Conformational Study of the Open-Chain and Furanose Structures of D-Erythrose and D-Threose ⇑ Luis Miguel Azofra A, Ibon Alkorta A, , José Elguero A, Paul L

Carbohydrate Research 358 (2012) 96–105

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Carbohydrate Research

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Conformational study of the open-chain and furanose structures of D-erythrose and 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, Spain b Manchester Interdisciplinary Biocentre (MIB), 131 Princess Street, Manchester M1 7DN, United Kingdom c School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom article info abstract

Article history: The potential energy surfaces for the different configurations of the D-erythrose and D-threose (open- Received 3 May 2012 chain, a- and b-furanoses) have been studied in order to find the most stable structures in the gas phase. Received in revised form 18 June 2012 For that purpose, a large number of initial structures were explored at B3LYP/6-31G(d) level. All the min- Accepted 19 June 2012 ima obtained at this level were compared and duplicates removed. A further reoptimization of the Available online 27 June 2012 remaining structures was carried out at B3LYP/6-311++G(d,p) level. We characterized 174 and 170 minima for the open-chain structures of D-erythrose and D-threose, respectively, with relative energies that Keywords: range over an interval of just over 50 kJ/mol. In the case of the furanose configurations, the number of D-Erythrose minima is smaller by approximately one to two dozen. G3B3 calculations on the most stable minima indi- D-Threose DFT cate that the a-furanose configuration is the most stable for both D-erythrose and D-threose. The intramo- NBO lecular interactions of the minima have been analyzed with the Atoms in Molecules (AIM) and Natural AIM Bond Orbital (NBO) methodologies. Hydrogen bonds were classified as 1-2, 1-3 or 1-4, based on the number of C–C bonds (1, 2 and 3, respectively) that separate the two moieties participating in the hydrogen bond. In general, the AIM and NBO methodologies agree in the designation of the moieties involved in hydrogen bond interactions, except in a few cases associated to 1-2 contact which have small OHO angles. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction preference of the smaller carbohydrates such as tetroses and pen- toses. D-Erythrose and D-threose are the two naturally occurring Carbohydrates are the most abundant organic compounds on members of the aldotetroses family (aldoses with a total of four car- Earth, in terms of their total mass found in living organisms. They bon atoms in their skeleton). The only difference between these two show a large number of functions, ranging from energy storage, over molecules is the configuration of the hydroxyl group attached to C2 structural material, to bacterial and viral recognition targets. The (Fig. 1). Experiment20,21 has shown that, in aqueous solution, open- structural properties of monosaccharides are mainly determined chain conformations of D-erythrose and D-threose are in equilibrium by the presence of a carbonyl group or a hemiacetal moiety and a with a mixture of the corresponding a- and b-furanoses, which arise variable number of hydroxyl groups. Numerous DFT and ab initio by internal hemiacetal cyclization. studies have shown the considerable conformational flexibility of To the best of our knowledge, only the open-chain conformations carbohydrates. Thus, it does not come as a surprise that the com- of the D-erythrose and D-threose have been studied in the literature plexity of the conformational space of numerous carbohydrates using DFT and ab initio methods.15 In the present article, the confor- has been described in the literature: glucose,1–9 allopyranose,10 mations of the two anomeric forms of the furanoses, a- and b-, as galactopyranose,11 mannopyranose,12 idopyranose,13 fructofura- well as the open-chain structures have been examined. nose14 as well as the open-chain configurations of erythrose and threose.15 In some cases, the effect of the inclusion of explicit 2. Computational methods solvent molecules on a monosaccharide’s conformation has been examined.6,16–19 In spite of the considerable interest in carbohy- The conformational searches were conducted in two steps. In drates, very few studies have focused on the conformational the first step, a large number of structures were generated for each of the three possible configurations (open-chain, a-furanose, and b-furanose). The initial structures of the open-chain configuration ⇑ Corresponding author. Fax: +34 91 564 48 53. E-mail address: [email protected] (I. Alkorta). were generated starting from the combination of three possible URL: http://www.iqm.csic.es/are. values of each rotatable bond: gauche, gauche,0 and trans (g, g0

Open-chain α-furanose β-furanose

0 0 OH OH O O 4 4 1 4 3 O 2 1 D-erythrose 2 3 3 2 HO 1 OH OH HO OH HO OH

OH 0 0 4 OH 3 O OH O OH O 4 1 4 D-threose 2 1 HO 1 3 3 OH 2 OH 2 HO HO

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.

