Tautomers of Gas-Phase Erythrose and Their Interconversion

Article pubs.acs.org/JPCA

Tautomers of Gas-Phase Erythrose and Their Interconversion Reactions: Insights from High-Level ab Initio Study Marek Szczepaniak and Jerzy Moc* Faculty of Chemistry, Wroclaw University, F. Joliot-Curie 14, 50-383 Wroclaw, Poland S Supporting Information *

ABSTRACT: D-Erythrose is a C4 monosaccharide with a biological and potential astrobiological relevance. We have investigated low-energy structures of D-erythrose and their interconversion in the gas phase with the highest-level calculations up-to-date. We have identified a number of structurally distinct furanose and open-chain isomers and predicted α ↔ α and β ↔ β furanose interconversion pathways involving the O−H rotamers. We have estimated relative Gibbs free energies of the erythrose species based on the CCSD(T)/aug-cc-pVTZ electronic energies and MP2/aug-cc-pVTZ vibrational frequencies. By using natural bond orbital theory we have also quantified a stabilization of erythrose conformers and interconversion transition states by intramolecular H-bonds.

Scheme 1. Tautomers of D-Erythrose

1. INTRODUCTION Carbohydrates play a key role in all ecosystems, being one of the four basic classes of biomolecules determining life on Earth. They are involved in production, energy storage, and building of cell structures in living systems, and are part of their genetic material.1 The simplest carbohydrates are monosaccharides, whose low-energy conformations can be reliably predicted by suitably chosen computational methods.2 Theoretical conformational studies appeared for glucose,3−10 fructose,11−18 ribose,19,20 deoxyribose,20,21 and erythrose.22−24 The availability of high-accuracy structural and spectroscopic data for gas-phase C4 and C5 monosaccharides is a prerequisite for their possible detection in space.25−30 D-Erythrose, C4 monosaccharide, belongs to aldotetroses and its biological relevance is evident by these examples. It is used as a carbon source by Alcaligenes Faecalis,31 and in the plant kingdom, it has been discovered as one of the product species in the Calvin regeneration phase cycle.32 When administered orally to rats, this monosaccharide is oxidized to carbon dioxide and water.33 In humans, as the erythrose-4-phosphate, it is involved in metabolic phosphogluconate pathway.34 Anticancer properties of erythrose have been examined by Wang and Wei35 and Liu et al.36 who observed that an administered dose of this sugar decreased viability or inhibited growth of cancer cells. The equilibrium percentage concentration ratio of the α-furanose to the β-furanose to the open-chain tautomers of 37,38 D-erythrose in water solution was determined with NMR spectroscopy to be 2:5.4:1, indicating the presence of the three tautomers (Scheme 1). In contrast to D-ribose39 and 40 D-fructose, no crystal structure of D-erythrose is available. In the first ever gas-phase study of D-erythrose of Cabezas et al.,22 two furanose structures were identified with Fourier transform microwave (FTMW) spectroscopy and assigned. It should be © 2015 American Chemical Society

noted that spectroscopic methods can not, in general, provide conformers’ relative energies,41 although as mentioned by one of the reviewers, with the FTMW technique one can assess these relative energies at least from a qualitative point of view. Aviles-Moreno and Huet explored a D-erythrose conformational space by using B3LYP density functional, which study revealed 14 low-energy open-chain conformers.23 In addition, they provided simulated infrared (IR) spectra and G3MP2B3 relative energies of these structures.23 Azofra et al.24 optimized about 200 D-erythrose geometries at the B3LYP level, the vast majority (174) were open-chain conformers. These authors also refined the energetics of the low-energy acyclic and cyclic erythrose structures found using the G3B3 method. In this context, we mention however the inadequacy of the B3LYP functional for evaluating the relative stability of the cyclic and acyclic monosaccharide conformers pointed out recently2 (in section 4.1, we will refer to the ab initio results for erythrose of Cabezas et al.22). None of the computational studies of D-erythrose have examined thoroughly both furanose and openchain tautomers at the high ab initio level to pinpoint their relative energies, including those of respective isomerization transition states. Received: August 8, 2015 Revised: October 8, 2015 Published: October 9, 2015 10946

DOI: 10.1021/acs.jpca.5b07720 J. Phys. Chem. A 2015, 119, 10946−10958

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The Journal of Physical Chemistry A

frequencies.58 To our knowledge, the current structural and energetic properties are established by the most accurate ab initio methodology applied for erythrose so far. Finally, donor−acceptor interactions are analyzed with natural bond orbital (NBO)59,60 theory, with second-order stabilization energy ΔEij(2) and corresponding charge transfer from a donor orbital (i) to an acceptor orbital (j). All calculations were performed using the Gaussian 0961 and Molpro62 software packages.

