Carbohydrate Research 358 (2012) 96–105

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Carbohydrate Research

journal homepage: www.elsevier .com/locate /carres

Conformational study of the open-chain and furanose structures of D-erythroseand D-threose

Luis Miguel Azofra a, Ibon Alkorta a,⇑, José Elguero a, Paul L. A. Popelier b,c

a Instituto de Química Médica, CSIC, Juan de la Cierva, 3, E-28006 Madrid, Spainb Manchester Interdisciplinary Biocentre (MIB), 131 Princess Street, Manchester M1 7DN, United Kingdomc School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

a r t i c l e i n f o

Article history:Received 3 May 2012Received in revised form 18 June 2012Accepted 19 June 2012Available online 27 June 2012

Keywords:D-ErythroseD-ThreoseDFTNBOAIM

0008-6215/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.carres.2012.06.011

⇑ Corresponding author. Fax: +34 91 564 48 53.E-mail address: ibon@iqm.csic.es (I. Alkorta).URL: http://www.iqm.csic.es/are.

a b s t r a c t

The potential energy surfaces for the different configurations of the D-erythrose and D-threose (open-chain, a- and b-furanoses) have been studied in order to find the most stable structures in the gas phase.For that purpose, a large number of initial structures were explored at B3LYP/6-31G(d) level. All the min-ima obtained at this level were compared and duplicates removed. A further reoptimization of theremaining structures was carried out at B3LYP/6-311++G(d,p) level. We characterized 174 and 170 min-ima for the open-chain structures of D-erythrose and D-threose, respectively, with relative energies thatrange over an interval of just over 50 kJ/mol. In the case of the furanose configurations, the number ofminima is smaller by approximately one to two dozen. G3B3 calculations on the most stable minima indi-cate that the a-furanose configuration is the most stable for both D-erythrose and D-threose. The intramo-lecular interactions of the minima have been analyzed with the Atoms in Molecules (AIM) and NaturalBond Orbital (NBO) methodologies. Hydrogen bonds were classified as 1-2, 1-3 or 1-4, based on the num-ber of C–C bonds (1, 2 and 3, respectively) that separate the two moieties participating in the hydrogenbond. In general, the AIM and NBO methodologies agree in the designation of the moieties involved inhydrogen bond interactions, except in a few cases associated to 1-2 contact which have small OH� � �Oangles.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Carbohydrates are the most abundant organic compounds onEarth, in terms of their total mass found in living organisms. Theyshow a large number of functions, ranging from energy storage, overstructural material, to bacterial and viral recognition targets. Thestructural properties of monosaccharides are mainly determinedby the presence of a carbonyl group or a hemiacetal moiety and avariable number of hydroxyl groups. Numerous DFT and ab initiostudies have shown the considerable conformational flexibility ofcarbohydrates. Thus, it does not come as a surprise that the com-plexity of the conformational space of numerous carbohydrateshas been described in the literature: glucose,1–9 allopyranose,10

galactopyranose,11 mannopyranose,12 idopyranose,13 fructofura-nose14 as well as the open-chain configurations of erythrose andthreose.15 In some cases, the effect of the inclusion of explicitsolvent molecules on a monosaccharide’s conformation has beenexamined.6,16–19 In spite of the considerable interest in carbohy-drates, very few studies have focused on the conformational

ll rights reserved.

preference of the smaller carbohydrates such as tetroses and pen-toses. D-Erythrose and D-threose are the two naturally occurringmembers of the aldotetroses family (aldoses with a total of four car-bon atoms in their skeleton). The only difference between these twomolecules is the configuration of the hydroxyl group attached to C2(Fig. 1). Experiment20,21 has shown that, in aqueous solution, open-chain conformations of D-erythrose and D-threose are in equilibriumwith a mixture of the corresponding a- and b-furanoses, which ariseby internal hemiacetal cyclization.

