2 4 À1 À1 Eto T3), b-D-erythrofuranose (from E0 to E), and a-D-threofura- 0.7 kJ mol and 5.4 kJ mol greater than the a-path and the 4 2 nose (from T3 to E), which corresponds to one, two, and three b-path for D-erythrose, respectively. The inclusion of the solvent ef- units of the Altona–Sundaralingam wheel, respectively. In contrast, fect through PCM–water model produces a small reduction of 2 À1 in the b-D-threofuranose, a change from T1 to E2 is observed which the barrier (less than 6.4 kJ mol ) for all the reactions of the corresponds to a transition of practically p radians. In the TS struc- D-erythrose. In the rest of the reactions for D-threose, an increment tures modeled in PCM–water, the C1–O5 distances are similar for of the barrier is observed, the maximum difference being À1 + all cases, being the value in the b-D-erythrofuranose slightly longer 23.1 kJ mol for the a-path of D-threose with H3O . than in the rest. In addition, the C1–O1 distance in the b-D-ery- Regarding the electronic reaction energies, they are spontane- throfuranose, that does not form a Na+ÁÁÁO1 interaction, is shorter ous in all cases (Table 5). These values range between À0.3 and (1.333 Å) than in the rest of the TS (1.345 Å in average). À67 kJ molÀ1 in reactions catalyzed by H+, and between À15 and À1 + À38 kJ mol in the processes catalyzed by H3O . The inclusion of + + 3.4. Catalysis with Brønsted acids, H and H3O the solvent effect by PCM–water model increases the electronic reaction energies in absolute value up to 33 kJ molÀ1, except in + The activation and reaction (electronic and free Gibbs) energies the formation of the b-D-threofuranose using H3O as catalyst + + À1 of the reactions catalyzed by the Brønsted acids, H and H3O , are where it is reduced in 4.3 kJ mol . reported in Tables 5 and 6, respectively. The electronic activation The presence of the Brønsted acids results in a change of the energy values obtained in this case are much smaller than those dihedral angle of the carbon chain, with values of À29.1° and previously found. Speciﬁcally, the electronic activation energies 178.3°; and À35.0° and À154.5° for D-erythrose and D-threose for + À1 + + for the catalysis with H are between 58 and 109 kJ mol and H and H3O , respectively. In the cyclic forms, Brønsted acids do L. M. Azofra et al. / Carbohydrate Research 372 (2013) 1–8 5

α-TS:BH3 α-D-threofuranose:BH3 C1O1: 1.385 C1O5: 1.537 O5H5: 1.172 O1H5: 1.334 O1B: 1.647

Open-chain D-threose:BH3

β-TS:BH3 β C1O1: 1.377 C1O5: 1.543 -D-threofuranose:BH3 O5H5: 1.167 O1H5: 1.349 O1B: 1.652

Figure 4. All ﬁve stationary points (minima and TS) located in gas phase for the mutarotation process catalyzed with BH3 for D-threose. The atoms involved in the reaction site are indicated in all the cases. The main interatomic distances in Å of the reaction site (for both TS) are shown.

β-TS:Na+ (vacuum) + + + β-D-erythrofuranose:Na Open-chain O2Na : 2.430 O3Na : 2.351 O5Na+: 2.498 C1O1: 1.286 + (vacuum) D-erythrose:Na (vacuum) C1O5: 1.855 O5H5: 1.265 O1H5: 1.244

β-TS:Na+ (PCM-water) Open-chain β + + + -D-erythrofuranose:Na D-erythrose:Na+ (PCM- O2Na : 2.359 O3Na : 2.360 C1O1: 1.333 C1O5: 1.601 (PCM-water) water) O5H5: 1.162 O1H5: 1.356

