Conformational Studies of Gas-Phase Ribose and 2-Deoxyribose By

Carbohydrate Research 384 (2014) 20–36

Contents lists available at ScienceDirect

Carbohydrate Research

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

Conformational studies of gas-phase ribose and 2-deoxyribose by density functional, second order PT and multi-level method calculations: the pyranoses, furanoses, and open-chain structures ⇑ Marek Szczepaniak , Jerzy Moc

Faculty of Chemistry, Wroclaw University, F. Joliot-Curie 14, 50-383 Wroclaw, Poland article info abstract

Article history: We present an extensive computational study of a complex conformational isomerism of two gas phase Received 1 June 2013 pentoses of biological and potential astrobiological importance, D-ribose and 2-deoxy-D-ribose. Both cyc- Received in revised form 9 September 2013 lic (a- and b-pyranoses, a- and b-furanoses) and open-chain isomers have been probed using second Accepted 18 October 2013 order Møller–Plesset perturbation theory (MP2), M06-2X density functional, and multi-level G4 methods. Available online 1 November 2013 This study revealed a multitude of existing minima structures. Numerous furanose conformers found are described with the Altona and Sundaralingam pseudorotation parameters. In agreement with the recent Keywords: gas-phase microwave (MW) investigation of Cocinero et al., the calculated free ribose isomers of lowest D-Ribose 1 4 energy are the two b-pyranoses with the C4 and C1 ring chair conformations. Both b-pyranoses lie 2-Deoxy-D-ribose MP2 within 0.9 kJ/mol in terms of DG(298 K) (G4), thus challenge the computational methods used to predict G4 the ribose global minimum. The calculated most favoured ribofuranose is the a-anomer having the twist 2 NBO T1 ring conformation, put 10.4 kJ/mol higher in DG than the global minimum. By contrast with D-ribose, the lowest energy 2-deoxy-D-ribose is the a-pyranose, with the most stable 2-deoxy-D-furanose (the a- anomer) being only 6.2 kJ/mol higher in free energy. For both pentoses, the most favoured open-chain isomers are signiﬁcantly higher in energy than the low-lying cyclic forms. A good overall agreement is observed between the M06-2X and MP2 results in terms of both the existing low-energy minima structures and intramolecular H-bonding geometrical parameters. The natural orbital analysis conﬁrms the occuring of the endo- and exo-anomeric effects and maximization of intramolecular H-bonding in the lowest-lying pyranoses and furanoses of both sugars. Crown Copyright Ó 2013 Published by Elsevier Ltd. All rights reserved.

1. Introduction 43(b-pyranose):42(a-pyranose):10(b-furanose):5(a-furanose) at 0 °C and of 15(a-pyranose):15(b-pyranose):9(a-furanose):11(b- Five-carbon sugars or pentoses perform various biological func- furanose) at 90 °C was reported.6 The distinction between a- and tions. They are components of nucleotides, nucleosides, nucleic b-sugar ring conformers or anomers arises from the actual orienta- 1 acids, certain vitamins, and coenzymes. D-Ribose and 2-deoxy-D- tion of the OH group at carbon C1 of the ring (Scheme 1). Even ribose being constituents of RNA and DNA, respectively, occur in more complex conformational typology of D-ribose as well as 2- these molecules in the b-furanose form (comprising the ﬁve-mem- deoxy-D-ribose arises if one takes into account their open-chain bered sugar ring, see Scheme 1). The occurrence of b-furanose in- (acyclic) structures, also shown in Scheme 1. stead of b-pyranose (the latter comprising the six-membered Simple sugars have been of interest in astrobiology (see e.g., Ref. sugar ring, Scheme 1) in nucleic acids is thought to be related to 7). In the interstellar space there have been found more than 140 the structural ﬂexibility of the former conformation.2 Based on chemical compounds, including the sugar building block—glycolal- the NMR spectroscopy studies it has been known3–6 however that dehyde. Glycolaldehyde is considered a main component of organ- 8 in aqueous solution both D-ribose and 2-deoxy-D-ribose exist as a ic transformations leading to aldoses or ketoses. Currently, mixture of the a- and b-pyranoses. For instance, the following detecting pentoses in space encounters problems caused by the equilibrium mixture for D-ribose was reported in Ref. 5: 62%(b- paucity of reliable data concerning their molecular structures and pyranose):20.3%(a-pyranose):11.6%(b-furanose):6.1%(a-furanose). spectroscopic properties.9 For 2-deoxy-D-ribose, which pentose lacks hydroxyl group at car- Compared to other common pentoses and hexoses, both D- bon C2, the aqueous solution percentage ratio of ribose and 2-deoxy-D-ribose can be regarded as structurally under- 10 explored. Indeed, for D-ribose, only recently its crystal structure has been reported. Although the early work aiming at crystallizing ⇑ Corresponding author. Mobile: +48 697013557. ribose was published already in 1956,11 there had been major E-mail address: [email protected] (M. Szczepaniak).

0008-6215/$ - see front matter Crown Copyright Ó 2013 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.carres.2013.10.013 M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36 21 difficulties for many years to isolate crystals appropriate for X-ray search strategy was adopted. First, the molecular mechanics (MM) analysis.12 In 2010, the successful combined X-ray crystal diffrac- method was used for extensive mappings of their PESs including tion and solid state 13C MAS (magic angle spinning) NMR spectros- both cyclic (a- and b-pyranoses and a- and b-furanoses) and 10 copy investigation of D-ribose by Sisak et al. was published. It open-chain structures (for the recent use of the MM method for was concluded from both structural analyses that the ribose crystal the initial conformational studies of various sugars, see for exam- 19–21 consisted of the b- and a-pyranoses, with the b/a-pyranose ratio of ple, Refs. 16–18). The force field employed here was MM3, 1.7–2:1. implemented in Scigress code22 (for the recent comparative study The condensed phase structural data are affected by possible of saccharides using eighteen force fields, including MM3, see Ref. contributions from crystal packing interactions and thus are not 23). A few hundred structures were MM3 preoptimized. Based on strictly comparable to the lowest energy isolated species. In the relative energies of the MM3 calculated structures, a set of con- 2012, the first successful gas-phase rotational study of D-ribose formers was selected for the subsequent quantum mechanical cal- 9 was reported by Cocinero et al. (the earlier such attempts failed culations after applying a cut-off at 62 kJ/mol. This MM3 followed due to a thermal instability of ribose). The Cocinero et al. investiga- by the quantum mechanical conformation search procedure was tion, which is most relevant to the current theoretical study, was employed before, for example, for complex conformational energy accomplished by combining microwave (MW) spectroscopy in surfaces of hexoses,24 including the structures with intramolecular supersonic jets with ultrafast UV laser vaporization.9 These O–HO hydrogen bonds. In this respect we mention the authors’ interpretation of the rotational transitions made with recent application/validation of the MM3 method for systems the help of quantum chemical calculations and Watson semi-rigid containing various types of non-covalent interactions such as rotor model led to the conclusion that six distinct conformers of D- non-conventional C–HO hydrogen bonding and pp stacking ribose were present under the experimental conditions. Of these, interactions.25 the two lowest energy structures assigned as the distinct b-pyra- All the conformers with relative energies 662 kJ/mol (about 340 noses were found to be essentially isoenergetic. The other four free structures) were reoptimized with both the M06-2X26 density ribose species assigned included exclusively the pyranoses. Neither functional and second-order Møller–Plesset perturbation theory 27 28 furanose nor open-chain structures of D-ribose have been observed (MP2) methods, with the 6-311++G(d,p) basis set, using GAUSS- 29 suggestive of their higher energies. Also, to our knowledge, no IAN 09 code. The choice of both the M06-2X and MP2 relied on experimental studies of the gas phase structure of 2-deoxy-D-ri- the recent test study of the relative energies of the gas phase hex- bose have been reported. We are aware of one experimental study ose isomers where the performance of various computational of 2-deoxy-D-ribose, published in 1960, where its structure in the methods was validated against the results of the coupled cluster crystalline state was determined by X-ray crystallography and CCSD(T) calculations extrapolated to the complete basis set limit found to be pyranose.13 (CBS).30 The importance of including diffuse functions in the basis In addition to the combined microwave spectroscopic and set to minimize the basis set superposition error (BSSE) in systems 9 theoretical investigation of D-ribose by Cocinero et al. mentioned with intramolecular hydrogen bonding (present in both pentoses 31 above, the computational quantum mechanical study of D-ribose studied here) is well known. Vibrational frequency analysis was structures of Guler et al.14 appeared in the literature in 2002. For carried out at the DFT level to confirm the minima on the PES. 2-deoxy-D-ribose, a limited conformational analysis by Ghosh All DFT calculations were carried out using a grid with 99 radial 15 et al. was recently reported. In this work, we set out to study shells and 590 angular points per atom called ‘ultrafine’ in GAUSSIAN extensively the potential energy surfaces (PESs) of the two ald- 09 (instead of the standard (75,302) integration grid). This was to opentoses involving their pyranose, furanose, and open-chain comply with the recent findings32 that the M06 type functionals26 structures. To this end, density functional theory (DFT) and corre- are sensitive to the integration-grid size. In fact, the choice of the lated ab initio as well as multi-level (composite) electronic struc- grid can matter for the M06-2X calculations of the lowest energy ture methods have been used. Main goals of this investigation ribopyranoses having minuscule energy differences (see below). are to elucidate a complex conformational isomerism of ribose In addition to the relative energies (including zero-point energy and deoxyribose, to find their most stable conformers and to com- (ZPE) corrections), DH(0 K), the 298 K free energy differences, pare their structural, energetic, and bonding properties in the gas DG(298 K), have been calculated at the M06-2X and MP2 levels. phase. The thermodynamic values were obtained by computing the ZPE, thermal and entropic contributions with the help of the M06-2X 2. Computational methods vibrational frequencies (used without scaling, except where scaling was part of a multi-level method, see below). The thermal and en- To predict low-energy conformations and conformational-en- tropy corrections were determined with the harmonic oscillator ergy differences of D-ribose and 2-deoxy-D-ribose, the following and rigid rotor approximations and assuming an ideal gas at

Scheme 1. Possible conformations of D-ribose. 22 M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36

Scheme 2. Atom numbering scheme for pyranose and furanose conformers.