To the best of our knowledge, only the open-chain conformationsof the D-erythrose and D-threose have been studied in the literatureusing DFT and ab initio methods.15 In the present article, the confor-mations of the two anomeric forms of the furanoses, a- and b-, aswell as the open-chain structures have been examined.

2. Computational methods

The conformational searches were conducted in two steps. Inthe first step, a large number of structures were generated for eachof the three possible configurations (open-chain, a-furanose, andb-furanose). The initial structures of the open-chain configurationwere generated starting from the combination of three possiblevalues of each rotatable bond: gauche, gauche,0 and trans (g, g0

Open-chain structures

0

10

20

30

40

50

60

0 50 100 150Ranking

Erel

(kJ/

mol

)

D-erythroseD-threose

Figure 2. Ranking of all open-chain conformations of D-erythrose and D-threoseaccording to the energies (B3LYP/6-311++G(d,p) level) relative to their respectiveglobal minima.

HOO

OH

OH

0

123

4

12

34

Open-chain

HOO

OH

OH1

234

D-erythrose

D-threose

α-furanose

OHHO OH

O0

1234

β-furanose

OH

HO OH

O

0

1

23

4

OHHO

OHO0

1

23

4OH

HO

OHO

Figure 1. Open-chain and a- and b-furanose configurations of D-erythrose and D-threose. This numeric labeling will be used throughout the article.

L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105 97

and t). In the open-chain configuration of D-erythrose and D-thre-ose, there are six rotatable bonds, and consequently the numberof initial structures is 729 (=36) for each molecule. In the case ofthe a- and b-furanose configurations, 20 different conformationsof the ring were taken into account (10 envelope and 10 twistconformations) for each case. In addition, three different possiblepositions of each hydroxyl group were examined (g, g0 and t). Thus,the total number of conformations initially considered for eachfuranose configurations is 540 (=20�33). All these structures wereoptimized at B3LYP/6-31G(d) level.22,23 The optimized structureswere compared among them in order to remove duplicates. Forthat purpose, an in-house program was written that systematicallycompared all the structures obtained and removed those that showroot mean square values smaller than 0.05 Å when all atomic coor-dinates are compared. This cutoff value separates the structuresinto two groups: those having similar geometries that only differdue to the numerical optimization procedure (<0.05 Å) and allthe others (>0.05 Å) that are considered different. The uniquestructures at B3LYP/6-31G(d) level were reoptimized at B3LYP/6-311++G(d,p)24 level and compared again; this led to the elimina-tion of some more structures. Vibrational frequencies were alsocalculated at B3LYP/6-311++G(d,p) level to confirm that the finalstructures indeed correspond to minima.

In some cases, G3B3 calculations25,26 were performed to obtainmore accurate energy values in vacuum for the most stable con-formers. The G3B3 method, which is a modification of the originalG3 method, uses optimized geometries at B3LYP/6-31G(d) level,and then carries out QCISD(T), MP4 and MP2 calculations with largebasis sets in order to improve the energy. Thus, it is computation-ally less expensive than the original G3 method with a similar qual-ity. All calculations were performed using the GAUSSIAN09 package.27

In order to characterize the conformation of the furanose rings,the pseudorotation parameter P and the amplitude Q were calcu-lated using the Cremer–Pople method.28 The ring puckering analy-sis methodology developed by Cremer and Pople is based on thesearch of structural parameters from the midplane of the ring.The two most important ones are the P parameter, which classifiesthe conformation of the ring (in the case of furanoses envelope ortwist), and the Q parameter, which describes the total puckeringamplitude, that is, how much the structure is distorted with re-spect to the planar case. The P and Q parameters were calculatedwith the RING96 program28,29 and automatically assigned to the cor-responding conformation of the Altona-Sundaralingam conforma-tion ring30,31 with a program written in our group.