The current high-level ab initio investigation of D-erythrose in the gas phase is therefore aimed at (i) an exhaustive searching of the conformational space to identify the low-energy isomers, (ii) predicting reaction paths for interconversions of the most stable conformers to assess the ease of their transformation. To achieve these goals we use second-order perturbation and coupled cluster theories with a large basis set (described in section 2) to characterize the most relevant stationary points and to estimate their relative Gibbs free energies.

3. LABELING OF CYCLIC CONFORMERS In the furanose (f ur) and open-chain (open) conformers of D-erythrose we used the atom numbering shown in Scheme 2. A furanose ring is known to be flexible,42 and Schemes 3 and 4

2. CONFORMATIONAL SEARCH AND COMPUTATIONAL METHODS A conformational searching of D-erythrose is complex because of (i) the existence of different tautomers (Scheme 1), (ii) the puckering of furanose42,43 rings and the presence of six rotatable bonds in the open-chain structures (cf. Scheme 2), (iii) the

Scheme 3. Ten Twist (T) Furanose Ring Puckerings (the Ring Plane Is Indicated by the Three Atoms Marked with Asterisks)

Scheme 2. Atom Numbering Used in the Furanose and Open-Chain Structures of Erythrose

possible multiple orientations of −OH groups (the existence of O−H rotamers), and (iv) the occurrence of intramolecular H-bonds (see below). The quest for the low-energy erythrose conformers was first carried out with the M06-2X density functional44 and basis set 6-311++G(d,p),45,46 based on the strong performance of this approach demonstrated for the C5 and C6 monosaccharides.2,11,20 The initial set of conformations considered comprised 2062 geometries and included both cyclic (α- and β-furanoses) and acyclic structures. It was generated using our homemade program and Scigress code,47 with all the rotatable bonds (open-chain structures) and 20 ring conformations for the furanose structures (described in section 3) taken into account. The M06-2X/6-311++G(d,p) geometry optimizations of these structures were next performed with ultraf ine numeric grid48 and tight optimization criteria, and those which collapsed to the same conformers were identified and removed. Finally, the 26 lowest-energy structures were selected from the M06-2X pursuit after applying a cutoff at about 25 kJ/mol and reoptimized tightly using second-order Møller−Plesset perturbation theory (MP2)49 with the larger aug-cc-pVTZ basis set.50 Simultaneously with identifying a set of the low-energy minima, we also located interconversion transition states (TSs) to estimate kinetic barriers separating the energetically closelying O−H rotamers. Local minima and TSs were confirmed by analysis of the Hessian eigenvalues. Connectivity of the TSs with the correct minima was ascertained by determining the intrinsic reaction coordinate (IRC).51,52 Throughout this work, relative energies are given in terms of relative enthalpies at 0 K, ΔH(0K) and relative Gibbs free energies at 298 K (p = 1 atm), ΔG(298 K), based especially on the CCSD(T)/aug-cc-pVTZ electronic energies (calculated using coupled-cluster theory with singles and doubles with perturbatively included triples53−57 and basis set aug-cc-pVTZ,50 CCSD(T)//MP2 level), and MP2/aug-cc-pVTZ vibrational

Scheme 4. Ten Envelope (E) Furanose Ring Puckerings (the Ring Plane Is Indicated by the Four Atoms Marked with Asterisks)

depict possible twist (T) and envelope (E) furanose ring puckerings, respectively. For example, 3E (E3) refers to the envelope conformation with carbon C3 above (below) the ring plane, whereas 2T3 (3T2) refers to the twist conformation with carbon C2(C3) above and carbon C3(C2) below the ring plane, and so on.42 To determine a furanose puckering conformation, we employed the pseudorotational phase angle P42,63 (for the formula used and a graphical illustration of the dependence of the furanose conformation on the P values, the pseudorotational wheel (PW), see SI). In our notation, α and β anomers are indicated as “a” and “b”, and clockwise and counterclockwise arrangements of intramolecular H-bonds are abbreviated as “c” and “cc”, respectively. 10947


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Figure 1. continued

10948


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Figure 1. MP2/aug-cc-pVTZ optimized structures of the lowest-energy α- and β-furanoses of D-erythrose, with HB distances (in Å) highlighted.

