Ab Initio Molecular Orbital Calculation of Carbohydrate Model

Ab Initio Molecular Orbital Calculation of Carbohydrate Model Compounds. 5. Anomeric .... Role of Sugar Puckering and Base Orientation on the Energeti...
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J. Phys. Chem. 1996, 100, 11305-11313

11305

Ab Initio Molecular Orbital Calculation of Carbohydrate Model Compounds. 5. Anomeric, Exo-Anomeric, and Reverse Anomeric Effects in C-, N-, and S-Glycosyl Compounds Igor Tvarosˇka* Institute of Chemistry, SloVak Academy of Sciences, SK-842 38 BratislaVa, SloVak Republic

Jeremy P. Carver* Department of Molecular and Medical Genetics, Faculty of Medicine, UniVersity of Toronto, Toronto, Ontario M5S1A8, Canada ReceiVed: April 8, 1996X

An ab initio study of the conformational behavior of R- and β-anomeric linkages in C-, N-, and S-glycosyl compounds has been carried out on axially and equatorially 2-substituted derivatives (2-ethyl, 2-methylamino, 2-thiomethyl, and 2-methylammonio) of tetrahydropyran as models. The geometry of the conformers about the anomeric C-X bond was determined by gradient optimization at the SCF level using the 6-31G* basis set. The potential of rotation has been calculated using the 6-31G* and 6-31+G* basis sets. Vibrational frequencies were calculated at the 6-31G* level and used to evaluate zero-point energies, thermal energies, and entropies for minima. Variations in calculated valence geometries for the compounds, display structural changes distinctive for the anomeric and exo-anomeric effects. Differences between bond lengths and bond angles for different conformers correlate with the importance of the lone pair delocalization interactions. The calculated conformational equilibria have been used to estimate the magnitudes of the anomeric, reverse anomeric, and exo-anomeric effects. It was found that the anomeric effect decreases in the following order: chlorine > methoxy ∼ fluorine > thiomethyl > methylamino > ethyl > methylammonio, with the methylamino, ethyl, and methylammonio groups exhibiting reverse anomeric effects. The sc preference of the methyl group over the ap orientation around the C1-C bond in 2-ethyltetrahydropyran is assumed to be entirely on basis of steric interactions. The exo-anomeric effect is expected to be present when the preference for the sc conformation is larger than that for the ethyl group. Thus, the exo-anomeric effect decreases in the order methoxy ∼ methylamino > thiomethyl. The methylammonio group does not show an exo-anomeric effect.

Introduction The empirical observation of the preference for a polar exocyclic substituent to occupy the axial over the equatorial position at the anomeric carbon of a pyranose ring led to the introduction of the anomeric effect.1,2 The terms exo-anomeric effect3 and reverse anomeric effect4 were later introduced for the orientational preference of the aglycon around the glycosidic C-O bond and for the enhanced trend of the quaternary nitrogen atom to adopt an equatorial position, respectively. First identified in carbohydrate chemistry, the anomeric effect is now recognized as being of a more general importance for all molecules having two (or more) heteroatoms linked to a tetrahedral center and was denoted as the generalized anomeric effect.5 The generalized anomeric effect describes the preference for synclinal (sc, gauche) over antiperiplanar (ap, trans) conformations in a class of compounds containing the R-XT-Y moiety, where X ) N, O, or S, Y ) Br, Cl, F, N, O, or S. Atoms R and T are of intermediate electronegativity, and T is usually C, P, Si, or S. The anomeric and related stereoelectronic effects have received very extensive experimental and theoretical examination6-17 (and references therein). From these studies, it has become increasingly apparent that the anomeric effect is a complex phenomenon characterized, apart from the conformational preferences, by unique variations of valence * Corresponding authors. Present address: GlycoDesign Inc., 480 University Avenue, Suite 900, Toronto, Ontario, Canada, M5G 1V2. Fax: (416) 593-8988. X Abstract published in AdVance ACS Abstracts, June 15, 1996.