The electron density of the systems has been analyzed by theAtoms In Molecules (AIM) methodology32,33 using the MORPHY98and AIMAll programs.34,35 The topological analysis of the electron

density function locates critical points, points where the gradientof the electron density is null. These critical points are classifiedbased on the sign of the local curvature of the electron density.Thus, it is possible to find maxima [denoted (3, �3)] or minima[(3, +3)], as well as two types of saddle points, (3, +1) and (3,�1). The (3, �3) critical points practically coincide with nuclearpositions, the (3, �1) points are known as bond critical points,the (3, +1) corresponds to ring critical points and the (3, +3) minimaare called cage critical points. In general, the bond critical pointscan provide elementary information on the covalent and weakinteractions present in molecules and molecular complexes. Herethey are used to characterize the intramolecular interactions ofthe molecules considered.

The Natural Bond Orbitals (NBO) theory36 analyzes the orbitalinteractions. Most of the donor–acceptor interactions, for examplehydrogen bonds, donate from a filled orbital of the electron donorto an empty orbital of the electron acceptor. These calculationswere carried out with the NBO-3.1 program.37

98 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105

3. Results and discussion

3.1. Energy and conformation of the minima

A total of 174 and 170 minima were found for the open-chainconfiguration of D-erythrose and D-threose, respectively. These

ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ ϕ

Figure 3. Molecular graphs of the most stable conformers of the open-chain configuratrelative energy with respect to the most stable conformer corresponds to B3LYP/6-311dihedral bond angles are given. The position of the bond and ring critical points calculat

numbers are much higher than those reported by Aviles-Morenoand Huet15 where only 14 and 15 conformers where described.The number of minima obtained in the furanose configurations ismuch smaller due to the restrictions imposed by the ring. Thus,the total number of minima is 14, 16, 22 and 19 for a-D-erythro-furanose, b-D-erythrofuranose, a-D-threofuranose and b-D-threo-

ϕ

ϕ

ϕ

ϕ

ion of the D-erythrose and D-threose calculated at B3LYP/6-311++G(d,p) level. The++G(d,p) and G3B3 (in parenthesis) computational levels. The values for the CCCCed within the AIM methodology is indicated with green and red dots, respectively.

ϕ

ϕϕ

ϕ

ϕ ϕ

Fig. 3 (continued)

L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105 99

furanose, respectively. The energies of the minima for theopen-chain configurations stretch over a range of 50 kJ/mol.Fig. 2 ranks all open-chain conformations of D-erythrose and D-threose according to the energies relative to their respective globalminima. In the case of D-erythrose, Fig. 3 shows 13 structures withan Erel smaller than 10 kJ/mol and only 5 structures below this en-ergy threshold in the case of D-threose.

The most stable minima in the open-chain configuration showan intramolecular hydrogen bond between the hydroxyl groupattached to C-2 and the carbonyl moiety (C1@O). Although intra-molecular hydrogen bonding is not a unique feature of the moststable structures, it occurs in the set with high frequency. Thefrequency of this hydrogen bond occurring decreases in the decilesof energy ranked open-chain D-erythroses: 1-10: 9 times, 11-20: 6times, 21-30: 3 times, 31-40: 3 times, 41-50: 2 times, 51-60: 4times, 61-100: 2 times, 101-174: 1 time. In addition, the moststable conformer of D-erythrose shows a C1H� � �O4 contact whilein D-threose the O4H interacts with O2, generating a hydrogenbond (HB) chain with the O2H� � �O1 HB. In some cases, stabilizinginteractions between oxygen atoms and the carbonyl carbon atomsimilar to the ones recently described in the conformational study

of the salicylic acid can be found.38 The conformations in whichthese interactions appear can be considered as the precursor tofuranose formation.