+ Figure 5. b-Path in the presence of Na in vacuum and PCM–water at the B3LYP/6-311++G(d,p) computational level for D-erythrose. The atoms involved in the reaction site are indicated in all the cases. The main interatomic distances in Å (even hydroxyl OÁÁÁNa+) of the reaction site (for both TS) are shown. not modify signiﬁcantly the ring conﬁguration, the largest change corresponds formally to a water molecule. This water molecule being two units in the Altona–Sundaralingam wheel. An interest- tends to dissociate from the rest of the system in gas phase ing feature of the furanose products in these reactions is the (Fig. 6) and thus O1ÁÁÁC1 distances of 2.465 and 1.593 Å are found + + presence of a protonated hydroxyl group attached to C1 which for the b-D-erythrofuranose with H and H3O , respectively. In 6 L. M. Azofra et al. / Carbohydrate Research 372 (2013) 1–8

Table 4 À1 + Electronic activation (Eac) and reaction (ER) energies and Gibbs free activation (DGac) and reaction (DGR) energies at 298 K in kJ mol for the process catalyzed by Na in vacuum and PCM–water at the B3LYP/6-311++G(d,p) computational level

Molecule Env. Eac a- Eac b- DGac a- DGac b- ER a- ER b- DGR a- DGR b-

D-Erythrose Vacuum 146.7 242.7 147.6 237.3 À24.5 13.3 À11.6 27.8

D-Erythrose PCM 145.9 165.3 140.9 158.7 À22.2 À13.4 À13.4 À6.6

D-Threose Vacuum 156.9 158.0 152.3 153.2 À17.1 À9.4 À9.1 À1.4

D-Threose PCM 149.0 153.6 144.7 151.0 À12.3 À7.7 À1.5 À5.1

Table 5 À1 + Electronic activation (Eac) and reaction (ER) energies and Gibbs free activation (DGac) and reaction (DGR) energies at 298 K in kJ mol for the process catalyzed by H in vacuum and PCM–water at the B3LYP/6-311++G(d,p) computational level

Molecule Env. Eac a- Eac b- DGac a- DGac b- ER a- ER b- DGR a- DGR b-

D-Erythrose Vacuum 105.7 109.3 95.7 98.4 À24.8 À17.4 À25.2 À34.9

D-Erythrose PCM 101.8 102.9 93.9 93.7 À19.3 À0.3 À17.4 À12.5

D-Threose Vacuum 58.5 82.3 58.1 82.9 À66.5 À62.3 À64.4 À62.4

D-Threose PCM 78.3 84.9 73.3 84.0 À42.2 À29.1 À33.9 À30.6

Table 6 À1 + Electronic activation (Eac) and reaction (ER) energies and Gibbs free activation (DGac) and reaction (DGR) energies at 298 K in kJ mol for the process catalyzed by H3O in vacuum and PCM–water at the B3LYP/6-311++G(d,p) computational level

Molecule Env. Eac a- Eac b- DGac a- DGac b- ER a- ER b- DGR a- DGR b-

D-Erythrose Vacuum 99.6 100.9 96.6 96.6 À31.5 À33.1 À23.9 6.6

D-Erythrose PCM 98.4 99.6 105.4 104.2 À26.7 À17.9 À10.9 5.2

D-Threose Vacuum 76.0 94.2 73.5 93.0 À23.5 À25.2 À14.1 À15.3

D-Threose PCM 99.1 105.0 102.6 105.0 À27.8 À15.2 À12.0 À1.2

β + Open-chain -TS:H β-D-erythrofuranose:H+ D-erythrose:H+ C1O1: 1.479 C1O5: 1.449 O5H5: 1.277 O1H5: 1.226 C1O1: 2.465 O1H+: 0.973

β-TS:H O+ Open-chain 3 + β-D-erythrofuranose:H3O + C1O1: 1.443 C1O5: 1.470 D-erythrose:H3O O5H5: 1.241 O1H5: 1.259 C1O1: 1.593 O1H+: 1.017

+ + Figure 6. b-path for D-erythrose in the presence of H and H3O in vacuum at the B3LYP/6-311++G(d,p) computational level. The atoms involved in the reaction site are indicated in all the cases. The main interatomic distances in Å of the reaction site (for both TS) are shown. Also, the blue circle in the products indicates the water molecule that tends to dissociate with indication of the C1–O1 distances in Å.