S0022-3654(96)01042-8 CCC: $12.00

geometry, reactivity, and other properties that have far-reaching consequences. However, in spite of clear progress in this area, our understanding of these effects still does not provide a totally integrated rationalization of this phenomenon. Recently we have undertaken an ab initio analysis of the stereoelectronic effects on the geometry and the conformational behavior of cyclic model compounds of carbohydrates. In the first papers of this series18-20 we have investigated the fluorine, chlorine, and methoxy derivatives of tetrahydropyran. In this paper, as a continuation of this effort, we present the results of a conformational analysis of 2-substituted tetrahydropyrans (XTHP) in both the axial and equatorial forms, namely the 2-ethyltetrahydropyran (CTHP), the 2-methylaminotetrahydropyran (NTHP), the 2-methylammoniotetrahydropyranyl cation (NHTHP), and the 2-methylthiotetrahydropyran (STHP). These compounds have been chosen to model the linkages in C-, N-, and S-glycosyl compounds. For the 2-methylaminotetrahydropyran, the nitrogen atom is a chiral center. Therefore, two different configurations, S-(S-NTHP) and R-(R-NTHP), were assumed. Although the anomeric effect has been studied extensively by theoretical methods,6-17 a study of the potential energy curves for internal rotation around the C-X bonds in these molecules, using ab initio methods with an extended basis set, has not been carried out. In this paper, we have performed such calculations to ascertain the energy differences between conformers and also the rotational barriers. The conformational properties of these molecules are of considerable interest since they span the whole © 1996 American Chemical Society

11306 J. Phys. Chem., Vol. 100, No. 27, 1996

Tvarosˇka and Carver freezing the dihedral angle Φ to locate the minimum on the rotational curve. Next, single-point calculations were performed for each point on the potential energy curve using the 6-31+G* basis set. It has been shown18,19 that inclusion of electron correlation at the MP2/6-31G* level does not improve the results and therefore electron correlation was not included in the present study. For all minima, the vibrational frequencies were calculated at the 6-31G* level, and the zero-point energy, thermal, and entropy corrections were evaluated. The calculations were carried out at the University of Toronto on an HP 735.

Figure 1. Schematic representation of AGT, ATG, AGG, EGT, ETG, and EGG conformers around the C1-X bond of 2-substituted tetrahydropyrans and labelling of atoms.

Figure 2. Schematic representation of S- and R- configurations of 2-methylaminotetrahydropyrans.

range of behavior from the anomeric effect to the reverse anomeric effect. The results obtained can also be used to improve the parametrization of the behavior of these fragments in force fields for molecular mechanics calculations on carbohydrate derivatives. Calculations The conformational equilibrium of XTHP is illustrated in Figure 1, which shows three staggered orientations for rotation about the glycosidic bond in both the axial and equatorial forms of XTHP. These are referred as AGT, ATG, AGG, EGT, ETG, and EGG. In this notation,19 the description of the anomeric form is stated first, then the torsion angle Φ ) Φ[O5-C1X-C], and finally the torsion angle Θ ) Θ[C2-C1-X-C]. In this way, e.g., AGT means that the substituent at C2 is in the axial position (A) and the angles Φ and Θ are in close to those in synclinal or gauche (G) and antiperiplanar or trans (T) conformation, respectively. The S- and R-configurations at the nitrogen atom are shown in Figure 2 for both anomers of NHTHP. The calculations were carried out using GAUSSIAN 9221 using standard basis sets.22 The optimization of the geometry was performed at the SCF level with the 6-31G* basis set. The geometries were fully optimized using the gradient optimization routines in the program without any symmetry constraints, except for the dihedral angle Φ, which was kept fixed. First, a 30° grid for the dihedral angle Φ[Φ ) Φ(O5-C1-X-C)] was used, and then the final refinement was carried without