The G3MB3 calculations return similar relative energies com-pared to those obtained at B3LYP/6-311++G(d,p) level shown inFigure 3. The two levels predict the same conformation as the moststable for both D-erythrose and D-threose. The most stable minimafound for the open-chain configuration of D-erythrose are exactlythe same as those described by Aviles-Moreno and Huet.15 How-ever, in the case of D-threose, the most stable minimum found bythese authors corresponds to the third minima in our search, witha relative energy of 5.8 and 6.3 kJ/mol at B3LYP/6-311++G(d,p) andG3B3 levels, respectively.

The comparison of the B3LYP/6-311++G(d,p) and G3B3 energiesshows that in the cases of a-D-erythrofuranose and b-D-threofura-nose, both levels predict the same conformation as the most stable.In the case of b-D-erythrofuranose and a-D-threofuranose, the moststable conformation changes from one level to the other sinceseveral minimum structures are found with very small relativeenergies (three minima less than 1 kJ/mol in a-D-threofuranoseand four less than 2 kJ/mol in b-D-erythrofuranose). For either case,

0

5

10

15

20

25

30

35

1 6 11 16 21Ranking

Erel

(kJ/

mol

)

alpha-erythrose beta-erythrose

alpha-threose beta-threose

Figure 4. Ranking of the conformers of a- and b-D-erythrose, and a- and b-D-threose according to the energies (B3LYP/6-311++G(d,p) level) relative to theirrespective global minima.

100 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105

the difference in relative energy is never larger than 2 kJ/mol forthe most stable conformers. The minima obtained for the furanoseconfigurations range between 25 and 35 kJ/mol with respect to themost stable conformation in each configuration (Fig. 4, the struc-tures have been numbered in increasing order of relative energies).The number of structures with relative energy smaller than 10 kJ/mol is, respectively, 5, 9, 7, and 4 for a-D-erythrofuranose, a-D-threofuranose, b-D-erythrofuranose, and b-D-threofuranose (Fig. 5).

The presence of stabilizing intramolecular HBs is a constant forall the low energy minima. The interacting moieties depend on therelative orientation of the hydroxyl groups. Thus, in the a-D-erythrofuranose, which presents the three hydroxyl groups onthe same side of the furanose ring, two HBs are found in severalconformations. In the rest of the configurations that show twohydroxyl groups on one side of the furanose ring, only one HB isobserved. In addition, some Oxygen–Oxygen interactions are foundwith bond paths that do not connect the expected hydrogen atomwith the oxygen atom.

At B3LYP level, the most stable structures correspond to anenvelope conformation of the ring, except in a-D-erythrofuranose,where a 2-exo 3-endo twist conformation (2T3) is the most stable.The most frequent configurations found in the most stable minimaare 2E and E2. Thus, 2E is present in two of the lowest energy con-formations of a-D-erythrofuranose and in another two of a-D-threofuranose, while E2 configuration is present in the b-form(twice in b-D-erythrofuranose and thrice in b-threofuranose). Agraphical representation of the puckering parameters (P and Q)of the most stable conformers (see Supplementary data, Table S1and Fig. S1) shows that most of the conformers are in ‘southern’forms.

Table 1 compares the energies of the most stable minima ineach configuration for erythrose and threose. In the case of ery-throse, the most stable configuration corresponds to the a-fura-nose at the two computational levels. In the case of threose,B3LYP/6-311++G(d,p) predicts that the open-chain is the moststable while the G3B3 method favors a-furanose. Discrepancies be-tween these two computational levels have previously been re-ported when comparing open and cyclic structures.39,40 Theanalysis of our results shows that the single point QCISD(T) calcu-

lations carried out within the G3B3 composite method agree withthe relative energies obtained at the G3B3 level.

The populations derived from the energy calculations for all theconformers agree with those reported in solution for threose indi-cating a population of 51% and 38% for the a- and b-furanose con-figurations, respectively,21 while the remaining 11% is present asthe aldehyde hydrate, which has not been considered in this work.