Scheme 3. Envelope furanose ring conformations (the four atoms marked with asterisk make up the plane).

Scheme 4. Twist furanose ring conformations (the three atoms marked with asterisk make up the plane). M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36 23

1 1 1 1pyr- C4-b 2pyr- C4-b 3pyr- C4-a

4 1 4 4pyr- C1-b 5pyr- C4-a 6pyr- C1-a

1 4 1 7pyr- C4-a 8pyr- C1-b 9pyr- C4-b

4 1 1 10pyr- C1-a 11pyr- C4-b 12pyr- C4-a

Figure 1. Structures of twenty four most stable pyranose conformers of D-ribose optimized at the M06-2X/6-311++G(d,p) and MP2/6-311++G(d,p) levels with the indicated HO distances of the possible HB interactions (in Å, the MP2 values are in parentheses).

1.0 atm. Additionally, the free energy differences for the most sta- aug-cc-pVTZ calculations) and multi-level G4 scheme.34 ble conformers of both pentoses were also evaluated using the Recently,35,36 the encouraging multi-level versus coupled cluster MP2 method with the aug-cc-pVTZ basis set33 (single point MP2/ CCSD(T) comparison for the prediction of the relative energies of 24 M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36

4 1 1 13pyr- C1-a 14pyr- C4-b 15pyr- C4-a

1 4 1 16pyr- C4-a 17pyr- C1-a 18pyr- C4-b

4 1 1 19pyr- C1-a 20pyr- C4-b 21pyr- C4-a

4 4 4 22pyr- C1-a 23pyr- C1-b 24pyr- C1-b

Fig. 1 (continued) the gas phase n-butanol rotamers was obtained. The optimized su- 3. Labeling of conformers gar structures were drawn with Chemcraft37 visualization soft- ware. Finally, the atom numbering scheme used for the pyranose Due to a large number of various type isomers of D-ribose and 2- and furanose conformers is given in Scheme 2. deoxy-D-ribose presented in this work, their unambiguous labeling M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36 25

2 2 3 1fur- T1-a 2fur- T1-a 3fur- T4-a

2 2 4fur- E-a 5fur-E1-a 6fur- E-a

2 3 7fur- T1-a 8fur-E2-b 9fur- T4-a

3 3 3 10fur- T2-b 11fur- T4-a 12fur- E-a

Figure 2. Structures of the twelve most stable furanose conformers of D-ribose optimized at the M06-2X/6-311++G(d,p) and MP2/6-311++G(d,p) levels with the indicated HO distances of the possible HB interactions (in Å, the MP2 values are in parentheses).

1 is of importance. Here, the conformational nomenclature em- of ribose with the C4 chair conformation, the b anomer; ‘1’ in front ployed is deﬁned. According to Scheme 1, pyranoses (pyr) which of this designation tells the pyranose conformer number. The 1 4 can assume either C4 or C1 chair ring conformations, can addi- deoxyribose pyranoses are denoted similarly. tionally be either a (denoted a)orb (denoted b) anomers depend- Furanose (fur) ring can exist in either envelope (E) or twist (T) ing on the orientation of OH group at the anomeric carbon conformations.38 Envelope conformations have one atom above 1 C1. Thus, for instance, 1pyr- C4-b refers to a pyranose conformer or below the plane of the ring formed by the four other ring atoms 26

Table 1 The relative energies, DH(0 K), Gibbs free energy differences, DG(298 K) (kJ/mol) and equilibrium rotational constants A–C (MHz) of the thirty eight most stable conformers of D-ribose and of the lowest-lying open-chain structure calculated at the two geometry optimization levelsa

Conformer M06-2X/6-311++G(d,p) (kJ/mol) MP2/6-311++G(d,p) (kJ/mol) Rotational constants b (MHz) D H (0 K) D G (298 K) D H (0 K) D G (298 K) A B C 1 1pyr-C4-b 0.00 0.00 0.00 0.62 1850.5 [1844.98735 (18)] 1312.7 [1305.135870 (74)] 1094.5 [1087.84195 (10] 1 2pyr- C4-b 0.89 0.81 1.25 1.79 1863.4 [1853.13790 (95)] 1305.7 [1301.195100 (89)] [1089.4 1081.87037 (10)] 1 3pyr- C4-a 1.03 0.65 1.11 1.34 1966.2 [1954.0129 (30)] 1269.9 [1267.42042 (25)] 1005.7 [1000.48929 (28)] 4 4pyr- C1-b 1.60 0.44 0.55 0.00 2060.4 [2048.18674 (41)] 1179.4 [1176.32050 (22)] 848.9 [845.23676 (21)] 1 5pyr- C4-a 2.10 1.90 3.25 3.67 1969.2 [1960.29176 (39)] 1279.5 [1272.44554 (21)] 995.9 [994.58926 (20)] 4 6pyr- C1-a 2.10 2.07 3.19 3.78 1886.1 [1886.47378 (71)] 1287.9 [1280.03450 (25)] 1000.5 [995.20684 (25)] 1 7pyr- C4-a 2.65 2.85 2.73 3.54 1967.0 [1960.29176 (39)] 1279.0 [1272.44554 (21)] 998.5 [994.58926 (20)]

4 20–36 (2014) 384 Research Carbohydrate / Moc J. Szczepaniak, M. 8pyr- C1-b 4.93 3.86 4.52 4.06 2059.4 1173.8 848.4 1 9pyr- C4-b 5.02 4.45 5.11 5.15 1824.6 1308.2 1103.6 4 10pyr- C1-a 6.25 6.04 7.79 8.20 1939.5 1272.3 992.7 1 11pyr- C4-b 6.38 5.60 6.70 6.54 1836.9 1297.5 1100.2 1 12pyr- C4-a 6.39 6.15 6.34 6.72 1939.8 1276.6 1007.7 4 13pyr- C1-a 10.16 9.10 10.27 9.82 1935.1 1270.1 966.4 1 14pyr- C4-b 12.96 11.93 11.28 10.86 1834.1 1301.4 1110.4 1 15pyr- C4-a 13.11 12.57 12.57 12.64 1958.7 1280.9 988.6 2 1fur- T1-a 14.56 11.53 11.15 8.74 2059.2 1065.6 997.6 1 16pyr- C4-a 16.13 15.50 15.71 15.71 1977.3 1272.0 995.6 2 2fur- T1-a 16.20 12.99 11.87 9.27 2017.8 1068.2 998.0 4 17pyr- C1-a 16.87 15.53 17.20 16.47 1891.2 1286.4 997.2 1 18pyr- C4-b 17.39 17.07 18.62 18.91 1852.5 1299.7 1080.8 4 19pyr- C1-a 17.84 16.66 17.02 16.46 1911.1 1277.1 976.5 3 3fur- T4-a 18.10 13.16 13.68 9.35 1931.4 1152.7 823.6 1 20pyr- C4-b 18.44 17.95 20.12 20.24 1866.9 1292.1 1077.6 4fur-2E-a 18.88 15.44 15.04 12.22 2039.2 1083.1 1019.2 5fur-E1-a 18.92 14.25 14.71 10.66 2041.8 1066.7 933.8 6fur-2E-a 19.03 15.72 15.83 13.14 2303.5 960.5 856.1 2 7fur- T1-a 20.01 16.43 15.68 12.70 2270.4 956.2 857.3 8fur-E2-b 21.08 15.91 14.91 10.35 1691.2 1295.2 923.6 1 21pyr- C4-a 20.23 18.97 20.03 19.39 1932.0 1277.2 999.5 4 22pyr- C1-a 20.67 20.04 21.10 21.09 1878.7 1287.2 992.5 4 23pyr- C1-b 21.05 19.17 18.33 17.06 2053.1 1175.9 852.0 3 9fur- T4-b 20.16 15.50 16.11 12.07 2210.8 1064.2 799.6 3 10fur- T2-b 21.42 16.86 15.20 11.26 1843.8 1169.0 873.4 3 11fur- T4-a 21.46 15.54 16.56 11.26 1830.2 1119.9 787.4 12fur-3E-a 21.61 16.42 16.47 11.90 1913.9 1157.5 824.0 2 13fur- T1-a 21.77 17.67 16.92 13.44 1999.1 1086.5 1016.4 4 14fur- T3-b 22.62 18.56 19.74 16.30 1721.1 1309.1 1004.6 4 24pyr- C1-b 22.66 21.10 20.39 19.44 2077.0 1164.8 851.3 1open 39.29 30.13 28.77 20.23 2535.8 778.3 616.7

a The D H(0 K) values include the harmonic zero-point energy (ZPE) corrections calculated at the M06-2X/6-311++G(d,p) level. The free energy differences (at T = 298 K and p = 1 atm), D G(298 K), were obtained by calculating the ZPE, thermal and entropic contributions with the help of the M06-2X/6-311++G(d,p) vibrational frequencies. In Table S1 (Supplementary data) the relative energiesD H(0 K) and free energy differences D G(298 K) of the remaining conformersD-ribose of investigated, given in the order of increasing relative energies, can be found. b The MP2/6-311++G(d,p) results; the values in square brackets are the experimental rotational constants from Ref. 9. M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36 27