Results and Discussion Table 1 summarizes the location, dipole moments, and energies of the minima for the compounds examined. Relative energies of these minima, calculated at the 6-31G* and 6-31+G*//6-31G* levels, are listed in Table 2. The relevant geometrical parameters are printed in Tables 3-6. The calculated conformational energy profiles are shown in Figure 3. For comparison, the previously calculated values19 for the oxygen derivative, 2-methoxytetrahydropyran (MTHP), are also included. Conformational Energies. 2-Ethyltetrahydropyran. Based on variable-temperature NMR studies23,24 it has been suggested that C-monoglycosyl compounds exist as an equilibrium mixture of conformers. It was also claimed that the preferred solution conformation of C-glycosyl compounds corresponds to that of the corresponding parent glycosides that exhibited the exoanomeric effect. In this conformation, the O5-C1-C-C sequence of atoms is sc (gauche), as in the GT conformer, rather than ap (trans), as in the TG conformer (Figure 1). This effect was termed the exo-deoxoanomeric effect.25 The 2-ethyl tetrahydropyran (CTHP) represents a model of C-glycosyl compounds. The conformations of the CTHP have previously been investigated by semiempirical quantum mechanical methods26,27 and more recently by ab initio methods.25 Ab initio calculations of the AGT, ATG, AGG, EGT, and EGG conformers using the 3-21G basis set gave energy differences with respect to the EGT conformer of 2.4, 3.6, 8.6, 0.0, 1.1, and 0.9 kcal/mol, whereas the energy differences calculated using 6-31G*//3-21G basis set were 3.3, 4.1, 8.2, 0.0, 0.7, and 1.2 kcal/mol. The calculated energy profiles for CTHP at the 6-31G* and 6-31+G* levels are shown in Figure 3a. Both methods give very similar results. Examination of the data in Table 1 shows that the most stable orientation of the methyl group is -sc orientation (Φ ) 298.1°, EGT) with respect to the ring oxygen in the equatorial form. The next most stable conformers are the ap (186.6°, ETG) and sc (60.5°, EGG) conformers of the equatorial form. The lowest energy conformer of the axial form is the sc orientation (54.4°, AGT). This conformer has an energy ∼3.4 kcal/mol higher than the energy of EGT. This is in contrast to 1.47 kcal/mol preferences for the axial AGT conformer over the equatorial conformer EGT in MTHP calculated at the 6-31G* level, a feature attributed to the presence of the anomeric effect. The calculated preference of 3.4 kcal/mol is larger than the observed equatorial preference of 1.5 kcal/mol for the ethyl group in cyclohexane.28 This indicates an additional stabilizing factor in the equatorial form of CTHP. It has been shown that interactions of the oxygen lone pair with the antibonding C-X orbitals destabilize conformers with less electronegative X.29 For CTHP, the carbon atom linked to the anomeric carbon C1 is less electronegative than hydrogen H1 and, therefore, the so-called superjacent orbital interactions29 favor the equatorial position of the ethyl

MO Calculation of Carbohydrate Model Compounds

J. Phys. Chem., Vol. 100, No. 27, 1996 11307

TABLE 1: Ab Initio Energies (hartrees) and Dipole Moments (D) and the Position of the Conformational Minima of 2-substituted Tetrahydropyrans Calculated at 6-31G* Level CH2CH3

OCH3a

SCH3

conformer

φ

µ

energy

φ

µ

energy

φ

µ

energy

AGT ATG AGG EGT ETG EGG

54.4 162.9 280.8 298.1 186.6 60.5

1.51 1.50 1.46 1.41 1.37 1.40

-348.087 173 4 -348.085 710 5 -348.079 006 6 -348.092 632 7 -348.091 251 2 -348.090 742 7

58.4 161.4 260.1 299.2 192.1 57.0

0.88 2.24 3.11 2.44 3.24 2.62

-706.561 633 7 -706.556 133 3 -706.551 233 8 -706.562 000 4 -706.557 362 0 -706.559 962 5

64.2 150.0b 270.0b 296.5 210.0b 54.3

0.33 1.76 3.03 1.86 2.71 2.10

-383.910 024 2 -383.903 652 8 -383.983 240 0 -383.907 683 7 -383.900 414 1 -383.903 042 3

R-NHCH3

NH2+CH3

S-NHCH3

conformer

φ

µ

energy

φ

µ

energy

φ

µ

energy

AGT ATG AGG EGT ETG EGG

66.5 150.0a 279.5 297.7 199.9 64.1

1.51 2.43 1.50 1.09 1.79 2.21

-364.074 970 3 -364.067 438 7 -364.065 569 9 -364.078 978 1 -364.072 398 9 -364.069 293 6

54.8 166.0 270.0a 292.8 189.4 59.5

1.61 1.02 2.23 2.13 2.19 1.06

-364.074 892 2 -364.0730673 -364.059 490 6 -364.073 345 4 -364.070 606 9 -364.075 958 5

56.0 155.8 288.7 294.3 187.8 62.3

5.24 5.24 5.48 5.59 5.61 5.72

-364.453 293 9 -364.452 207 3 -364.446 394 3 -364.458 865 1 -364.457 915 5 -364.456 283 3

a

From ref 18. b Conformer is not a minimum on the internal rotation potential energy curve.

TABLE 2: Comparison of the ab Initio Relative Energies (kcal/mol) of 2-Substituted Tetrahydropyran Conformers Calculated by Different Methods conformer

CH2

R-NH

S-NH

NH2+

S

O

3.50 4.18 7.83 0.0 0.60 1.62

0.23 3.68 6.76 0.0 2.91 1.28

0.0 4.0 10.53 1.47 6.03 4.38

3.89 4.44 7.87 0.0 0.46 1.70

0.22 3.62 6.58 0.0 2.91 1.31

0.0 3.82 10.1 1.08 5.58 4.05

AGT ATG AGG EGT ETG EGG

3.43 4.34 8.55 0.0 0.87 1.19

2.51 7.24a 8.41 0.0 4.13 6.08

6-31G* 2.56 3.70 12.22 3.53 5.25 1.89

AGT ATG AGG EGT ETG EGG

3.57 4.30 8.41 0.0 0.75 1.24

2.83 7.22 8.35 0.0 3.83 5.98

6-31+G* 2.76 3.93 11.88 3.35 5.08 1.9

a Conformer is not a minimum on the internal rotation potential energy curve.