3.2. Analysis of the intramolecular interactions: AIM and NBO

In order to analyze the intramolecular hydrogen bond interac-tions, two methodologies were used: the topological analysis ofthe electron density within the AIM method and the Natural BondOrbital (NBO). In the AIM approach, the presence/absence of aninteratomic BCP determines the existence/non-existence of a HBinteraction. In contrast, in the NBO method, a numerical value isobtained for the interaction of the lone pair of the oxygen atomwith the r⁄ H–O orbital. The AIM and NBO analyses will be dis-cussed separately first and then compared.

3.3. Aim

The hydrogen bonds (HB) are characterized in the AIM method-ology by the presence of a BCP associated with a bond path be-tween an HB acceptor, here an oxygen atom, and the hydrogenatom of the HB donor moiety, here a hydroxyl group. In theopen-chain configuration, the presence of CH� � �O HB interactionswhere the CH group corresponds to the terminal acetal group(C-1) was observed in nine conformations. In general, and depend-ing on the conformation, all oxygen atoms can be involved in HBinteractions, the only exception being the oxygen atom of the fura-nose ring, which is never involved in any BCP for all the exampleswe have studied. However, the possibility that the ring oxygenatom can be involved in HB interaction has been described forthe sucrose disaccharide.41

Based on the AIM criteria, the HBs have distances that range be-tween 1.87 and 2.44 Å in the open configurations, and between1.92 and 2.33 Å in the furanose configurations. The values of theelectron density at the BCP range between 0.030 and 0.010 auand the corresponding Laplacian between 0.107 and 0.033 au,which are within the ranges proposed almost two decades ago42

to characterize HBs based on electron density descriptors.Figs. 3 and 5 show the molecular graphs, which include the crit-

ical points and bond paths of the most stable conformations ofopen chain and each furanose configuration. The hydrogen bondshave been classified as 1-2, 1-3, and 1-4 based on the number ofC–C bonds (1, 2, and 3, respectively) that separate the two interact-ing moieties. The total number of HB contacts of each type charac-terized for all the conformers are gathered in Table 2.

The representation of the interatomic distance H� � �O versus theOH� � �O angle (Fig. 6) shows clearly the three types of HBs. Thus, fora given interatomic distance, the smaller angles are associatedwith a 1-2 HB, the intermediate angles with a 1-3 HB, and thelargest angles with a 1-4 HB. This classification is a clear indicationof the geometrical restrictions on the interaction due to the size ofthe pseudo-ring formed.

The representation of q and r2q versus the intermoleculardistance (Fig. 7) shows again a clear differentiation between thethree different types of HBs. Thus, the largest values of q and r2qare associated with 1-2 interactions, being smaller for the 1-4 HBs.These results follow the tendencies described previously for thosecases where the interaction forms a cyclic structure; thus, for a givendistance, the values of the electron density descriptor become smal-ler as the size of the ring increases.43 These exponential relationshipsbetween q and r2q versus the interatomic distance are in agree-ment with previous reports on intermolecular interactions.44,45

α

1

23

4

α

β

Figure 5. Molecular graph of the most stable conformers of a-D-erythrofuranose, a-D-threofuranose, b-D-erythrofuranose and b-D-threofuranose calculated at B3LYP/6-311++G(d,p) level. The relative energy with respect to the most stable conformer corresponds to B3LYP/6-311++G(d,p) and G3B3 (in parenthesis) levels. The conformationassigned is indicated. The position of the bond and ring critical points calculated within the AIM methodology is indicated with green dots and red dots, respectively.

L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105 101

3.4. NBO analysis

As an example of the orbitals involved in a HB interactionbased on the NBO methodology, those responsible of one of

the HBs in the most stable conformer of the open-chain of D-ery-throse and b-D-erythrofuranose have been represented in Figure8. We bring in the standard cutoff value of 2.1 kJ/mol for theorbital interactions, and only considered interactions with an

β

Fig. 5 (continued)

102 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105

energy exceeding this threshold. A total of 597 interactions thatcan be associated to HB interactions were found. The largest en-ergy value of the orbital interaction is 42.8 kJ/mol.