ΔG(298K) [kJ/mol]

1pyr-1C4-b 2pyr-1C4-b 3pyr-1C4-a 4pyr-4C1-b 5pyr-1C4-a 6pyr-4C1-a 7pyr-1C4-a 8pyr-4C1-b 9pyr-1C4-b 10pyr-4C1-a 11pyr-1C4-b 12pyr-1C4-a 13pyr-4C1-a 14pyr-1C4-b 15pyr-1C4-a 1fur-2T1-a Furanose 16pyr-1C4-a 2fur-2T1-a 17pyr-4C1-a 18pyr-1C4-b 19pyr-4C1-a 3fur-3T4-a 20pyr-1C4-b 4fur-2E-a 5fur-E1-a 6fur-2E-a 7fur-2T1-a 8fur-E2-b 21pyr-1C4-a 22pyr-4C1-a 23pyr-4C1-b 9fur-3T4-b 10fur-3T2-b 11fur-3T4-a 12fur-3E-a 13fur-2T1-a 14fur-4T3-b 24pyr-4C1-b 15fur-E4-a 16fur-3T2-b 17fur-OT1-a 25pyr-4C1-b 18fur-2E-a 26pyr-1C4-b 27pyr-4C1-b 19fur-4E-b 20fur-1T2-b 28pyr-1C4-a 21fur-E2-b 22fur-1T2-b 23fur-2T1-a 24fur-3E-a 25fur-2T1-a 26fur-1T2-b 27fur-E2-b 28fur-E2-b 29fur-3T4-a 30fur-E4-a 29pyr-1C4-b 31fur-2E-a 32fur-3T4-a 30pyr-4C1-a 33fur-E4-a 34fur-2E-b 35fur-2T1-a 36fur-2T1-a 37fur-3T2-b 38fur-4E-b 39fur-4E-b 40fur-E2-b 41fur-2E-b 1open Open 2open 42fur-E2-b 43fur-3E-a 3open 4open

Figure 3. Relative Gibbs free energy DG(298 K) results for the seventy seven distinct D-ribose structures calculated at the M06-2X/6-311++G(d,p) level (ranked in order of increasing DH(0 K) relative energy). Arrows indicate the most stable furanose and open-chain structures found.

(Scheme 3). Twist conformations have one atom displaced above To describe a furanose ring conformation or puckering mathe- and one atom displaced below the plane of the ring formed by matically we have adopted the model of Altona and Sundaralingam the three other ring atoms (Scheme 4). Schemes 3 and 4 illustrate (AS)39 which utilizes two parameters: pseudorotational phase an- 38,39 ten possible E and 10 possible T furanose ring conformations, gle, P, and puckering amplitude, Um. In the AS method, P values respectively, along with the corresponding notation. For instance, being odd multiples of 18° (P =18°,54°,90°, etc.) correspond to 2 the term E(E2) denotes the envelope conformation with atom (symmetrical) E conformations, whereas P values being even mul- 4 3 C2 above (below) the ring plane, whereas the term T3 ( T4) tiples of 18° (P =0°,36°,72°, etc.) correspond to (symmetrical) T denotes the twist conformation with C4(C3) atom above and conformations—a graphical representation of the dependence of C3(C4) atom below the ring plane, etc.38,39 the furanose ring conformation on the full range of P values 28 M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36

Table 2 Table 1 indicates that at least twelve most stable gas phase ri- The relative energies, DH(0 K) and Gibbs free energy differences, DG(298 K) (kJ/mol) bose structures are the pyranoses, seven of which are within a of the seven most stable D-ribopyranoses along with those of the lowest-lying D- range of less than 4 kJ/mol. Specifically, they lie within a range of ribofuranose and the lowest-lying open-chain structure of D-ribose calculated at the MP2/aug-cc-pVTZ and G4 levels 2.85 kJ/mol and 3.54 kJ/mol of the global minimum in terms of DG at the M06-2X/6-311++G(d,p) and MP2/6-311++G(d,p) levels, Conformer G4 (kJ/mol) MP2/aug-cc-pVTZ (kJ/mol) respectively. These four a- and three b-anomers assume either DH(0 K) DG(298 K) DH(0 K) DG(298 K) 1 4 the C4 or C1 ring chair conformations and are suggested to com- 1 1pyr- C4-b 0.00 0.88 0.00 0.00 prise intramolecular hydrogen-bonded interactions (this issue is 1 2pyr- C4-b 1.21 1.92 1.30 1.21 discussed in more detail in Section 4.4). 1 3pyr- C4-a 2.55 3.05 3.18 2.80 4 Among the seven low-lying ribopyranoses, we have identified 4pyr- C1-b 0.63 0.00 2.34 1.17 1 six isomers which were reported to be detected using MW spec- 5pyr- C4-a 3.55 4.23 3.05 2.85 4 6pyr- C1-a 1.88 2.43 0.79 3.05 troscopy by Cocinero et al., whose authors’ structure assignment 1 7pyr- C4-a 2.55 3.68 1.80 1.92 was made employing the quantum mechanically calculated rota- 2 1fur- T1-a 12.22 10.42 11.97 8.91 tional parameters.9 The following correspondence exists between 1open 33.9 25.68 39.08 29.87 our lowest energy structures (Fig. 1) and the MW detected ones (the Ref. 9 isomer designations are given within parentheses): 38,39 1 1 1 4 (0° 6 P 6 360°) constitutes a ‘pseudorotational wheel’ (see 1pyr- C4-b (A), 2pyr- C4-b (C), 3pyr- C4-a (D), 4pyr- C1-b (B), 4 1 Scheme S2 in Supplementary data). In the AS model, parameter 6pyr- C1-a (F) and 7pyr- C4-a (E). It should be stressed here that Um describes the extent of the puckering from the four-atom-ring- all the lowest-energy ribose isomers we have arrived at are the or three-atom-ring-plane (Schemes 3 and 4). The parameter P can outcome of our independent systematic conformational search be determined from five endocyclic torsion angles, U0–U4 (defined strategy detailed above. in Scheme S2) via Eq. 1, whereas the parameter Um can be deter- Both our M06-2X/6-311++G(d,p) and MP2/6-311++G(d,p) cal- 1 mined via Eq. 2: culations have predicted that the two b-pyranoses, 1pyr- C4-b 4 1 4 and 4pyr- C1-b (Fig. 1) with the C4 and C1 ring chair conforma- ðU2 þ U4ÞðU1 þ U3Þ tan P ¼ ð1Þ tions, respectively, compete for the lowest energy gas phase ribose ðsin 36 þ sin 72Þ isomer (Table 1). This is in agreement with the MW investigation,9 where the two conformers were established to be essentially iso- U0 U ¼ ð2Þ energetic based on the DG values evaluated from the relative m cos P intensities of the observed rotational transitions. In more detail, 1 Each furanose structure can be again either the a (a)orb (b) the 1pyr- C4-b structure presents a cyclic counter-clockwise hydro- anomer, depending on the orientation of OH at C1 (Scheme 1). gen-bonded (HB) chain OH4ðaxÞ!OH3ðeqÞ!OH2ðaxÞ (discussed Combining the anomer type with the furanose ring conformation in more detail in 4.4). Our result concerning the lowest energy description affords the furanose conformer notation employed ribose isomers is also in accord with the early B3LYP density func- 2 14 1 here. For instance, 1fur- T1-a refers to a first furanose twist con- tional calculations of Guler et al. who found the ( C4) b-pyranose former with C2 above the plane and C1 below the plane, the a- to be its most stable gas phase structure. It is noted that two low- 1 1 anomer. energy a-anomers given in Figure 1, 5pyr- C4-a and 7pyr- C4-a In the vast majority of the quantum mechanical structure opti- differ mostly by the rotation of the OH groups at C2, C3, and C4, mizations performed in this work, the MP2 and M06-2X methods with the former structure being apparently neither reported earlier provided the same conformer/structure type, especially for the computationally14 in that energy range nor observed.9 furanoses, thus their common labeling in the figures presented be- The comparison between the MP2/6-311++G(d,p) calculated and low is justified. The few qualitatively different MP2 optimized experimental9 values of the rotational constants in Table 1 leads to a structures (compared to the M06-2X ones), concerning the higher relatively easy ‘conformational assignment’. Recall that six of these energy isomers, are marked with asterisk in the figures. conformers were MW spectroscopically detected/assigned in Ref. 9 with the help of the ab initio determined rotational parameters. 1 1 4. Results and discussion Actually, for the 5pyr- C4-a and 7pyr- C4-a pyranose conformer pair, where the latter species was assigned9 as the structure ‘E’, Table 1 1 4.1. D-Ribose conformers shows that an alternative assignment to 5pyr- C4-a is likely (using the rotational constants alone). From an additional comparison of In Figures 1 and 2, the M06-2X/6-311++G(d,p) and MP2/6- the M06-2X/6-311++G(d,p) calculated rotational constants (given 311++G(d,p) calculated structures of the most stable pyranoses in Supplementary data) with the experimental values, a somewhat and furanoses of D-ribose are presented, with those of the remain- worse agreement arises than with the MP2/6-311++G(d,p) ing cyclic as well as open-chain isomers, lying higher in energy, constants. This suggests that our MP2 structural parameters of the shown in Supplementary data (Figs. S1–S3). The relative energies, ribose conformers are expected to be of higher accuracy compared DH(0 K), and free energy differences, DG(298 K) of thirty eight to the M06-2X ones, at least for the pyranoses. most stable D-ribose conformers and those of the lowest lying Table 1 further reveals that the lowest-lying ribofuranose is the 2 2 open-chain isomer are compiled in Table 1 (wherein they are a-anomer with the twist T1 conformation, 1fur- T1-a, put 11.53 kJ/ ranked in order of increasing M06-2X relative energy). The MP2/ mol at M06-2X/6-311++G(d,p) and 8.74 kJ/mol at MP2/6- 6-311++G(d,p) calculated equilibrium rotational constants (A–C) 311++G(d,p) higher in free energy than the most stable ribopyra- along with those available from experiment9 are also included in nose calculated at these respective levels. This energetically most Table 1. The DH(0 K) and DG(298 K) values for the remaining thirty favoured ribofuranose appears to be more stable than the optimal nine D-ribose isomers of higher energy can be found in Table S1 of gas phase ribofuranose reported from the earlier MP2/6-31G(d,p) 40 Supplementary data. In order to make a meaningful comparison calculations by Jalbout et al. which corresponds to the 8fur-E2-b 9 with the results of the MW study, the relative stabilities of D-ri- conformer in Figure 2. According to Table 1, the latter species is bose isomers are discussed in terms of Gibbs free energy differ- predicted to be 3.76 kJ/mol higher in energy (DH(0 K)) than 2 ences. Figure 3 summarizes graphically the DG(298 K) results of 1fur- T1-a at our MP2/6-311++G(d,p) level (we note that only b- all the D-ribose structures calculated here. furanose isomers were considered for ribose by the latter authors). M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36 29