the −O1H1 group, with the H1−O1−C1−C2 dihedral angle (DA) of −178.9° and 63.3°, respectively, which enables formation of the O1−H1···O3 HB only in the former. The geometries of 2fur-2T1-a-c and 5fur-2T1-a-c differ by rotation of the −O1H1 group, the respective DA values are 177.2° and −58.4°. This causes similarly that the O1−H1···O2 HB occurs solely in the second conformer of the two, but results otherwise in a relatively minor variation in their rotational constants. In turn, on passing from the conformer 2fur-2T1-a-c to the 4fur-OT1-a-cc one, the −O2H2 group reorients in such a way that this alters its role from a proton donor to proton acceptor, respectively. From these structural relations follows that possible interconversions between the low-energy α-erythrofuranose −OH rotamers will result in breaking/reshaping of the intramolecular H-bonds. In section 4.4 we will examine the actual interconversion paths involving these rotamers. The most stable β-furanose conformer predicted by us is 6fur-1E-b-cc, placed 8.86 kJ/mol higher in free energy than the global minimum (Table 1). A good match between the MP2/aug-cc-pVTZ computed and spectroscopic data (with the theoretical rotational constants larger by 19−25 MHz) supports the original assignment of the experimentally identified species.22 In fact, the relevant “Rotamer B” was assigned22 to the furanose conformer β-1T2-cc having the different 1T2 puckering than that in the 6fur-1E-b-cc structure. We will attempt to explain this discrepancy below. As evident from Figure 3, we actually discovered a “cluster” of the low-energy β-anomers consisting of seven E type conformers, with the free energies within 1.22 (10.08) kJ/mol of the 6fur-1E-b-cc (global minimum). In summary, we agree with Cabezas et al.22 as to the identity of the erythrose global minimum. Yet, the calculated ring conformation of our second most stable furanose structure

4. RESULTS AND DISCUSSION The lowest-energy structures of D-erythrose optimized at the MP2/aug-cc-pVTZ level are depicted in Figure 1 (furanoses) and Figure 2 (chains). Both figures highlight intramolecular hydrogen bonds (HBs) formed by the adjacent −OH groups. The associated relative energies are collected in Table 1 that also lists the equilibrium rotational constants and electric dipole moment components. The relative free energies of the cyclic and chain erythrose structures are summarized graphically in Figure 3. Unless noted otherwise, the relative free energies we discuss below are based on the CCSD(T)/aug-cc-pVTZ electronic energies and MP2/aug-cc-pVTZ vibrational frequencies. 4.1. Lowest-Energy Erythrofuranoses. We find the 17 (MP2) and 14 (CCSD(T)//MP2) most stable structures of D-erythrose to be furanoses (Table 1). At both ab initio levels, the predicted global minimum is 1fur-2E-a-cc with the envelope 2 E conformation. The five lowest-energy structures are actually α-anomers, with the free energies within 5.59 kJ/mol of the global minimum. Significantly, 1fur-2E-a-cc corresponds to the first D-erythrose structure observed in the MW experiment (“Rotamer A”), assigned therein to the α-furanose labeled α-2E-cc.22 Indeed, a close (although not ideal) match between our MP2/aug-cc-pVTZ calculated and experimental spectroscopic parameters (with the theoretical rotational constants larger by 3−40 MHz) lends support to the original assignment. Even though we found some other low-energy α-furanose structures having significant dipole moment components (Table 1), they have apparently not been MW detected. Table 1 further reveals that rotational constants A and B calculated for the structures 1fur-2E-a-cc and 4fur-OT1-a-cc are essentially the same, yet their C constants are distinctive. These conformers exhibit significantly different orientations of 10949


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Figure 2. MP2/aug-cc-pVTZ optimized structures of the lowest-energy open-chains of D-erythrose, with HB distances (in Å) and the C1−C2−C3−C4 dihedral angles (in degrees) highlighted.