All the HBs predicted by the AIM method are confirmed bythe NBO analysis except for a few cases where the energy is belowthe 2.1 kJ/mol cutoff, the smallest value being 1.34 kJ/mol. Of those

0.008

0.013

0.018

0.023

0.028

0.033

0.038

1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5

H···O Distance

ρBC

P

1-2 HB

1-3 HB

1-4 HB

(a)

0.02

0.04

0.06

0.08

0.10

0.12

0.14

1.8 2.0 2.2 2.4

H···O Distance

LAP

BC

P

1-2 HB

1-3 HB

1-4 HB

(b)

Figure 7. (a) Electron density and (b) Laplacian at the BCP (au) versus theinteratomic distance (Å). The exponential relationships have square correlationcoefficients, R2, of 0.92, 0.98 and 0.99 for the electron density of the 1-2, 1-3 and 1-4HBs and of 0.81, 0.98, and 0.99 for the Laplacian, respectively.

110115120125130135140145150155160

1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5H···O Distance

OH·

··O A

ngle

1-2 HB1-3 HB1-4 HB

Figure 6. Distribution of the H� � �O distance (Å) versus the OH� � �O (�) angles for the1-2, 1-3 and 1-4 HB interactions.

Table 2Total number of HB interactions based on the AIM methodology found in all thecharacterized conformers

1-2 HB 1-3 HB 1-4 HB

D-Erythrose (open-chain) 36 62 17

D-Threose (open-chain) 52 62 19

a-D-Erythrofuranose 18 4 —b-D-Erythrofuranose 10 — —a-D-Threofuranose — 10 —b-D-Threofuranose 8 — —

Table 1Relative energy of the most stable minima of each configuration (kJ/mol) andpredicted population for each configuration at the G3B3 computational levela

Open-chain a-Furanose b-Furanose

Erythrose B3LYP 7.3 0.0 9.4G3B3 16.7 (0%) 0.0 (91%) 7.7 (9%)

Threose B3LYP 0.0 4.8 1.6G3B3 8.6 (1%) 0.0 (69%) 1.3 (29%)

a All minima calculated for each configuration have been considered.

L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105 103

interactions predicted by NBO but without the BCP that AIM wouldrequire, the largest orbital interaction energy obtained was 8.4 kJ/mol. Most interactions present in the NBO analysis but absent in

Open Chain D-erythrose

Oxygen lone pair σ* H-O orbital

Figure 8. Orbitals associated to the HB interaction in the most stable co

the AIM analysis are associated with 1-2 interactions with OH� � �Oangles close to 110� or less.

The second order perturbation energy analysis within the NBOmethodology identifies those orbital interactions that stabilizethe energy of the system. The value of the orbital interactionenergy, E(2), provides an estimate of the donor–acceptor interac-tion. Here this interaction corresponds to the interaction of a lonepair of an oxygen atom and the r⁄ of the interacting OH bond.The representation of the E(2) versus the corresponding H� � �Ointeratomic distance (Fig. 9) for the three types of HBs, showsthat their values are mixed, especially for the 1-3 and 1-4 HBs.

β-D-erythrofuranose

Oxygen lone pair σ* H-O orbital

nformation of the open-chain D-erythrose and b-D-erythrofuranose.

0

5

10

15

20

25

30

35

40

45

0.008 0.013 0.018 0.023 0.028 0.033ρBCP

E(2

)

1-2HB

1-3HB

1-4HB

Figure 10. Electron density at the BCP, qBCP (au) versus second order perturbationNBO energy, E(2), (kJ/mol).

0

5

10

15

20

25

30

35

40

45

1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50

O···H Distance

E(2

)

1-2HB

1-3HB

1-4HB

Figure 9. Second order perturbation NBO energy, E(2), (kJ/mol) versus the O� � �Hinteratomic distance (Å).