4 1 1 1pyr- C1-a 2pyr- C4-b 3pyr- C4-b

1 1 4 4pyr- C4-a 5pyr- C4-b 6pyr- C1-a

1 4 4 7pyr- C4-b 8pyr- C1-b 9pyr- C1-b

4 1 4 10pyr- C1-b 11pyr- C4-a 12pyr- C1-b

Figure 4. Structures of the twenty four most stable pyranose conformers of 2-deoxy-D-ribose optimized at the M06-2X/6-311++G(d,p) and MP2/6-311++G(d,p) levels with the indicated HO distances of the possible HB interactions (in Å, the MP2 values are in parentheses).

2 Because the seven lowest energy ribopyranoses lie within only for the most favoured ribofuranose, 1fur- T1-a, and most favoured 4 kJ/mol, the additional more accurate calculations on their rela- open-chain ribose, 1open (the latter is given in Fig. S3). It is seen tive stabilities have been performed at the MP2/aug-cc-pVTZ and from Table 2 that the energetic preference of the two b-pyranoses 1 4 G4 levels of theory. Table 2 presents these results along with those 1pyr- C4-b and 4pyr- C1-b is maintained with the corresponding 30 M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36

4 1 1 13pyr- C1-b 14pyr- C4-a 15pyr- C4-a

4 1 1 16pyr- C1-b 17pyr- C4-a 18pyr- C4-a

1 1 19pyr- C4-b 20pyr-skewed-a 21pyr- C4-a

1 4 1 22pyr- C4-a 23pyr- C1-a 24pyr- C4-b

Fig. 4 (continued) minuscule DG of 1.17 kJ/mol (MP2/aug-cc-pVTZ) and 0.88 kJ/mol od dependent (Tables 1 and 2). The cyclic-open chain energy (G4), where the former (latter) conformer is the global minimum differences correspond to the energies of the reactions of the ring at the MP2/aug-cc-pVTZ (G4) level. With this reﬁned energetics, opening and can be calculated accurately with ab initio methods 2 the most favoured furanose molecule 1fur- T1-a is predicted as including dynamic correlation. Our MP2/aug-cc-pVTZ and G4 ener- 8.91 kJ/mol and 10.42 kJ/mol higher in free energy than the global getics (Table 2) yields the free energy difference between the most 1 minimum structure at these respective levels. stable pyranose (1pyr- C4-b) and open-chain (1open) structures of Unlike the pyranose–furanose energy differences, those be- ribose at 29.87 and 25.68 kJ/mol, respectively. Note that the tween the cyclic and open-chain isomers are more strongly meth- respective M06-2X/6-311++G(d,p) value of 30.13 kJ (Table 1) M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36 31

2 2 2 1fur- T1-a 2fur- T1-a 3fur- E-a

4 4 2 4fur- E-b 5fur- E-b 6fur- T1-a

4 2 7fur- E-b 8fur-E2-b 9fur- E-a

2 1 3 10fur- E-a 11fur-T2 -b *11fur- T2-b

12fur-E2-b

Figure 5. Structures of the twelve most stable furanose conformers of 2-deoxy-D-ribose optimized at the M06-2X/6-311++G(d,p) and MP2/6-311++G(d,p) levels with the indicated HO distances of the possible HB interactions (in Å, the MP2 values are in parentheses). The MP2 structure marked with asterisk is qualitatively different from the M06-2X one. 32 M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36

Table 3 The relative energies, DH(0 K), Gibbs free energy differences, DG(298 K) (kJ/mol) and equilibrium rotational constants A–C (MHz) of the thirty seven most stable conformers of a 2-deoxy-D-ribose and of the lowest-lying open-chain structure calculated at the two geometry optimization levels

Conformer M06-2X/6-311++G(d,p) (kJ/mol) MP2/6-311++G(d,p) (kJ/mol) Rotational constantsb (MHz) DH(0 K) DG(298 K) DH(0 K) DG(298 K) A B C

4 1pyr- C1-a 0.00 0.00 0.00 0.00 2485.4 1529.5 1246.7 1 2pyr- C4-b 5.60 4.54 4.30 3.25 2441.3 1523.3 1154.8 1 3pyr- C4-b 9.74 8.23 6.67 5.17 2457.3 1519.8 1146.7 1 4pyr- C4-a 9.84 8.59 8.06 6.82 2497.3 1392.3 1074.2 1 5pyr- C4-b 10.63 8.76 8.67 6.80 2449.2 1518.5 1151.0 4 6pyr- C1-a 11.39 10.95 11.28 10.84 2505.4 1516.3 1246.3 1 7pyr- C4-b 11.55 10.06 8.44 6.95 2441.0 1524.3 1147.4 2 1fur- T1-a 12.25 9.00 6.19 2.95 2519.5 1375.9 1151.4 4 8pyr- C1-b 12.89 11.08 10.54 8.73 2948.6 1276.2 1027.4 4 9pyr- C1-b 13.27 11.50 11.36 9.59 2941.2 1270.0 1025.4 4 10pyr- C1-b 13.98 12.08 11.49 9.60 2940.1 1275.9 1026.2 1 11pyr- C4-a 14.30 12.81 12.98 11.49 2506.0 1376.9 1065.4 2 2fur- T1-a 15.55 11.78 9.43 5.67 2618.5 1258.7 1032.1 4 12pyr- C1-b 16.72 14.96 14.86 13.10 2954.8 1268.4 1025.5 4 13pyr- C1-b 16.94 14.92 15.68 13.66 2948.4 1261.3 1023.9 1 14pyr- C4-a 17.68 14.60 15.53 12.46 2524.1 1373.8 1061.0 1 15pyr- C4-a 17.72 15.79 14.28 12.36 2541.2 1375.9 1053.6 4 16pyr- C1-b 17.85 15.72 15.96 13.82 2946.0 1268.1 1024.5 3fur-2E-a 17.88 14.09 11.22 7.43 2569.0 1367.3 1168.5 1 17pyr- C4-a 18.67 16.64 16.12 14.10 2543.0 1362.7 1051.7 1 18pyr- C4-a 19.05 16.61 17.32 14.88 2525.5 1361.4 1057.4 1 19pyr- C4-b 19.14 17.44 19.55 17.85 2442.5 1506.8 1144.6 4fur-4E-b 19.64 16.95 15.25 12.56 2126.1 1623.0 1241.6 20pyr-skewed-a 20.36 19.61 21.09 20.34 2379.7 1480.9 1359.9 1 21pyr- C4-a 20.50 18.43 17.17 15.11 2517.9 1381.4 1053.9 5fur-4E-b 20.53 17.28 16.51 13.26 2109.6 1635.0 1237.7 2 6fur- T1-a 20.58 16.96 14.46 10.85 2569.3 1359.0 1146.4 1 22pyr- C4-a 20.90 18.65 18.35 16.09 2518.8 1368.7 1051.8 7fur-4E-b 21.02 17.80 16.92 13.70 2101.4 1638.4 1236.4 4 23pyr- C1-a 21.84 20.94 20.72 19.82 2484.3 1517.0 1227.7 1 24pyr- C4-b 22.18 20.51 19.67 18.00 2384.9 1539.1 1151.8