PCM–water these distances decrease in the b-D-erythrofuranose to water molecules. Similar features have been described in the 2.176 and 1.425 Å, respectively. These results demonstrate the sta- literature theoretically4,41 and experimentally42 for protonated + bilizing role of the implicit (PCM model) and explicit (H3O case) alcohols. In the structure of the TS the C1–O5 distances range L. M. Azofra et al. / Carbohydrate Research 372 (2013) 1–8 7

Table 7 À1 Electronic activation (Eac) and reaction (ER) energies and Gibbs free activation (DGac) and reaction (DGR) energies at 298 K in kJ mol for the process catalyzed by one bridge-H2O + molecule and H3O in vacuum and PCM–water at the B3LYP/6-311++G(d,p) computational level

Molecule Env. Eac a- Eac b- DGac a- DGac b- ER a- ER b- DGR a- DGR b-

D-Erythrose Vacuum 29.9 21.3 38.3 34.8 À15.6 9.4 –7.6 8.6

D-Erythrose PCM 19.0 13.1 22.9 16.9 À20.6 À1.1 –19.4 À0.9

D-Threose Vacuum 42.7 40.6 43.8 44.1 9.3 1.4 16.1 6.7

D-Threose PCM 23.6 25.2 33.2 31.2 4.3 À2.0 9.2 À2.0

between 1.447 and 1.475 Å which are the second shorter of all the implicit water molecules reduces the possibility of elimination of TS studied in the present work. a water molecule in the processes where a Brønsted acid is used.