and t). In the open-chain configuration of D-erythrose and D-thre- density function locates critical points, points where the gradient ose, there are six rotatable bonds, and consequently the number of the electron density is null. These critical points are classified of initial structures is 729 (=36) for each molecule. In the case of based on the sign of the local curvature of the electron density. the a- and b-furanose configurations, 20 different conformations Thus, it is possible to find maxima [denoted (3, 3)] or minima of the ring were taken into account (10 envelope and 10 twist [(3, +3)], as well as two types of saddle points, (3, +1) and (3, conformations) for each case. In addition, three different possible 1). The (3, 3) critical points practically coincide with nuclear positions of each hydroxyl group were examined (g, g0 and t). Thus, positions, the (3, 1) points are known as bond critical points, the total number of conformations initially considered for each the (3, +1) corresponds to ring critical points and the (3, +3) minima furanose configurations is 540 (=2033). All these structures were are called cage critical points. In general, the bond critical points optimized at B3LYP/6-31G(d) level.22,23 The optimized structures can provide elementary information on the covalent and weak were compared among them in order to remove duplicates. For interactions present in molecules and molecular complexes. Here that purpose, an in-house program was written that systematically they are used to characterize the intramolecular interactions of compared all the structures obtained and removed those that show the molecules considered. root mean square values smaller than 0.05 Å when all atomic coor- The Natural Bond Orbitals (NBO) theory36 analyzes the orbital dinates are compared. This cutoff value separates the structures interactions. Most of the donor–acceptor interactions, for example into two groups: those having similar geometries that only differ hydrogen bonds, donate from a filled orbital of the electron donor due to the numerical optimization procedure (<0.05 Å) and all to an empty orbital of the electron acceptor. These calculations 37 the others (>0.05 Å) that are considered different. The unique were carried out with the NBO-3.1 program. structures 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 also D-erythrose Open-chain structures calculated at B3LYP/6-311++G(d,p) level to confirm that the final D-threose structures indeed correspond to minima. 60 In some cases, G3B3 calculations25,26 were performed to obtain more accurate energy values in vacuum for the most stable conformers. The G3B3 method, which is a modification of the original 50 G3 method, uses optimized geometries at B3LYP/6-31G(d) level, and then carries out QCISD(T), MP4 and MP2 calculations with large basis sets in order to improve the energy. Thus, it is computation- 40 ally less expensive than the original G3 method with a similar qual- 27 ity. All calculations were performed using the GAUSSIAN09 package. In order to characterize the conformation of the furanose rings, 30 the pseudorotation parameter P and the amplitude Q were calcu- (kJ/mol) 28 lated using the Cremer–Pople method. The ring puckering analy- rel sis methodology developed by Cremer and Pople is based on the E 20 search of structural parameters from the midplane of the ring. The two most important ones are the P parameter, which classifies the conformation of the ring (in the case of furanoses envelope or 10 twist), and the Q parameter, which describes the total puckering amplitude, that is, how much the structure is distorted with respect to the planar case. The P and Q parameters were calculated 28,29 0 with the RING96 program and automatically assigned to the cor- 0 50 100 150 responding conformation of the Altona-Sundaralingam conforma- Ranking tion ring30,31 with a program written in our group. The electron density of the systems has been analyzed by the Figure 2. Ranking of all open-chain conformations of D-erythrose and D-threose 32,33 Atoms In Molecules (AIM) methodology using the MORPHY98 according to the energies (B3LYP/6-311++G(d,p) level) relative to their respective 34,35 and AIMAll programs. The topological analysis of the electron global minima. 98 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105

3. Results and discussion numbers are much higher than those reported by Aviles-Moreno and Huet15 where only 14 and 15 conformers where described. 3.1. Energy and conformation of the minima The number of minima obtained in the furanose conﬁgurations is much smaller due to the restrictions imposed by the ring. Thus, A total of 174 and 170 minima were found for the open-chain the total number of minima is 14, 16, 22 and 19 for a-D-erythro- conﬁguration of D-erythrose and D-threose, respectively. These furanose, b-D-erythrofuranose, a-D-threofuranose and b-D-threo-

ϕ ϕ ϕ

Figure 3. Molecular graphs of the most stable conformers of the open-chain conﬁguration of the D-erythrose and D-threose 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) computational levels. The values for the CCCC dihedral bond angles are given. The position of the bond and ring critical points calculated within the AIM methodology is indicated with green and red dots, respectively. L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105 99