8fur-E2-b 22.20 16.10 16.45 10.36 1879.4 1685.8 1131.5 9fur-2E-a 23.24 19.33 17.14 13.23 2675.1 1245.8 1029.5 25pyr-skewed-b 23.25 21.74 22.74 21.23 2853.2 1351.4 1144.9 10fur-2E-a 23.33 18.94 16.34 11.96 2819.6 1227.6 1028.2 1 11fur- T2-b 23.52 18.00 16.92 11.40 1879.4 1685.8 1131.5

12fur-E2-b 24.07 19.05 17.18 12.17 2408.9 1352.6 1035.6 1open 33.83 25.00 22.33 13.50 3823.2 816.1 711.3

a The DH(0 K) values include the harmonic zero-point energy (ZPE) corrections calculated at the M06-2X/6-311++G(d,p) level. The free energy differences (at T = 298 K and p = 1 atm), DG(298 K), were obtained by calculating the ZPE, thermal and entropic contributions with the help of the M06-2X/6-311++G(d,p) vibrational frequencies. In Table S2 (Supplementary data) the relative energies DH(0 K) and free energy differences DG(298 K) of the remaining conformers of 2-deoxy-D-ribose investigated, given in the order of increasing relative energies, can be found. b The MP2/6-311++G(d,p) results.

compares well with these two estimates. In the recent conforma- Table 3 first shows that compared to D-ribose, the seven deoxy- tional analysis of the gas phase hexoses,30 the open-chain forms ribose conformers of top stability are contained in a wider energy were also found significantly less stable than the ring structures. range of 10.9 kJ/mol. Second, the most favoured furanose of deoxyribose lies relatively low in energy at the correlated MP2 level. 4.2. 2-Deoxy-D-ribose conformers These observations reflect an important difference between the conformational energy landscapes of ribose and deoxyribose Figures 4 and 5 show the M06-2X/6-311++G(d,p) and MP2/6- caused by the presence of the OH group at C2 in the former and 311++G(d,p) calculated structures of the most stable pyranoses and the absence of this group in the latter sugar. Both the M06-2X/6- furanoses of 2-deoxy-D-ribose, with those of the remaining cyclic as 311++G(d,p) and MP2/6-311++G(d,p) calculations have found (Ta- well as open-chain isomers which lie higher in energy included in ble 3) that the lowest energy conformer of 2-deoxy-D-ribose is the 4 4 Supplementary data (Figs. S4–S6). The relative energies, DH(0 K), free a-pyranose with the C1 ring chair, 1pyr- C1-a. It is hoped that the energy differences, DG(298 K) of thirty seven most stable conformers calculated rotational constants in Table 3, especially those corre- of 2-deoxy-D-ribose and those of the lowest lying open-chain isomer sponding to the most stable isomers, may facilitate their future as predicted using the two methods are summarized in Table 3 detection in the gas phase using MW spectroscopy. (wherein they are ordered by their M06-2X relative energies). The With Table 3, the lowest-lying 2-deoxy-D-ribofuranose is the a- 2 2 MP2/6-311++G(d,p) calculated equilibrium rotational constants (A– anomer having the twist T1 ring conformation, 1fur- T1-a (Fig. 5), C) are also included in Table 3.TheDH(0 K) and DG(298 K) results similar to the lowest energy D-ribofuranose species. Figure 5 also 2 for the remaining sixty five isomers of deoxyribose can be found in shows that the second most stable furanose of deoxyribose, 2fur- T1- 2 Table S2. As for ribose, the relative stabilities of the deoxyribose iso- a, differs from 1fur- T1-a mostly by the rotation of the extracyclic mers will be discussed in terms of Gibbs free energy differences. Fig- CH2OH group. It is also of relevance to note that the most stable 41 ure 6 summarizes graphically the DG(298 K) values of all the 2- gas phase 2-deoxy-D-ribofuranose reported by Vannier et al. has deoxy-D-ribose structures calculated in this work. the envelope ring conformation (E2) and corresponds to our higher M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36 33

ΔG (298K(298K)) [k[kJ/mJ/molol]

1pyr-44C1-a 2pyr-11C4-b 3pyr-11C4-b 4pyr-11C4-a 5pyr-11C4-b 6pyr-44C1-a 7pyr-11C4-b 1fur-22T1-a FFurauranosose 8pyr-44C1-b 9pyr-44C1-b 1010pyr-44C1-b 111pyr-11C4-a 2fur-22T1-a 1212pyr-44C1-b 1313pyr-44C1-b 114pyr-11C4-a 115pyr-11C4-a 1616pyr-44C1-b 3furur-2E-a 117pyr-11C4-a 118pyr-11C4-a 1919pyr-11C4-b 4furur-4E-b 20pyryr-skewewed-a 221pyr-11C4-a 5furur-4E-b 6fur-22T1-a 222pyr-11C4-a 7furur-4E-b 223pyr-44C1-a 2424pyr-11C4-b 8furur-E2-b 9furur-2E-a 25pyryr-skewewed-b 10furur-2E-a 11fur-11 1T2-b 12furur-E2-b 13furur-2E-a 14fur-21 2T1-a 15furur-E2-b 16furur-2E-a 17fur-11 1T2-b 26pyryr-skewewed-a 18furur-4E-b 19furur-E4-a 20fur-12 1T2-b 21furur-E2-b 227pyr-11C4-a 22furur-E2-b 23furur-2E-a 24furur-4E-b 25furur-E4-a 26fur-12 1T2-b 27fur-22 2T1-a 28fur-12 1T2-b 29fur-22 2T1-a 30furur-4E-b 31furur-E4-a 32furur-4E-b 28pyryr-skewewed-b 33f3fur-C44-endoo-4E-b 229pyr-11C4-a 34furur-4E-b 35furur-E4-a 36furur-E2-b 337fur-33T2-b 38furur-4E-b 39furur-E4-a 40furur-3E-b 1o1open 2o2open OpenO en 41furur-E3-a 3o3open 42furur-4E-a 4o4open 330pyr-11C4-a 43furur-4E-b 44furur-4E-b 45furur-2E-b 46fur-14 1T2-b 5o5open 47fur-34 3T2-b 48furur-E2-b 49furur-E4-a 50fur-35 3T4-a 51furur-3E-b 52fur-15 1T2-b 53furur-2E-a 54fur-35 3T4-a 6o6open 7o7open 55fur--EO-b 56fur-25 2T1-a 57fur-O5 OT4-a 58furur-4E-b 59fur-O5 OT4-a 60furur-E4-a 8o8open 61furur-E4-a 662fur-22T3-b 9o9open 10o10open 11o11open

Figure 6. Relative Gibbs free energy DG(298 K) results for one hundred and three distinct structures of 2-deoxy-D-ribose calculated at the M06-2X/6-311++G(d,p) level (ranked in order of increasing DH(0 K) relative energy). Arrows indicate the most stable furanose and open-chain structures found. energy furanose 15fur-E2-b (Fig. S5, Table S2), lying 15.73 kJ/mol Table 4 presents the DH(0 K) and DG(298 K) results of higher 2 above 1fur- T1-a in terms of DH(0 K) at MP2/6-311++G(d,p). accuracy, at MP2/aug-cc-pVTZ and G4, for the eleven lowest energy 34 M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36