3.5. Catalysis with a bridge-H2O molecule and the Brønsted acid Acknowledgments + H3O L.M.A. thanks the Ministerio de Ciencia e Innovación for a PhD The results discussed in the previous sections of this article Grant (No. BES-2010-031225). We also thank the Ministerio de prove that the explicit presence of Brønsted acids reduces the acti- Ciencia e Innovación (Project No. CTQ2012-35513-C02-02) and vation barriers, as well as the presence of a molecule in the proton the Comunidad Autónoma de Madrid (Project MADRISOLAR2, ref. transfer process, in agreement with the results of Alkorta and S2009/PPQ-1533) for ﬁnantial support. Gratitude is also due to 12 Popelier. For this reason, we have considered a combined strat- the CESGA and the CTI (C.S.I.C.) for an allocation of computer time. + egy using the cation H3O and a water molecule that can assist the proton transfer process. + Supplementary data The reactions catalyzed with H3O and one bridge-H2O molecule present the smallest electronic activation barriers (Table 7) of all Supplementary data associated with this article can be found, in the processes studied in the present article. The values of the elec- the online version, at http://dx.doi.org/10.1016/j.carres.2013. tronic activation barrier range between 21 and 43 kJ molÀ1 in gas 01.013. phase. The inclusion of the PCM–water model produces a reduction of the activation barriers in all cases, with values between 13 and References 25 kJ molÀ1. These results contrast with the small catalytic effect of a single water molecule interacting with the aldehyde group, 1. Dubrunfaut, A. P. Ann. Chim. Phys. 1846, 18, 99. as described for the mutarotation of glucopyranose.17 2. Hudson, C. S. J. Am. Chem. Soc. 1910, 32, 889. The electronic reaction energies are spontaneous for all the 3. Sorensen, P. E.; Jencks, W. P. J. Am. Chem. Soc. 1987, 109, 4675. 4. Azofra, L. M.; Alkorta, I.; Elguero, J.; Toro-Labbé, A. J. Phys. Chem. A 2012, 116, reactions in which a Brønsted acid participates, with the exception 8250. + of the b-product in D-erythrose in gas phase when H acts as 5. Grindley, T. B.; Fraser-Reid, B. O.; Tatsuta, K.; Thiem, J., Eds.; Glycoscience, catalyst. chemistry and chemical biology; Springer: Berlin, Heidelberg, 2008; p 3. 6. Flood, A. E.; Johns, M. R.; White, E. T. Carbohydr. Res. 1996, 288, 45. The presence of Brønsted acid and a water molecule has similar 7. Capon, B. Chem. Rev. 1969, 69, 407. effect on the furanose geometries of the minima as that described 8. Brönsted, J. N.; Guggenheim, E. A. J. Am. Chem. Soc. 1927, 49, 2554. previously for the presence of Brønsted acids alone, with the 9. Risley, J. M.; Van Etten, R. L. Biochemistry 1982, 21, 6360. 2 3 10. Serianni, A. S.; Pierce, J.; Huang, S. G.; Barker, R. J. Am. Chem. Soc. 1982, 104, exception of the a-D-threofuranose that changes from Eto E, 4037. which corresponds to eight units in the Altona–Sundaralingam 11. Hudson, C. S. J. Am. Chem. Soc. 1907, 29, 1571. wheel. In this case, the possibility of the dissociation of a water 12. Alkorta, I.; Popelier, P. L. A. Carbohydr. Res. 2011, 346, 2933. molecule in the furanose products is minimized due to the solva- 13. Casadei, M. A.; Galli, C.; Mandolini, L. J. Am. Chem. Soc. 1984, 106, 1051. 14. Yamabe, S.; Ishikawa, T. J. Org. Chem. 1999, 64, 4519. tion of the mentioned group with two explicit water molecules, 15. Silva, A. M.; da Silva, E. C.; da Silva, C. O. Carbohydr. Res. 2006, 341, 1029. being the O1–C1 distance between 1.413 and 1.431 Å in gas phase 16. Silva, C. Theor. Chim. Acta 2006, 116, 137. and between 1.402 and 1.411 Å in PCM–water. The structures of 17. Lewis, B. E.; Choytun, N.; Schramm, V. L.; Bennet, A. J. J. Am. Chem. Soc. 2006, 128, 5049. their TS are characterized by a six-membered ring. The C1–O5 dis- 18. Schmidt, R. K.; Karplus, M.; Brady, J. W. J. Am. Chem. Soc. 1996, 118, 541. tances in the TS structures present values between 1.440 and 19. Morpurgo, S.; Brahimi, M.; Bossa, M.; Morpurgo, G. O. PCCP 2000, 2, 2707. 1.460 Å, which are the smallest of all the TS studied here. 20. Morpurgo, S.; Bossa, M. PCCP 2003, 5, 1181. 21. Morpurgo, S.; Grandi, A.; Zazza, C.; Bossa, M. THEOCHEM 2005, 729, 71. 22. Fragoso-Serrano, M.; Pereda-Miranda, R.; Cerda-Garcia-Rojas, C. M. Tetrahedron 4. Conclusions 2006, 62, 11916. 23. Toro-Labbé, A. Theoretical Aspects of Chemical Reactivity; Elsevier: Amsterdam, 2007; Vol. 19. p. 2–141. A theoretical study at B3LYP/6-311++G(d,p) level has been car- 24. Azofra, L. M.; Alkorta, I.; Elguero, J.; Popelier, P. L. A. Carbohydr. Res. 2012, 358, ried out for the hemiacetal formation from the open-chain to the 96. furanose conﬁgurations of D-erythrose and D-threose in vacuum 25. Becke, A. D. J. Chem. Phys. 1993, 98, 5648. and in solution, through the application of the PCM–water model. 26. Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. Rev. B 1988, 37, 785. 27. Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. The acid catalysis has been studied taking into account the effect 28. Tomasi, J.; Mennucci, B.; Cammi, R. Chem. Rev. 2005, 105, 2999. of: (i) a classical Lewis acid as BH3; (ii) a classical hard-Pearson acid 29. Peng, C.; Ayala, P. Y.; Schlegel, H. B.; Frisch, M. J. J. Comp. Chem. 1996, 17, 49. + + + 30. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; as Na ; (iii) two classical Brønsted acids such as H and H3O ; and + Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; (iv) the combined strategy using H3O and one bridge-H2O mole- Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; cule as an assistant in the proton transfer. The use of Brønsted Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; acids shows the best values of catalysis that can be improved with Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; the use of the combined strategy (iv). Its interval of activation Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; energies is between 21 and 43 kJ molÀ1 in gas phase and between Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; 13 and 25 kJ molÀ1 in PCM–water model, the lowest values being Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; those of the reactions of D-erythrose. The presence of explicit and 8 L. M. Azofra et al. / Carbohydrate Research 372 (2013) 1–8

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