104 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105

For a given intermolecular distance, the 1-2 HBs exhibit, in gen-eral, small values of E(2) when compared to those obtained in 1-3 and 1-4 HBs.

The analysis of E(2) versus the electron density (Fig. 10) indi-cates that the 1-2 HBs show larger electron density values at theBCP, for a given value of the E(2), than found in 1-3 and 1-4 HBs.These results are associated with the larger values of the electrondensity present in the smaller pseudo-rings.

4. Conclusions

A computational study of the conformational profile of ery-throse and threose in the gas phase has been carried out. Threepossible configurations for both carbohydrates were studied:open-chain, a-furanose, and b-furanose. A large number of confor-mational minima were obtained, especially for the open-chain con-figurations. The furanose conformations have been characterizedusing the Cremer–Pople puckering parameters, P and Q. TheG3B3 calculations predict that the a-furanose configuration is themost stable for both erythrose and threose.

An analysis of the electron density of the conformers character-ized the intramolecular H� � �O hydrogen bonds. They were classi-fied according to the relative position of the interacting moietiesas 1-2, 1-3, and 1-4. The properties of the HBs within each groupare characteristic for a given group and differ from those obtainedfor the other groups.

The NBO analysis shows the presence of more potential HBinteractions than those found by the AIM method. However, allinteractions detected with the NBO method but not with AIM showsmall orbital interaction energy values and, in general, are associ-ated with 1-2 contacts that have small OH� � �O angles.

Acknowledgments

L.M.A. thanks the Ministerio de Ciencia e Innovación for a Ph.D.grant (No. BES-2010-031225). I.A. thanks the Ministerio de Educa-ción (PR2009-0171) and the Royal Society of Chemistry for a travelgrant that allowed him to stay at the University of Manchester. Wealso thank the Ministerio de Ciencia e Innovación (Project No.CTQ2009-13129-C02-02) and the Comunidad Autónoma de Ma-drid (Project MADRISOLAR2, ref. S2009/PPQ-1533) for continuingsupport. Gratitude is also due to the CTI (CSIC) for an allocationof computer time and to Dr. Eric Elguero (IRD, Montpellier, France)for the statistical analysis.

Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.carres.2012.06.011.

References

1. Schnupf, U.; Willett, J. L.; Momany, F. Carbohydr. Res. 2010, 345, 503–511.2. Araujo-Andrade, C.; Ruiz, F.; Martínez-Mendoza, J. R.; Terrones, H. Theochem

2005, 714, 143–146.3. Suzuki, T.; Kawashima, H.; Sota, T. J. Phys. Chem. B 2006, 110, 2405–2418.4. Mason, P. E.; Neilson, G. W.; Enderby, J. E.; Saboungi, M.-L.; Cuello, G.; Brady, J.

W. J. Chem. Phys. 2006, 125, 224505–224509.5. Barnett, C. B.; Naidoo, K. J. J. Phys. Chem. B 2008, 112, 15450–15459.6. Momany, F. A.; Appell, M.; Strati, G.; Willett, J. L. Carbohydr. Res. 2004, 339,

553–567.7. Appell, M.; Strati, G.; Willett, J. L.; Momany, F. A. Carbohydr. Res. 2004, 339, 537–551.8. Barrows, S. E.; Dulles, F. J.; Cramer, C. J.; French, A. D.; Truhlar, D. G. Carbohydr.

Res. 1995, 276, 219–251.9. Polavarapu, P. L.; Ewig, C. S. J. Comput. Chem. 1992, 13, 1255–1261.