2fur-2T1-a-c seemingly differs from the α-2E-c counterpart22 obtained from the MP2/6-311++G(d,p) calculations, and the same concerns the 3fur-E4-a-cc structure (the ref 22 analogue is α-3T4-cc) and the lowest-energy β-anomer. To explain this problem, we reoptimized the furanose structures in question at their22 MP2/6-311++G(d,p) level, starting from our MP2/aug-cc-pVTZ optimized geometries. For 2fur-2T1-a-c, this did not change the puckering conformation, yet we arrived otherwise at the “structure” of the authors in ref 22, based on the perfect agreement between the MP2/ 6-311++G(d,p) computed spectroscopic parameters found in both works. Moreover, our 3fur-E4-a-cc and 6fur-1E-b-cc conformers converged exactly to those of ref 22. This result agrees with observation of Cramer et al.64 that the predicted furanose ring puckering is sensitive to the level of theory (note that the 2T1 adjoins the 2E on the PW, and the same holds true for the E4 and 3 T4, and the 1E and 1T2 conformational pairs, see SI).

4.2. Chain Conformers. We now address the relative energies of the open-chain erythrose structures. In terms of ΔH(0K) (Table 1), the two most stable structures are 1open and 2open (Figure 2) that are separated by 1.65 kJ/mol, with the former being favored. However, when the difference in free energies ΔG(298 K) is considered, this energy gap decreases to 0.40 kJ/mol. This is caused by the thermochemical effect, mostly the entropy (Figure 4). Indeed, to maximize the H-bonding effect, the 1open assumes the gauche-like orientation of the C1−C2−C3−C4 chain (see section 4.3), with the dihedral angle of −51.3°. This DA is in a good agreement with the B3LYP results.23,24 The gauche-like oriented C4 chain makes the entropy of the structure 1open lower compared to that in the 2open form (Figure 4) as the latter adopts the more “relaxed” trans-like C4 open chain. Figure 4 also shows that all the open-chain erythrose conformers are entropically65 favored at T = 298.15 K relative to the cyclic 10950


10951

0.00

3.07 6.22 7.45 6.53 9.60

9.53 10.90 13.34 11.38 12.66 9.92 12.71 13.95 14.25 15.22 11.74 18.02 19.92 15.79 20.51 21.08 21.83 24.75 21.49 23.44

1fur-2E-a-cc

2fur-2T1-a-c 3fur-E4-a-cc 4fur-OT1-a-cc 5fur-2T1-a-c 6fur-1E-b-cc

7fur-4E-b-c 8fur-E2-b-c 9fur-E3-b-cc 10fur-E2-b-cc 11fur-EO-b-c 12fur-2T3-a-c 13fur-E2-b-c 14fur-E4-a-c 15fur-3T4-a-c 16fur-4E-b-c 17fur-4TO-a-c 1open 2open 18fur-2E-b-cc 3open 4open 5open 6open 19fur-1E-a-c 20fur-2E-b-c

9.12 9.24 9.27 9.43 9.64 9.76 9.82 11.43 11.68 12.03 12.09 13.09 13.74 14.21 14.84 14.99 16.03 18.14 20.63 20.76

2.88 4.48 5.60 5.99 8.86

0.00

ΔG(298 K) [kJ/mol] 2626.00 [2586.9010(11)] 2641.75 3281.13 2623.20 2659.35 3134.49 [3109.2009(98)] 2996.92 3160.97 2823.80 3136.37 3137.80 2607.63 3157.11 3226.75 3360.53 3013.64 2841.53 2890.54 3663.82 2800.35 3739.38 4209.18 4218.60 3117.83 3565.00 2789.44

A [MHz] 2355.66 [2353.0907(14)] 2271.17 2005.93 2358.42 2319.72 1874.82 [1856.1295(11)] 2094.74 1829.50 2161.77 1817.39 1968.59 2301.03 1822.58 2027.14 1969.97 2068.22 2278.08 1694.75 1351.62 2155.90 1337.32 1194.18 1184.99 1586.97 1856.94 2144.63

B [MHz]

rotational contantsb

1796.36 [1773.23221(65)] 1820.11 1456.98 1659.21 1807.64 1639.52 [1616.55508(98)] 1478.05 1603.51 1432.22 1603.01 1511.62 1822.02 1604.00 1463.36 1446.49 1454.59 1584.85 1339.55 1100.61 1422.98 1103.55 992.365 986.082 1178.02 1445.83 1423.45

C [MHz]

9.73 11.05 13.58 11.45 12.19 10.14 12.96 13.82 14.39 15.24 12.33 16.25 17.90 15.71 18.90 19.35 19.76 21.87 21.11 23.02

3.20 6.19 6.91 6.13 9.60

0.00

ΔH(0K) [kJ/mol]

9.33 9.39 9.51 9.50 9.17 9.98 10.08 11.31 11.82 12.06 12.68 11.33 11.73 14.13 13.24 13.26 13.96 15.25 20.25 20.35

