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Carbohydrate Research 358 (2012) 96–105 Contents lists available at SciVerse ScienceDirect Carbohydrate Research journal homepage: www.elsevier.com/locate/carres 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 min- ima 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 num- ber 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 OHÁÁÁO 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 0008-6215/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.carres.2012.06.011 L. M. Azofra et al. / Carbohydrate Research 358 (2012) 96–105 97 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, À3)] 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 À1). The (3, À3) critical points practically coincide with nuclear positions of each hydroxyl group were examined (g, g0 and t). Thus, positions, the (3, À1) 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 (=20Á33). 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 con- formers. 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 re- spect 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.

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