Table 4 Table 6 The relative energies, DH(0 K), and Gibbs free energy differences, DG(298 K) (kJ/mol) Natural bond orbital analysis of the endo- and exo-anomeric effects in the lowest of the eleven most stable 2-deoxy-D-ribopyranoses along with those of the three energy pyranoses of 2-deoxy-D-ribose lowest-lying 2-deoxy-D-ribofuranoses and the lowest-lying open-chain structure of 2- Conformera Orbital ð2Þ b r⁄ occupancy deoxy-D-ribose calculated at the MP2/aug-cc-pVTZ and G4 levels jDEnrj (kcal/ c hyperconjugation mol) (e) Conformer G4 (kJ/mol) MP2/aug-cc-pVTZ (kJ/mol) 4 ⁄ 1pyr- C1-a (ax) n(O5)?r (C1–O1) 16.14 0.056 DH(0 K) DG(298 K) DH(0 K) DG(298 K) n(O1)?r⁄(C1–O5) 11.79 0.051 4 2pyr-1C -b (ax) n(O5)?r⁄(C1–O1) 13.66 0.048 1pyr- C1-a 0.00 0.00 0.00 0.00 4 1 n(O1)?r⁄(C1–O5) 15.23 0.058 2pyr- C4-b 4.43 3.39 5.40 3.01 1 3pyr-1C -b (ax) n(O5)?r⁄(C1–O1) 15.64 0.053 3pyr- C4-b 7.91 6.44 9.75 6.90 4 1 n(O1)?r⁄(C1–O5) 13.67 0.053 4pyr- C4-a 7.85 6.56 8.87 6.90 1 4pyr-1C -a (eq) n(O1)?r⁄(C1–O5) 14.05 0.058 5pyr- C4-b 8.93 6.93 11.21 8.03 4 4 n(O5)?r⁄(C1–O1) 4.51 0.029 6pyr- C1-a 10.75 10.38 12.43 10.67 1 1fur-2T -a (ax) n(O4)?r⁄(C1–O1) 17.66 0.058 7pyr- C4-b 9.50 8.30 10.50 7.70 1 4 n(O1)?r⁄(C1–O4) 12.33 0.051 8pyr- C1-b 10.75 8.91 12.51 9.41 4 9pyr- C1-b 11.25 9.29 13.51 10.42 a 4 ‘ax’/‘eq’ indicates that the OH group at the anomeric C1 is oriented axially/ 10pyr- C1-b 12.17 10.54 13.14 9.92 1 equatorially. 11pyr- C4-a 11.96 10.50 13.18 10.38 b ð2Þ jDEnrj is the stabilization energy corresponding to hyperconjugation assessed 2 with the second-order perturbation theory. 1fur- T1-a 9.46 6.22 10.88 6.32 c 2 Electron occupancy of antibonding orbital. 2fur- T1-a 12.26 8.72 13.64 8.58 3fur-2E-a 13.92 10.11 15.61 10.46 1open 29.41 20.21 34.43 24.27 mination of the ionization energy of deoxyribose. Table 4 also shows that, similar to the ribose case, the most favoured open- Table 5 chain isomer of deoxyribose (1open, Fig. S6) is not thermodynam- Natural bond orbital analysis of the endo- and exo-anomeric effects in the lowest ically competitive with its low-lying cyclic forms, being 24.27 kJ/ energy pyranoses of D-ribose mol (MP2/aug-cc-pVTZ) and 20.21 kJ/mol (G4) higher in free en- Conformera Orbital ð2Þ b r⁄ occupancy 4 jDEnrj (kcal/ ergy than the global minimum 1pyr- C1-a structure. c hyperconjugation mol) (e)

1 ⁄ 1pyr- C4-b (ax) n(O5)?r (C1–O1) 14.32 0.048 4.3. Natural bond orbital analysis of the anomeric effect n(O1)?r⁄(C1–O5) 15.33 0.055 1 ⁄ 2pyr- C4-b (ax) n(O5)?r (C1–O1) 14.39 0.045 The anomeric effect refers to a stabilization of a pyranose sugar n(O1)?r⁄(C1–O5) 14.93 0.055 3pyr-1C -a (eq) n(O1)?r⁄(C1–O5) 9.70 0.048 with a chair conformation having an electronegative substituent X 4 42,43 n(O5)?r⁄(C1–O1) 4.97 0.031 (like OH group) at the anomeric C1 position. The endo-anomer- 4 ⁄ 4pyr- C1-b (eq) n(O1)?r (C1–O5) 14.23 0.051 ic effect involves interaction of the endocyclic O5 oxygen atom ⁄ n(O5)?r (C1–O1) 4.51 0.031 with the substituent X, whereas the exo-anomeric effect involves 5pyr-1C -a (eq) n(O1)?r⁄(C1–O5) 18.19 0.061 4 interaction of the exo-cyclic X substituent with O5. Currently, n(O5)?r⁄(C1–O1) 4.34 0.026 4 ⁄ one observes an ongoing discussion concerning the main origin 6pyr- C1-a (ax) n(O5)?r (C1–O1) 15.73 0.054 44 n(O1)?r⁄(C1–O5) 13.85 0.050 of the anomeric effect, with no general consensus achieved yet. 1 ⁄ 7pyr- C4-a (eq) n(O1)?r (C1–O5) 18.60 0.061 The reported explanations of this origin include hyperconjuga- n(O5)?r⁄(C1–O1) 4.35 0.027 45 ⁄ 46,47 2 ⁄ tion nO?r CX, electrostatic/steric interactions and 1fur- T1-a (ax) n(O4)?r (C1–O1) 17.71 0.054 48 n(O1)?r⁄(C1–O4) 14.24 0.050 exchange effects. Combining infra-red spectroscopy and theoretical natural bond orbital (NBO) analysis,49 Cocinero et al.43 pro- a ‘ax’/‘eq’ indicates that the OH group at the anomeric C1 is oriented axially/ vided recently the evidence that hyperconjugation is responsible equatorially. b 2 for the exo-anomeric effect in methyl D-galactopyranoside in the jDEð Þ j is the stabilization energy corresponding to hyperconjugation assessed nr 44 with the second-order perturbation theory. gas phase. Also, the recent computational study by Freitas has c Electron occupancy of antibonding orbital. demonstrated that hyperconjugation depends on the kind of substituent X at C1 and on the medium. In the following, we analyze pyranoses of deoxyribose along with those for its lowest-lying with NBO the anomeric effects in the most stable gas phase pyra- furanoses and open-chain structure. As seen, the a-pyranose nose structures of ribose and deoxyribose. 4 1pyr- C1-a is retained the global minimum deoxyribose structure, In this perturbation theory (PT) analysis of Fock matrix in NBO ð2Þ now put 3.01 kJ/mol (MP2/aug-cc-pVTZ) and 3.39 kJ/mol (G4) low- basis, the second-order energy corrections jDEij j (stabilization 1 49 er in DG than the second most stable b-pyranose 2pyr- C4-b. Inter- energies) are calculated for possible NBO i?j delocalizations. Ta- 2 ð2Þ estingly, Table 4 also indicates that the furanose 1fur- T1-a is now bles 5 and 6 summarize the relevant jDEij j values with the corre- predicted to be only 6.22 kJ/mol (MP2/aug-cc-pVTZ) and 6.32 kJ/ sponding charge transfer qi?j values calculated at the M06-2X/6- mol (G4) higher in free energy than the global minimum structure, 311++G(d,p) level for the selected pyranose conformers of D-ribose becoming actually the third most stable isomer of 2-deoxy-D-ri- and 2-deoxy-D-ribose. The ‘ax’ and ‘eq’ in Tables 5 and 6 refer to the bose in terms of DG. This pyranose–furanose energy separation is structures with the OH group occupying the axial and equatorial apparently reduced compared to the free ribose counterpart of positions, respectively. In these tables, the endo-anomeric effect 8.91 and 10.42 kJ/mol, respectively (Table 2). corresponds to the n(O5)?r⁄(C1–O1) hyperconjugative interac- Our calculated pyranose–furanose energy separation of 2- tion, whereas the exo-anomeric effect is related to the n(O1)? ⁄ deoxy-D-ribose is signiﬁcantly smaller than the value of 33.10 kJ/ r (C1–O5) hyperconjugation. mol (7.9 kcal/mol) reported recently by Ghosh et al.15 based on Table 5 shows that for the three ribopyranoses with the axially 1 the density functional xB97x/cc-pVTZ calculations (note that the oriented OH, including the global minimum structure 1pyr- C4-b, relative energy of Ghosh et al. should be directly compared with the operating endo- and exo-anomeric effects are strong and of 2 ð2Þ our DH(0 K) results for 1fur- T1 of 9.46 and 10.88 kJ/mol in Table 4). comparable magnitude in terms of the jDEnrj stabilization energy However, in Ref. 15, only a limited search of the conformational en- and the electronic orbital occupancy for the r⁄(C1–O1)/r⁄(C1–O5) ergy surface was done as the study focused primarily on the deter- orbitals. By contrast, for the four ribopyranoses with the equatori- M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36 35

Table 7 4.4. Natural bond orbital analysis of the intramolecular HB Natural bond orbital analysis of the intramolecular HB interactions in the lowest a interactions energy pyranoses of D-ribose