3.01 4.45 5.07 5.59 8.86

0.00

ΔG(298 K) [kJ/mol]

CCSD(T)/aug-cc-pVTZ//MP2c μa [D]

−2.0914 2.6375 −1.5087 0.1135 2.2160 [observed] −0.6748 0.6685 −1.0399 −1.5498 −0.3277 2.8121 0.9209 −4.3624 −4.3859 1.1488 2.4938 1.1331 1.1320 −0.0859 3.5208 −3.0720 −1.8871 −0.6065 −0.5201 3.7200

0.3027

−2.1913 −0.8300 1.1068 1.7955 −0.6825 −2.6491 −2.1904 −0.2932 0.7485 −2.9775 −0.1908 −1.0925 −0.2643 0.8482 −0.1760 −0.1727 0.1200 1.2296 −0.0476 −2.0268

μc [D] −1.2367 [observed] 0.0703 0.2721 −0.6228 −1.0484 0.9741 [observed] −0.1647 2.2823 0.7534 −0.6450 0.9276 −0.2787 1.4014 2.0196 0.6255 0.8440 1.7531 −2.0672 −0.5930 2.5158 −0.2351 1.3431 −0.4045 0.0415 0.7505 1.8131

μb [D] −1.7480 [observed] −0.3605 0.6772 −0.4853 0.6706 −0.0565

dipole momente

Based on the MP2/aug-cc-pVTZ electronic energies and MP2/aug-cc-pVTZ vibrational frequencies. bThe MP2/aug-cc-pVTZ results; the values in brackets are taken from the MW study (ref 22). cAt the MP2/aug-cc-pVTZ optimized geometries; based on the CCSD(T)/aug-cc-pVTZ electronic energies and MP2/aug-cc-pVTZ vibrational frequencies. dRanked in order of increasing MP2 free energy (see footnote “a”). eThe MP2/aug-cc-pVTZ results; the annotation “[observed]” refers to the MW experiment (ref 22).

a

ΔH(0K) [kJ/mol]

conformerd

MP2/aug-cc-pVTZa

Table 1. Relative Energies, Equilibrium Rotational Constants, and Dipole Moment Components of the Low-Energy Furanose and Open-Chain Structures of D-Erythrose Calculated at the MP2 and CCSD(T)//MP2 Levels

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Figure 3. Relative Gibbs free energies (in kJ/mol, at T = 298 K) of the 26 lowest-energy structures of D-erythrose compared to global minimum, based on the MP2/aug-cc-pVTZ electronic energies and MP2/aug-cc-pVTZ vibrational frequencies.

Figure 4. Comparison of the entropic contributions (−TS) (in kJ/mol, at T = 298 K) to the free energy of the cyclic and open-chain conformers of D-erythrose.

that the open-chain erythrose structures found are placed at least 11.33 kJ/mol higher in free energy than the global minimum. 4.3. Intramolecular H-Bonds Analyzed with NBO. To quantify a stabilization of the low-energy D-erythrose structures by intramolecular O(i)...H−O(j) H-bonds, we describe them by

structures. The similar example was provided recently by Shubert et al.66 who observed that, upon inclusion of the entropy contribution (at T = 450 K), the “extended-chain” conformers of O-(2-acetamidoethyl)-N-acetyltyramine (OANAT) were stabilized with respect to the H-bonded structures. Table 1 indicates 10952


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Figure 5. Localized orbitals involved in the (a) nO3 → σ*O1−H1 and nO1 → σ*O2−H2 H-bond interactions in 1fur-2E-a-cc and those involved in the (b) nO4 → σ*O2−H2 and nO2 → σ*O3−H3 H-bond interactions in 6fur-1E-b-cc.

of 0.017 e. The low-energy α-furanose structure 3fur-E4-a-cc features the O1···H2−O2···H3−O3 HB chain, with the nO1 → σ*O2−H2 interaction shown by NBO to be predominating, as coupled with the short H-bond distance of 1.875 Å (Figure 1). Both the geometric and NBO data support the existence of a cyclic network of three H-bonds also in the conformer 5f ur-2T1-a-c, with their individual strengths (in terms of the second-order energy and charge transfer, Table S1) being similar to those in 1fur-2E-a-cc. So, why is the former not a global minimum of erythrose instead of the 1fur-2E-a-cc structure? The answer could possibly be obtained by comparing a stabilization by the nO4 → σ*C1−O1 and nO1 → σ*C1−O4 hyperconjugations (exemplified in Figure 6). By analogy with the well described64,69,70 anomeric effect in a pyranose ring chair, these hyperconjugations can be related to the endo and exo anomeric effects, respectively (Table S2, Figure S1). This NBO analysis reveals a comparable stabilization of 1fur-2E-a-cc and 5fur-2T1-a-c by the nO4 → σ*C1−O1 interaction, but that by the nO1 → σ*C1−O4 interaction is found to be significantly