ϕ ϕ ϕ

ϕ ϕ

Fig. 3 (continued) furanose, respectively. The energies of the minima for the of the salicylic acid can be found.38 The conformations in which open-chain configurations stretch over a range of 50 kJ/mol. these interactions appear can be considered as the precursor to Fig. 2 ranks all open-chain conformations of D-erythrose and D- furanose formation. threose according to the energies relative to their respective global The G3MB3 calculations return similar relative energies com- minima. In the case of D-erythrose, Fig. 3 shows 13 structures with pared to those obtained at B3LYP/6-311++G(d,p) level shown in an Erel smaller than 10 kJ/mol and only 5 structures below this en- Figure 3. The two levels predict the same conformation as the most ergy threshold in the case of D-threose. stable for both D-erythrose and D-threose. The most stable minima The most stable minima in the open-chain configuration show found for the open-chain configuration of D-erythrose are exactly an intramolecular hydrogen bond between the hydroxyl group the same as those described by Aviles-Moreno and Huet.15 How- attached to C-2 and the carbonyl moiety (C1@O). Although intra- ever, in the case of D-threose, the most stable minimum found by molecular hydrogen bonding is not a unique feature of the most these authors corresponds to the third minima in our search, with stable structures, it occurs in the set with high frequency. The a relative energy of 5.8 and 6.3 kJ/mol at B3LYP/6-311++G(d,p) and frequency of this hydrogen bond occurring decreases in the deciles G3B3 levels, respectively. of energy ranked open-chain D-erythroses: 1-10: 9 times, 11-20: 6 The comparison of the B3LYP/6-311++G(d,p) and G3B3 energies times, 21-30: 3 times, 31-40: 3 times, 41-50: 2 times, 51-60: 4 shows that in the cases of a-D-erythrofuranose and b-D-threofura- times, 61-100: 2 times, 101-174: 1 time. In addition, the most nose, both levels predict the same conformation as the most stable. stable conformer of D-erythrose shows a C1HO4 contact while In the case of b-D-erythrofuranose and a-D-threofuranose, the most in D-threose the O4H interacts with O2, generating a hydrogen stable conformation changes from one level to the other since bond (HB) chain with the O2HO1 HB. In some cases, stabilizing several minimum structures are found with very small relative interactions between oxygen atoms and the carbonyl carbon atom energies (three minima less than 1 kJ/mol in a-D-threofuranose similar to the ones recently described in the conformational study and four less than 2 kJ/mol in b-D-erythrofuranose). For either case, 100 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105

alpha-erythrose beta-erythrose lations carried out within the G3B3 composite method agree with the relative energies obtained at the G3B3 level. alpha-threose beta-threose The populations derived from the energy calculations for all the conformers agree with those reported in solution for threose indi- 35 cating a population of 51% and 38% for the a- and b-furanose con- ﬁgurations, respectively,21 while the remaining 11% is present as 30 the aldehyde hydrate, which has not been considered in this work.

25 3.2. Analysis of the intramolecular interactions: AIM and NBO

20 In order to analyze the intramolecular hydrogen bond interactions, two methodologies were used: the topological analysis of 15 the electron density within the AIM method and the Natural Bond