10. Schnupf, U.; Willett, J. L.; Bosma, W. B.; Momany, F. A. Carbohydr. Res. 2007,342, 196–216.

11. Momany, F. A.; Appell, M.; Willett, J. L.; Schnupf, U.; Bosma, W. B. Carbohydr.Res. 2006, 341, 525–537.

12. Appell, M.; Willett, J. L.; Momany, F. A. Carbohydr. Res. 2005, 340, 459–468.13. Kurihara, Y.; Ueda, K. Carbohydr. Res. 2006, 341, 2565–2574.14. Chung-Phillips, A.; Chen, Y. Y. J. Phys. Chem. A 1999, 103, 953–964.15. Aviles-Moreno, J.-R.; Huet, T. R. Theochem 2008, 858, 113–119.16. Momany, F. A.; Appell, M.; Willett, J. L.; Bosma, W. B. Carbohydr. Res. 2005, 340,

1638–1655.17. Simons, J. P.; Jockusch, R. A.; ÇarÇabal, P.; Hünig, I.; Kroemer, R. T.; Macleod, N.

A.; Snoek, L. C. Int. Rev. Phys. Chem. 2005, 24, 489–531.18. Molteni, C.; Parrinello, M. J. Am. Chem. Soc. 1998, 120, 2168–2171.19. Cramer, C. J.; Truhlar, D. G. J. Am. Chem. Soc. 1993, 115, 5745–5753.20. Risley, J. M.; Van Etten, R. L. Biochemistry 1982, 21, 6360–6365.21. Serianni, A. S.; Pierce, J.; Huang, S. G.; Barker, R. J. Am. Chem. Soc. 1982, 104,

4037–4044.22. Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. Rev. B 1988, 37, 785–789.23. Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652.24. Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265–3269.25. Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. J. Chem.

Phys. 1998, 109, 7764–7776.26. Baboul, A. G.; Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. J. Chem. Phys. 1999,

110, 7650–7657.27. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;

Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.;Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.;Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.;Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.;Montgomery, J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.;Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.;Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; 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.; Pomelli, C.;Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.;Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman,J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. GAUSSIAN 09; Gaussian, Inc., 2009.

28. Cremer, D.; Pople, J. A. J. Am. Chem. Soc. 1975, 97, 1354–1358.29. Cremer, D. J. Phys. Chem. 1990, 94, 5502–5509.

L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105 105

30. Altona, C.; Sundaralingam, M. J. Am. Chem. Soc. 1972, 94, 8205–8212.31. Altona, C.; Sundaralingam, M. J. Am. Chem. Soc. 1973, 95, 2333–2344.32. Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon Press: Oxford,

1990.33. Popelier, P. L. A. Atoms in Molecules. An introduction; Prentice Hall: Harlow,

England, 2000.34. Popelier, P. L. A. Chem. Phys. Lett. 1994, 228, 160–164.35. Keith, T. A. AIMAll (Version 11.10.16), TK Gristmill Software

(aim.tkgristmill.com), 2011.36. Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899–926.37. Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. NBO Version 3.1.38. Choudhary, A.; Kamer, K. J.; Raines, R. T. J. Org. Chem. 2011, 76, 7933–7937.

39. Alkorta, I.; Blanco, F.; Elguero, J.; Claramunt, R. M. Tetrahedron 2010, 66, 2863–2868.

40. Alkorta, I.; Popelier, P. L. A. Carbohydr. Res. 2011, 346, 2933–2939.41. Jaradat, D. M. M.; Mebs, S.; Checinska, L.; Luger, P. Carbohydr. Res. 2007, 342,

1480–1489.42. Koch, U.; Popelier, P. L. A. J. Phys. Chem. 1995, 99, 9747–9754.43. Solimannejad, M.; Massahi, S.; Alkorta, I. Int. J. Quantum Chem. 2011, 111,

3057–3069.44. Alkorta, I.; Zborowski, K.; Elguero, J.; Solimannejad, M. J. Phys. Chem. A 2006,

110, 10279–10286.45. Mata, I.; Alkorta, I.; Molins, E.; Espinosa, E. Chem. Eur. J. 2010, 16, 2442–2452.