nO(i) → σ*O(j)‑H interactions59,60 (in Table S1). For the global minimum species, these NBO results support the occurrence of the cyclic cc network of three O3...H1−O1...H2−O2...H3−O3 HBs (in agreement with ref 22.), whose strength is augmented by the cooperativity effects.67 The O1...H2−O2 interaction (Figure 5a) is indicated to be most important, with the secondorder energy and σ*O2−H2 occupation of 13.64 kJ/mol and 0.016 e, respectively, consistent with the shortest HB distance at 2.09 Å (Figure 1). The existence of a cyclic H-bond network was recently detected11,18 in the most stable gas-phase fructopyranose structure, which was identified spectroscopically.18 The orientation of the −O1H1 group in the α-furanose conformer 2fur-2T1-a-c prevents this group from serving both a donor and acceptor of hydrogen bond that results in the formation of only two H-bonds. However, the stabilizing O1···H3−O3 interaction exhibits an inclination toward linearity, manifested in the O−H...O angle of 133.1° (Table S1; a perfect HB tends to approach a 180° angle68), and in a comparatively large stabilization energy of 18.32 kJ/mol and charge transfer 10953


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Figure 6. Localized orbitals involved in the nO1 → σ*C1−O4 and nO4 → σ*C1−O1 hyperconjugative interactions in 12fur-2T3-a-c.

Figure 7. (a) MP2/aug-cc-pVTZ optimized transition states (TSs) for interconversion of the low-energy α-erythrofuranose conformers, with HB distances (in Å) and relevant dihedral angles (H1−O1−C1−H, H2−O2−C2−H, and H3−O3−C3−H, in degrees) highlighted. The harmonic vibrational frequencies of the imaginary modes for TS-1fur ↔ 4fur, TS-4fur ↔ 2fur, and TS-2fur ↔ 5fur are 207i, 330i, and 331i cm−1, respectively. (b) MP2/aug-cc-pVTZ optimized TS for interconversion of the low-energy β-erythrofuranose conformers with relevant dihedral angles (H2−O2− C2−H and H3−O3−C3−H, in degrees) highlighted. The harmonic vibrational frequency of the imaginary mode is 338i cm−1.

For the β-anomers, the three −OH groups are not positioned on the same side of the ring, which limits the attainable H-bonds. The most stable β-furanose structure 6fur-1E-b-cc benefits from the O4···H2−O2···H3−O3 H-bond linkage. Here, the O2···H3−O3 HB (Figure 5b) appears to be a dominating interaction characterized by the second-order energy/charge transfer of 12.2 kJ/mol/0.016 e. This is supplemented by the weaker O4···H2−O2 one, wherein the ring oxygen O4 acts as

weaker in the latter structure (Figure S1). Structurally, the O1−H1 bond is oriented approximately gauche to the C1−O4 bond in the four (more stable) 1fur-2E-a-cc, 2fur-2T1-a-c, 3furE4-a-cc, and 4fur-OT1-a-cc structures with the H1−O1−C1−O4 DA of 51.4−66.6°, whereas this orientation is approximately trans in the (less stable) 5fur-2T1-a-c structure with the DA of −172.7°, which suggests that the exo anomeric effect69 influences the relative stability. 10954


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Table 2. Barrier Heights for Interconversion of the Four Low-Energy α-Erythrofuranose Rotamers and Two Low-Energy β-Erythrofuranose Rotamers Calculated at the MP2 and CCSD(T)//MP2 Levels MP2/aug-cc-pVTZc [kJ/mol] forward transition state TS-1fur TS-4fur TS-2fur TS-6fur

↔ ↔ ↔ ↔

4fur 2fur 5fur 13fur

a

CCSD(T)/aug-cc-pVTZ//MP2d [kJ/mol]

backward

b

forwarda

backwardb

ΔH‡(0 K)

ΔG‡(298 K)

ΔH‡(0 K)

ΔG‡(298 K)

ΔH‡(0 K)