Conformerb Orbital interaction ð2Þ c r⁄ occupancy 49 jDEnrj In the NBO model, intramolecular H-bonded O–HO com- d (kcal/mol) (e) plex can be characterized as donor acceptor complex of 1 ⁄ 1pyr- C4-b (ax) n(O2)?r (O3–H3) 1.77 0.013 nO rOH type driven by electron delocalization from donor lone ⁄ n(O3)?r (O4–H4) 0.64 0.009 electron pair nO of one OH group into the acceptor rOH orbital n(O4)?r⁄(O2–H2) 2.48 0.015 1 ⁄ of the other OH group. 2pyr- C4-b (ax) n(O2)?r (O4–H4) 1.92 0.014 ⁄ In Tables 7 and 8 we provide NBO analysis of the intramolecular n(O3)?r (O2–H2) 0.62 0.009 n(O4)?r⁄(O3–H3) 1.98 0.013 HB interactions in the selected lowest energy pyranoses and fura- 1 e ⁄ 3pyr- C4-a (eq) n(O2) ?r (O4–H4) 1.30 0.016 noses of D-ribose and 2-deoxy-D-ribose. This analysis of the n(O2)f?r⁄(O4–H4) 2.76 0.016 nO rOH donor–acceptor interactions reflects either the strength n(O4)?r⁄(O3–H3) 0.78 0.011 or not detection of the indicated O–HO HB in these systems n(O1)?r⁄(O2–H2) [<0.5] — 4 ⁄ (within the standard cutoff for orbital interactions of 0.5 kcal/mol 4pyr- C1-b (eq) n(O3)?r (O4–H4) 0.61 0.010 n(O2)?r⁄(O3–H3) [<0.5] — used in the NBO calculations). ⁄ 1 n(O1)?r (O2–H2) [<0.5] — For the 1pyr- C4-b pyranose (Table 7), being one of the two most 1 ⁄ 5pyr- C4-a (eq) n(O2)?r (O4–H4) 1.23 0.013 stable ribose structures, the NBO analysis detects three intramolec- n(O4)?r⁄(O3–H3) 2.05 0.014 ular hydrogen bonds making a co-operative HB system, in agree- n(O2)?r⁄(O1–H1) [<0.5] — 4 e ⁄ ment with Ref. 9 Similarly, the co-operative HB network is 6pyr- C1-a (ax) n(O1) ?r (O3–H3) 3.69 0.017 f ⁄ 1 4 n(O1) ?r (O3–H3) 1.23 0.017 confirmed by this analysis for the 2pyr- C4-b, 6pyr- C1-a and n(O3)?r⁄(O2–H2) 0.61 0.010 1 4 7pyr- C4-a pyranoses. In the case of the low-energy 4pyr- C1-b pyra- ⁄ n(O3)?r (O4–H4) 1.45 0.013 ⁄ 1 ⁄ nose, the natural orbital calculation confirms the n(O3)-r (O4–H4) 7pyr- C4-a (eq) n(O2)?r (O3–H3) 1.42 0.011 n(O2)?r⁄(O1–H1) 1.12 0.013 donor–acceptor interaction, whereas the remaining two HBs associ- ⁄ ⁄ n(O3)?r⁄(O4–H4) 0.56 0.008 ated with the n(O1)-r (O2–H2) and n(O2)-r (O3–H3) interactions n(O4)e?r⁄(O2–H2) 0.55 0.017 ð2Þ (shown in Fig. 1) are indicated to have jDEnrj stabilization energies f ⁄ n(O4) ?r (O2–H2) 3.01 0.017 smaller than 0.5 kcal/mol. These two weaker HB interactions in 2 ⁄ 1fur- T1-a (ax) n(O1)?r (O2–H2) 2.14 0.014 4 ⁄ 4pyr- C -b are most likely caused by the ‘acute’ O–HO angles of n(O2)? (O3–H3) 0.81 0.010 1 r 50 n(O3)?r⁄(O1–H1) 2.12 0.014 104.7° and 107.6° in these H-bonds. Our NBO calculations also confirmed the existence of the cooperative arrangement of three a This NBO analysis of the n r donor–acceptor interactions reflects either O OH O–HO bonds in the lowest energy ribofuranose, 1fur-2T -a, involv- the strength or not detection of the indicated O–HO HB in these pyranose 1 isomers. ing the OH groups attached to the C1, C2, and C3 ring carbons. b ‘ax’/‘eq’ indicates that the OH group at the anomeric C1 is oriented axially/ In 2-deoxy-D-ribose, the missing OH group at C2 precludes its equatorially. involvement in hydrogen bonding, and consequently, the number c jDEð2Þ j is the stabilization energy corresponding to n r donor–acceptor nr O OH of intramolecular H-bonds formed in this molecule is effectively interaction assessed with the second-order perturbation theory. The [<0.5] bracket ð2Þ reduced compared to those in D-ribose. Yet, the lowest energy indicates that the jDE j value is smaller than 0.5 kcal/mol (the latter is the stan- nr 4 2 dard cutoff for the orbital interactions used in the NBO calculations). deoxyribopyranose 1pyr- C1-a and deoxyribofuranose 1fur- T1-a d Electron occupancy of antibonding orbital. e Lone pair (1). Table 8 f Lone pair (2). Natural bond orbital analysis of the intramolecular HB interactions in the lowest a energy pyranoses of 2-deoxy-D-ribose

Conformerb Orbital interaction ð2Þ c r⁄ occupancy jDEnrj (kcal/ d 4 mol) (e) ally positioned OH, including the 4pyr- C1-b isomer, the exo-ano- 4 e ⁄ meric effect is the most significant, with the endo-anomeric contri- 1pyr- C1-a n(O1) ?r (O3– 3.20 0.015 bution being much smaller, both in terms of jDEð2Þ j and the (ax) H3) 1.36 0.015 nr n(O1)f?r⁄(O3– 1.44 0.014 electronic orbital occupancy for the relevant antibonding orbital. H3) Although the original definition of the anomeric effect concerns n(O3)?r⁄(O4–H4) 42,43 1 ⁄ six-membered sugar rings Table 5 shows that the two types 2pyr- C4-b n(O4)?r (O3–H3) 0.93 0.011 ⁄ of hyperconjugative interaction are also present in the lowest-lying (ax) n(O5)?r (O4–H4) 0.60 0.011 1 ⁄ 2 3pyr- C4-b n(O3)?r (O4–H4) [<0.5] — (five-membered ring) furanose 1fur- T1-a having the axially ori- 2 (ax) ented OH at C1. In the 1fur- T -a structure, the endo-anomeric ef- 1 ⁄ 1 4pyr- C4-a n(O4)?r (O3–H3) 0.97 0.012 fect involves the O4 ring atom and is associated with the (eq) n(O5)?r⁄(O4–H4) 0.67 0.011 ⁄ 2 e ⁄ n(O4)?r (C1–O1) hyperconjugative interaction, whereas the exo- 1fur- T1-a (ax) n(O1) ?r (O3– 1.18 0.011 H3) 0.89 0.007 anomeric effect, involving O1 lone pair, corresponds to the f ⁄ ⁄ n(O1) ?r (O3– [<0.5] — n(O1)?r (C1–O4) hyperconjugation. H3) The similar considerations generally apply to the lowest energy n(O4)?r⁄(O5–H5) pyranoses and furanoses of 2-deoxy-D-ribose (Table 6). However, a This NBO analysis of the n r donor–acceptor interactions reflects either for the deoxyribose species with the axially oriented OH at C1, O OH the strength or not detection of the indicated O–HO HB in these pyranose either the endo-orexo-anomeric contribution is somewhat greater, isomers. depending on the conformer, especially in terms of the second-or- b ‘ax’/‘eq’ indicates that the OH group at the anomeric C1 is oriented axially/ 1 equatorially. der PT energy. The ‘equatorial’ species 4pyr- C4-a exhibits again the c jDEð2Þ j is the stabilization energy corresponding to n r donor–acceptor significant exo-anomeric effect, however with the much smaller nr O OH interaction assessed with the second-order perturbation theory. The [<0.5] bracket endo-anomeric contribution. Both endo-anomeric interaction indicates that the jDEð2Þ j value is smaller than 0.5 kcal/mol (the latter is the stan- ⁄ ⁄ nr n(O4)!r (C1–O1) and exo-anomeric interaction n(O1)!r dard cutoff for the orbital interactions used in the NBO calculations). d (C1–O4) present in the lowest-lying 2-deoxy-D-ribofuranose Electron occupancy of antibonding orbital. 2 e Lone pair (1). (1fur- T1-a)(Table 6) are of very similar magnitude to those seen f Lone pair (2). in the D-ribofuranose counterpart (Table 5). 36 M. Szczepaniak, J. Moc / Carbohydrate Research 384 (2014) 20–36 exhibit two and one HB interactions, respectively, as supported by Acknowledgements the NBO results in Table 8. Interestingly, second-order perturbative analysis in this table shows the involvement of the O5 ring lone Both reviewers are thanked for their helpful suggestions and re- 1 1 pair in the formation of the HB in the 2pyr- C4-b and 4pyr- C4-a marks. The authors acknowledge a generous support of computer pyranose structures (not shown explicitly in Fig. 4). However, the time at the Wroclaw Center for Networking and Supercomputing, H-bonding comprising the ring oxygen O4 in the deoxyribofura- WCSS. 2 ⁄ nose 1fur- T1-a associated with the n(O4)-r (O5–H5) interaction is not confirmed. Supplementary data