Erel (kJ/mol) Orbital (NBO). In the AIM approach, the presence/absence of an interatomic BCP determines the existence/non-existence of a HB 10 interaction. In contrast, in the NBO method, a numerical value is obtained for the interaction of the lone pair of the oxygen atom 5 with the r⁄ H–O orbital. The AIM and NBO analyses will be dis- cussed separately first and then compared. 0 1 6 11 16 21 3.3. Aim Ranking The hydrogen bonds (HB) are characterized in the AIM method- Figure 4. Ranking of the conformers of a- and b-D-erythrose, and a- and b-D- ology by the presence of a BCP associated with a bond path be- threose according to the energies (B3LYP/6-311++G(d,p) level) relative to their respective global minima. tween an HB acceptor, here an oxygen atom, and the hydrogen atom of the HB donor moiety, here a hydroxyl group. In the open-chain configuration, the presence of CHO HB interactions the difference in relative energy is never larger than 2 kJ/mol for where the CH group corresponds to the terminal acetal group the most stable conformers. The minima obtained for the furanose (C-1) was observed in nine conformations. In general, and depend- configurations range between 25 and 35 kJ/mol with respect to the ing on the conformation, all oxygen atoms can be involved in HB most stable conformation in each configuration (Fig. 4, the struc- interactions, the only exception being the oxygen atom of the fura- tures have been numbered in increasing order of relative energies). nose ring, which is never involved in any BCP for all the examples The number of structures with relative energy smaller than 10 kJ/ we have studied. However, the possibility that the ring oxygen mol is, respectively, 5, 9, 7, and 4 for a-D-erythrofuranose, a-D- atom can be involved in HB interaction has been described for 41 threofuranose, b-D-erythrofuranose, and b-D-threofuranose (Fig. 5). the sucrose disaccharide. The presence of stabilizing intramolecular HBs is a constant for Based on the AIM criteria, the HBs have distances that range be- all the low energy minima. The interacting moieties depend on the tween 1.87 and 2.44 Å in the open configurations, and between relative orientation of the hydroxyl groups. Thus, in the a-D- 1.92 and 2.33 Å in the furanose configurations. The values of the erythrofuranose, which presents the three hydroxyl groups on electron density at the BCP range between 0.030 and 0.010 au the same side of the furanose ring, two HBs are found in several and the corresponding Laplacian between 0.107 and 0.033 au, conformations. In the rest of the configurations that show two which are within the ranges proposed almost two decades ago42 hydroxyl groups on one side of the furanose ring, only one HB is to characterize HBs based on electron density descriptors. observed. In addition, some Oxygen–Oxygen interactions are found Figs. 3 and 5 show the molecular graphs, which include the crit- with bond paths that do not connect the expected hydrogen atom ical points and bond paths of the most stable conformations of with the oxygen atom. open chain and each furanose configuration. The hydrogen bonds At B3LYP level, the most stable structures correspond to an have been classified as 1-2, 1-3, and 1-4 based on the number of envelope conformation of the ring, except in a-D-erythrofuranose, C–C bonds (1, 2, and 3, respectively) that separate the two interact- 2 where a 2-exo 3-endo twist conformation ( T3) is the most stable. ing moieties. The total number of HB contacts of each type charac- The most frequent configurations found in the most stable minima terized for all the conformers are gathered in Table 2. 2 2 are E and E2. Thus, E is present in two of the lowest energy con- The representation of the interatomic distance HO versus the formations of a-D-erythrofuranose and in another two of a-D- OHO angle (Fig. 6) shows clearly the three types of HBs. Thus, for threofuranose, while E2 configuration is present in the b-form a given interatomic distance, the smaller angles are associated (twice in b-D-erythrofuranose and thrice in b-threofuranose). A with a 1-2 HB, the intermediate angles with a 1-3 HB, and the graphical representation of the puckering parameters (P and Q) largest angles with a 1-4 HB. This classification is a clear indication of the most stable conformers (see Supplementary data, Table S1 of the geometrical restrictions on the interaction due to the size of and Fig. S1) shows that most of the conformers are in ‘southern’ the pseudo-ring formed. forms. The representation of q and r2q versus the intermolecular Table 1 compares the energies of the most stable minima in distance (Fig. 7) shows again a clear differentiation between the each configuration for erythrose and threose. In the case of ery- three different types of HBs. Thus, the largest values of q and r2q throse, the most stable configuration corresponds to the a-fura- are associated with 1-2 interactions, being smaller for the 1-4 HBs. nose at the two computational levels. In the case of threose, These results follow the tendencies described previously for those B3LYP/6-311++G(d,p) predicts that the open-chain is the most cases where the interaction forms a cyclic structure; thus, for a given stable while the G3B3 method favors a-furanose. Discrepancies be- distance, the values of the electron density descriptor become smal- tween these two computational levels have previously been re- ler as the size of the ring increases.43 These exponential relationships ported when comparing open and cyclic structures.39,40 The between q and r2q versus the interatomic distance are in agree- analysis of our results shows that the single point QCISD(T) calcu- ment with previous reports on intermolecular interactions.44,45 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105 101

4 1 3 2

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 conformation assigned 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.

3.4. NBO analysis the HBs in the most stable conformer of the open-chain of D-erythrose and b-D-erythrofuranose have been represented in Figure As an example of the orbitals involved in a HB interaction 8. We bring in the standard cutoff value of 2.1 kJ/mol for the based on the NBO methodology, those responsible of one of orbital interactions, and only considered interactions with an 102 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105

Fig. 5 (continued)

energy exceeding this threshold. A total of 597 interactions that All the HBs predicted by the AIM method are conﬁrmed by can be associated to HB interactions were found. The largest en- the NBO analysis except for a few cases where the energy is below ergy value of the orbital interaction is 42.8 kJ/mol. the 2.1 kJ/mol cutoff, the smallest value being 1.34 kJ/mol. Of those L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105 103