ΔG‡(298 K)

ΔH‡(0 K)

ΔG‡(298 K)

11.92 9.75 9.21 20.96

11.69 10.97 10.31 19.99

4.47 14.12 5.76 17.85

6.08 13.69 7.20 19.01

11.48 9.98 8.97 20.41

11.24 11.19 10.07 19.44

4.56 13.69 6.05 17.05

6.16 13.26 7.48 18.21

a

The barrier in the forward direction (cf. Figure 8). bThe barrier in the backward direction (cf. Figure 8). cBased on the MP2/aug-cc-pVTZ electronic energies and MP2/aug-cc-pVTZ vibrational frequencies. dAt the MP2/aug-cc-pVTZ optimized geometries; based on the CCSD(T)/ aug-cc-pVTZ electronic energies and MP2/aug-cc-pVTZ vibrational frequencies.

Figure 8. (a) Sequential interconversion pathway involving the four low-energy α-erythrofuranose conformers with relative Gibbs free energies (in kJ/mol, at T = 298 K) compared to global minimum. The energies are based on the CCSD(T)/aug-cc-pVTZ electronic energies and MP2/ aug-cc-pVTZ vibrational frequencies. The values indicated within the vertical arrows refer to the isomerization barriers in the forward direction (1fur-2E-a-cc → 4fur-OT1-a-cc → 2fur-2T1-a-c → 5fur-2T1-a-c). (b) An interconversion path involving the two low-energy β-erythrofuranose conformers with relative Gibbs free energies (in kJ/mol, at T = 298 K) compared to global minimum. The energies are based on the CCSD(T)/ aug-cc-pVTZ electronic energies and MP2/aug-cc-pVTZ vibrational frequencies.

with the free energies within 5.6 kJ/mol of the global minimum, the question of their interconversion is relevant. For the two most stable conformers, this reaction is found to happen stepwise. Assuming that we start from the conformer 1fur-2E-a-cc, its transition to the 4fur-OT1-a-cc “intermediate” occurs first via TS-1fur ↔ 4fur (Figure 7a), and it involves a major internal rotation of the −O1H1 group. This transformation causes a breakage of the O3···H1O1 HB at the TS-1fur ↔ 4fur that contributes to the isomerization barrier. The actual free energy barrier calculated for this step is 11.24 kJ/mol (Table 2, Figure 8a). The second step to move from the conformer 4fur-OT1-a-cc to the 2fur-2T1-a-c one through TS-4fur ↔ 2fur (Figure 7a)

the LP donor (Figure 5b) with the respective 2.7 kJ/mol/0.011 e values. The similar two H-bond chain that involves the ring O4 also exists in the 7fur-4E-b-cc. The other low-energy β-furanose structures found feature single H-bond (Table S1, Figure 1). Among the open-chain species, the 1open (Figure 2) exhibits the longest H-bond network, made possible by the gauche-like C4 chain, with the nO1 → σ*O2−H2 and nO3 → σ*O4−H4 interactions indicated to be most and least stabilizing, respectively (Table S1), with the other chain conformers presented featuring at most two noncooperative H-bonds. 4.4. Interconversion of the Low-Energy O−H Rotamers. Because we have predicted five α-erythrofuranose structures 10955