Supplementary data associated with this article can be found, in 5. Conclusions the online version, at http://dx.doi.org/10.1016/j.carres.2013.10.013. Using computational methods, we have probed the conforma- References tional space of two pentoses of biological and potential astrobiological importance, D-ribose and 2-deoxy-D-ribose, including a- and 1. Moran, L. A.; Scrimgeour, K. G.; Horton, H. R.; Ochs, R. S.; Rawn, J. D. b-pyranoses, a- and b-furanoses and open-chain structures. Our Biochemistry, 2nd ed.; Neil Patterson/Prentice-Hall: Englewood Cliffs, NJ, 1994. study revealed a multitude of existing minima structures. Numerous 2. Levitt, M.; Warshel, A. J. Am. Chem. Soc. 1978, 100, 2607–2613. 3. Rudrum, M.; Shaw, D. F. J. Chem. Soc. 1965, 52–57. furanose conformers found are described with the Altona and Sun- 4. Lemieux, R. U.; Stevens, J. D. Can. J. Chem. 1966, 44, 249–262. daralingam pseudorotation parameters. In agreement with the re- 5. Breitmaier, E.; Hollstein, U. Org. Magn. Reson. 1976, 8, 573–575. cent gas-phase MW investigation of Cocinero et al.,9 the two most 6. Lemieux, R. U.; Anderson, L.; Conner, A. H. Carbohydr. Res. 1971, 20, 59–72. stable free ribose isomers predicted here are the b-pyranoses with 7. Irvine, W. M.; Brown, R. D.; Cragg, D. M.; Friberg, P.; Godfrey, P. D.; Kaifu, N.; Matthews, H. E.; Ohishi, M.; Suzuki, H.; Takeo, H. Astrophys. J. 1988, 335, L89. 1 4 the C4 and C1 ring chair conformations. Both b-pyranoses lie within 8. Orgel, L. E. Crit. Rev. Biochem. Mol. Biol. 2004, 39, 99–123. 0.9 kJ/mol in terms of DG(298 K), thus challenge the computational 9. Cocinero, E. J.; Lesarri, A.; Écija, P.; Basterretxea, F. J.; Grabow, J.-U.; Fernández, methods used to predict the free ribose global minimum. At the G4 J. A.; Castaño, F. Angew. Chem., Int. Ed. 2012, 51, 3119–3124. 10. Sisak, D.; McCusker, L. B.; Zandomeneghi, G.; Meier, B. H.; Bläser, D.; Boese, R.; level, the seven lowest energy ribopyranoses are within 4.2 kJ/mol of Schweizer, W. B.; Gilmour, R.; Dunitz, J. D. Angew. Chem., Int. Ed. 2010, 49, the global minimum. The predicted most favorable ribofuranose is 4503–4505. the a-anomer with the twist 2T ring conformation, being 10.4 kJ/ 11. Furberg, S.; Hordvik, A.; Taulbøl, K. Acta Chem. Scand. 1956, 10, 135–136. 1 12. Saenger, W. Angew. Chem., Int. Ed. 2010, 49, 6487–6489. mol higher in free energy than the global minimum. 13. Furberg, S. Acta Chem. Scand. 1960, 14, 1357–1363. By contrast with D-ribose, the calculated most stable isomer of 14. Guler, L. P.; Yu, Y.-Q.; Kenttämaa, H. I. J. Phys. Chem. A 2002, 106, 6754–6764. 15. Ghosh, D.; Golan, A.; Takahashi, L. K.; Krylov, A. I.; Ahmed, M. J. Phys. Chem. Lett. free 2-deoxy-D-ribose is the a-pyranose, whose most favoured 2012, 3, 97–101. furanose structure (the a-anomer) is only 6.2 kJ/mol less stable 16. Mayorkas, N.; Rudic, S.; Davies, B. G.; Simons, J. P. Chem. Sci. 2011, 2, 1128–1134. (in DG). Additionally, we have reported the equilibrium rotational 17. Mayorkas, N.; Rudic, S.; Cocinero, E. J.; Davies, B. G.; Simons, J. P. Phys. Chem. constants for the lowest energy structures of the two sugars, which Chem. Phys. 2011, 13, 18671–18678. 18. Cocinero, E. J.; Stanca-Kaposta, E. C.; Scanlan, E. M.; Gamblin, D. P.; Davis, B. G.; can be useful for their future spectroscopic detection in the gas Simons, J. P. Chem. Eur. J. 2008, 14, 8947–8955. phase, especially deoxyribose species. For the two pentoses, the 19. Allinger, N. L.; Yuh, Y. H.; Lii, J. H. J. Am. Chem. Soc. 1989, 111, 8551–8566. open-chain isomers lie significantly higher in energy than the 20. Lii, J. H.; Allinger, N. L. J. Am. Chem. Soc. 1989, 111, 8576–8582. low-lying cyclic species. A good overall agreement is observed be- 21. Allinger, N. L.; Li, F. B.; Yan, L. Q.; Tai, J. C. J. Comput. Chem. 1990, 11, 868–895. 22. Fujitsu Limited, Scigress (http://www.fqs.pl). tween the M06-2X/6-311++G(d,p) and MP2/6-311++G(d,p) results 23. Stortz, C. A.; Johnson, G. P.; French, A. D.; Csonka, G. I. Carbohydr. Res. 2009, 344, in terms of both the existing low-energy minima structures and 2217–2228. intramolecular H-bonding geometrical parameters. The natural 24. Ma, B.; Schaefer, H. F. III.; Allinger, N. L. J. Am. Chem. Soc. 1998, 120, 3411–3422. 25. Simeon, T. M.; Ratner, M. A.; Schatz, G. C. J. Phys. Chem. A 2013, 117, 7918–7927. orbital analysis confirms the occurence of the endo- and exo-ano- 26. Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, 215–241. meric effects and maximization of intramolecular H-bonding in 27. Møller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618–622. the lowest-lying pyranoses and furanoses of both sugars. 28. Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650–654. 29. Frisch, M. J. et al GAUSSIAN 09 Revision C.01; GAUSSIAN: Wallingford, CT, 2010. In summary, the furanose forms of D-ribose and 2-deoxy-D-ribose 30. Sameera, W. M. C.; Pantazis, D. A. J. Chem. Theory Comput. 2012, 8, 2630–2645. are known to be constituents of many compounds that are essential 31. Lii, J. H.; Ma, B.; Allinger, N. L. J. Comput. Chem. 1999, 20, 1593–1603. for life such as DNA, RNA, ATP etc. In the gas phase, however, the 32. Wheeler, S. E.; Houk, K. N. J. Chem. Theory Comput. 2010, 6, 395–404. 33. Dunning, T. H. J. Chem. Phys. 1989, 90, 1007–1023. pyranose forms are energetically more favoured for both sugars. 34. Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. J. Chem. Phys. 2007, 126, 084108. 35. Moc, J.; Simmie, J. M. J. Phys. Chem. A 2010, 114, 5558–5564. Note added in the proof 36. Moc, J.; Simmie, J. M.; Curran, H. J. J. Mol. Struct. 2009, 928, 149–157. 37. Zhurko G. A.; Zhurko D. A. Chemcraft (http://www.chemcraft.prog.com). 38. Taha, H. A.; Richards, M. R.; Lowary, T. L. Chem. Rev. 2013, 113, 1851–1876. After accepting our work for publication, the paper by Peña 39. Altona, C.; Sundaralingam, M. J. Am. Chem. Soc. 1972, 94, 8205–8212. et al.51 appeared. By using Fourier-transform microwave spectros- 40. Jalbout, A. F.; Adamowicz, L.; Ziurys, L. M. Chem. Phys. 2006, 328, 1–7. 41. Vannier, L. A.; Yao, C.; Turecek, F. Collect. Czech. Chem. Commun. 2005, 70, 1769– copy and laser ablation methods combined with quantum-mechan- 1786. ical calculations, these authors identified two a- and four b- 42. Juaristi, E.; Cuevas, G. The Anomeric Effect; CRC Press: Boca Raton, FL, 1995. pyranose conformers of 2-deoxy-D-ribose. Among these conform- 43. Cocinero, E. J.; Carcabal, P.; Vaden, T. D.; Simons, J. P.; Davis, D. G. Nature 2011, 469, 76–80. ers there are five low-energy structures which have been reported 44. Freitas, M. P. Org. Biomol. Chem. 2013, 11, 2885–2889. in our work as inferred by comparing both the geometrical struc- 45. Salzner, U.; Schleyer, P. V. R. J. Org. Chem. 1994, 59, 2138–2155. tures (Figure 4) and the MP2 rotational constants (Table 3) with 46. Mo, Y. Nat. Chem. 2010, 2, 666–671. 51 47. Huang, Y.; Zhong, A.-G.; Yang, Q.; Liu, S. J. Chem. Phys. 2011, 134, 084103–084109. those provided by Peña et al. The following correspondence exists 48. Bauerfeldt, G. F.; Cardoo, T. M.; Pereira, M. S.; da Silva, C. S. Org. Biomol. Chem. between our predicted 2-deoxy-D-ribose structures and the MW 2013, 11, 299–308. detected ones (the Ref.51 designations are given within the paren- 49. Weinhold, F.; Landis, C. R. Valency and Bonding: A Natural Bond Orbital Donor– 4 1 1 Acceptor Perspective; Cambridge University Press, 2005. theses): 1pyr- C1-a (Rotamer V), 2pyr- C4-b (Rotamer I), 3pyr- C4-b 50. Azofra, L. M.; Alkorta, I.; Elguero, J.; Popelier, P. L. A. Carbohydr. Res. 2012, 358, 4 4 (Rotamer II), 8pyr- C1-b (Rotamer III), 9pyr- C1-b (Rotamer IV). 96–105. 4 Based on the MP2 rotational constants alone, our 6pyr- C1-a 51. Peña, I.; Cocinero, E. J.; Cabezas, C.; Lesarri, A.; Mata, S.; Écija, P.; Daly, A. M.; matches Rotamer VI in Ref.51, but the latter was assigned by Peña Cimas, Á.; Bermúdez, C.; Basterretxea, F. J.; Blanco, S.; Fernández, J. A.; López, J. C.; Castaño, F.; Alonso, J. L. Angew. Chem. Int. Ed. 2013, 52, 11840–11845. et al. to the other (4C1) b-pyranose form.