Table 1 Relative energy of the most stable minima of each conﬁguration (kJ/mol) and (a) 0.038 predicted population for each conﬁguration at the G3B3 computational levela 0.033 1-2 HB Open-chain a-Furanose b-Furanose 1-3 HB Erythrose B3LYP 7.3 0.0 9.4 0.028 1-4 HB G3B3 16.7 (0%) 0.0 (91%) 7.7 (9%) Threose B3LYP 0.0 4.8 1.6 0.023 G3B3 8.6 (1%) 0.0 (69%) 1.3 (29%) BCP ρ

a All minima calculated for each conﬁguration have been considered. 0.018

0.013

Table 2 Total number of HB interactions based on the AIM methodology found in all the 0.008 characterized conformers 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5

1-2 HB 1-3 HB 1-4 HB H···O Distance

D-Erythrose (open-chain) 36 62 17 (b) 0.14 D-Threose (open-chain) 52 62 19 a-D-Erythrofuranose 18 4 — 0.12 1-2 HB b-D-Erythrofuranose 10 — — 1-3 HB a-D-Threofuranose — 10 — 0.10 b-D-Threofuranose 8 — — 1-4 HB

0.08 LAP BCP LAP 0.06 160

155 1-2 HB 0.04 150 1-3 HB 1-4 HB 0.02 145 1.8 2.0 2.2 2.4 140 H···O Distance 135 Figure 7. (a) Electron density and (b) Laplacian at the BCP (au) versus the 130 interatomic distance (Å). The exponential relationships have square correlation

OH···O Angle OH···O 125 coefﬁcients, R2, of 0.92, 0.98 and 0.99 for the electron density of the 1-2, 1-3 and 1-4 HBs and of 0.81, 0.98, and 0.99 for the Laplacian, respectively. 120 115 110 the AIM analysis are associated with 1-2 interactions with OHO 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 angles close to 110° or less. The second order perturbation energy analysis within the NBO H···O Distance methodology identiﬁes those orbital interactions that stabilize the energy of the system. The value of the orbital interaction Figure 6. Distribution of the HO distance (Å) versus the OHO(°) angles for the 1-2, 1-3 and 1-4 HB interactions. energy, E(2), provides an estimate of the donor–acceptor interaction. Here this interaction corresponds to the interaction of a lone pair of an oxygen atom and the r⁄ of the interacting OH bond. interactions predicted by NBO but without the BCP that AIM would The representation of the E(2) versus the corresponding HO require, the largest orbital interaction energy obtained was 8.4 kJ/ interatomic distance (Fig. 9) for the three types of HBs, shows mol. Most interactions present in the NBO analysis but absent in that their values are mixed, especially for the 1-3 and 1-4 HBs.

Open Chain D-erythrose β-D-erythrofuranose

Oxygen lone pair σ* H-O orbital Oxygen lone pair σ* H-O orbital

Figure 8. Orbitals associated to the HB interaction in the most stable conformation of the open-chain D-erythrose and b-D-erythrofuranose. 104 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105

45 The NBO analysis shows the presence of more potential HB interactions than those found by the AIM method. However, all 40 interactions detected with the NBO method but not with AIM show 35 1-2HB 1-3HB small orbital interaction energy values and, in general, are associ- 30 1-4HB ated with 1-2 contacts that have small OHO angles. 25 Acknowledgments E(2) 20 15 L.M.A. thanks the Ministerio de Ciencia e Innovación for a Ph.D. 10 grant (No. BES-2010-031225). I.A. thanks the Ministerio de Educa- ción (PR2009-0171) and the Royal Society of Chemistry for a travel 5 grant that allowed him to stay at the University of Manchester. We 0 also thank the Ministerio de Ciencia e Innovación (Project No. 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 CTQ2009-13129-C02-02) and the Comunidad Autónoma de Ma- O···H Distance drid (Project MADRISOLAR2, ref. S2009/PPQ-1533) for continuing support. Gratitude is also due to the CTI (CSIC) for an allocation Figure 9. Second order perturbation NBO energy, E(2), (kJ/mol) versus the OH of computer time and to Dr. Eric Elguero (IRD, Montpellier, France) interatomic distance (Å). for the statistical analysis.

Supplementary data 45 40 Supplementary data associated with this article can be found, in 1-2HB the online version, at http://dx.doi.org/10.1016/j.carres.2012.06.011. 35 1-3HB 30 1-4HB References 25 1. Schnupf, U.; Willett, J. L.; Momany, F. Carbohydr. Res. 2010, 345, 503–511.

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