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The Journal of Physical Chemistry A entails at first mostly a rotation of the −O3H3 group, bringing about an extreme weakening of the O2···H3−O3 interaction in the transition state (the latter H-bond is eventually broken in the 2fur-2T1-a-c). Indeed, the NBO second-order energy of the nO2 → σ*O3−H3 interaction at the TS-4fur ↔ 2fur is less than a threshold of 2.1 kJ/mol (see Table S1), in keeping with the HB distance/O−H···O angle of 2.38 Å/108.7°. The passage from the TS-4fur ↔ 2fur to the 2fur-2T1-a-c minimum appears actually to be more complex because, in addition to the continued −O3H3 rotation, it involves a major reorientation of the −O2H2 group to “restore” both H-bonds in the latter rotamer. The transition state TS-4fur ↔ 2fur is placed 16.26 kJ/mol higher in free energy than the global minimum, implying the isomerization barrier of 11.19 kJ/mol. A 2fur-2T1-a-c → 5fur-2T1-a-c transformation is a direct one. An internal rotation of the −O1H1 group is this reaction’s coordinate with the transition state TS-2fur ↔ 5fur (Figure 7a) and free energy barrier of 10.07 kJ/mol involved. The isomerization barrier originates from the weakening of the O1···H3O3 HB in the TS relative to that in the conformer 2fur-OT1-a-cc due to the changed position of the (−O1H1) lone pair (LP) donor (the H-bond in the latter and former species involves two and one O1 LPs, respectively, Table S1). For the conformer 3fur-E4-a-cc we could not locate a direct transition state (or determine a stepwise interconversion) transforming it to the other low-energy α-furanose conformer. Overall, our calculated free energy barriers for the sequential interconversion 1fur-2E-a-cc → 4fur-OT1-a-cc → 2fur-2T1-a-c → 5fur-2T1-a-c of 10.1−11.2 kJ/mol (Table 2, Figure 8a) are comparable in magnitude to the energy needed to break hydrogen bond in an isolated species, of 1000 cm−1.71 At the same time, they significantly exceed those involving only −OH group reorientation (without H-bond breaking) of 200−300 cm−1, as found recently for interconversion of D-threoninol conformers.71 Based on Table 2 and Figure 8a, an interconversion of the higher-energy α-furanose rotamers to the lower-energy ones,72 4fur-OT1-a-cc → 1fur-2E-a-cc and 5fur-2T1-a-c → 2fur-2T1-a-c, is especially viable with the barriers as low as 6.16 and 7.48 kJ/mol at 298 K and 4.56 and 6.05 kJ/mol at 0 K. Compared to these α ↔ α furanose isomerization barriers, a direct 6fur-1E-b-cc → 13fur-E2-b-c transformation of the lowenergy β-furanose O−H rotamers via TS-6fur ↔ 13fur (Figure 7b) involves an appreciably larger barrier of 19.44 kJ/mol (Figure 8b) as the TS lacks an internal H-bond stabilization. We note in passing that an interconversion of the α- and β-anomers (α ↔ β) comprises the ring-opening73 and thus will require surmounting a much higher kinetic barrier(s) (in the gas phase) than those predicted here.

and 5fur-2T1-a-c and the β-furanose structure 6fur-1E-b-cc at 3.01, 4.45, 5.07, 5.59, and 8.86 kJ/mol, respectively, in terms of ΔG(298 K). For the latter β-furanose conformer, our MP2/ aug-cc-pVTZ calculated rotational constants agree well with the spectroscopic data22 for the observed β-furanose structure (within 19−25 MHz). The different ring puckering conformation (1T2) assigned22 to the observed β-furanose species may arise from the difference in computational levels and/or the fact that we have employed tight61 optimization criteria. We have identified a sequential interconversion pathway involving the four of the five most stable α-furanose rotamers found, 5fur-2T1-a-c → 2fur-2T1-a-c →4fur-OT1-a-cc → 1fur-2E-a-cc, with the consecutive free energy barriers (at 298 K) of 7.48, 13.26, and 6.16 kJ/mol. By using natural bond orbital theory we have also quantified a stabilization of the erythrose conformers and interconversion transition states by intramolecular H-bonds.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b07720. Full citation for refs 61 and 62. The pseudorotational wheel (PW) of the erythrofuranose conformations (Scheme S1), illustration of “c” and “cc” arrangements of intramolecular H-bonds (Scheme S2), NBO analyses (Tables S1−S2, Figure S1), and MP2/aug-cc-pVTZ optimized Cartesian coordinates of all the structures presented in the study (Tables S3) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel: (48)(71) 375-7267. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the reviewers for their valuable comments. They also gratefully acknowledge a generous support of computer time at the Wroclaw Center for Networking and Supercomputing, WCSS.

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REFERENCES

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5. CONCLUSIONS With the highest-level calculations for D-erythrose up-to-date we have investigated the gas-phase structures and their interconversion reactions. We have predicted MP2/aug-cc-pVTZ optimized structures of about 25 low-energy furanose and open-chain D-erythrose tautomers and a number of transition states for the α ↔ α and β ↔ β furanose interconversion involving the energetically close-lying O−H rotamers. We have estimated relative Gibbs free energies of the erythrose species based on the CCSD(T)/aug-cc-pVTZ electronic energies and MP2/aug-cc-pVTZ vibrational frequencies. These results place the α-furanose structure 1fur-2E-a-cc lowest in energy, in agreement with the recent MW study,22 followed by the other four α-furanose structures 2fur-2T1-a-c, 3fur-E4-a-cc, 4fur-OT1-a-cc, 10956


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Tautomers of Gas-Phase Erythrose and Their Interconversion

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