group over the axial position. Thus, both steric interactions and superjacent orbital interactions are responsible for the higher relative energy of the axial form. Also, a comparison of the C1-C bond length in the axial and equatorial anomers reveals that there is still a small delocalization from the oxygen lone pairs (nO) into the antibonding C1-C orbital (σC-C*). This delocalization is possible only in axial conformers. As a result, there is a small but clear difference between these bond lengths (Tables 3 and 4). The C1-C bond lengths are larger in the axial conformers (1.5329-1.5383 Å) than in the equatorial conformers (1.5228-1.5263 Å). The preference of the GT conformer for each anomer of the CTHP is similar to the results for the parent oxygen compound MTHP and consistent with the preference due to the exoanomeric effect in MTHP. However, this is the only similarity between the conformational properties around the C1-X bond of the 2-ethyl and 2-methoxy derivatives of tetrahydropyran. The torsional potential and the relative energies of conformers in MTHP are influenced by the exo-anomeric effect.19 Since the carbon linked to the anomeric carbon does not have lone pair electrons, the exo-anomeric effect does not operate in CTHP. Dipole moments of CTHP conformers (1.35-1.51 D) are nearly equivalent, due to the nonpolar character of the exocylic C1-C bond. This is in contrast to MTHP where a large variation from 0.3 to 3.0 D was calculated.19 As a result, the energy profiles for MTHP (Figure 3f) and CTHP are very

different. Compared to those for MTHP, the barriers for the transition between CTHP conformers are considerably lower. Minima at the ap orientation are deep and the energy differences between the GT and TG conformers in CTHP are less than 1 kcal/mol, whereas in MTHP, this energy difference is ∼4 kcal/ mol. In the preferred GT conformers of CTHP, the O5-C1C-C segment is in the sc and the C2-C1-C-C segment in the ap conformation. In the TG conformers the O5-C1-C-C segment is in the ap and the C2-C1-C-C segment in the sc conformation. It is well-known that the sc conformation of C-C-C-C arrays of atoms in alkanes is less stable than the ap by ∼0.8 kcal/mol.30 In contrast, in the O-C-C-C segment, the sc conformation is essentially identical in energy or more stable than the ap conformer.25 Qualitatively, a simple addition of these two single interactions suggests that the GT conformer should be ∼0.8 kcal/mol lower in energy than the TG. This indicates that steric interactions are responsible for the preference of the GT conformers in CTHP. However, a stabilizing electrostatic interaction between the methyl and the ring oxygen can also contribute to this preference, as was recently suggested.25 The role of steric interactions is also supported by differences in the structural parameters between conformers. Indeed, a comparison of the C1-C bond length and C1-C-C bond angle for different rotamers around the C1-C bond shows that both parameters increase as the energy increases. The distortion of the O5-C1-C-C torsional angles (Φ) from ideal staggered conformations is smaller in CTHP than in MTHP due to the absence of delocalization interactions. In the AGG and EGG conformers the methyl is oriented inside or over the ring. The repulsive steric interactions of the methyl with the ring protons have a destabilizing effect on these conformers in MTHP. The C1-C bond in the CTHP is larger than the C1-O bond in MTHP, 1.51 vs 1.40 Å. This reduces the repulsive interactions to some extent in CTHP, and the relative energies of the EGG and AGG conformers appear to be 2-3 kcal/mol lower than those of the corresponding MTHP conformers. 2-Methylaminotetrahydropyran. Earlier semiempirical calculations31 on 2-methylaminotetrahydropyran (NTHP) revealed a dependence of the rotational profiles on the absolute configuration at nitrogen. They also indicated slight preference for the equatorial anomer.27,31 Previous ab initio calculations32,33 were carried out only on minima of 2-aminotetrahydropyran. All the results predicted the equatorial form to be more stable, although the calculated energy differences (0.6 and 2.8 kcal/ mol) are quite sensitive to the type of calculation and basis set

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Figure 3. Ab initio potential energy of rotation about C1-X linkage for the axial (2, 4) and equatorial (b, O) form of the (a) 2-ethyltetrahydropyran (CTHP), (b) R-2-methylaminotetrahydropyran (R-NTHP), (c) S-2-methylaminotetrahydropyran (S-NTHP), (d) 2-methylammoniotetrahydropyran (NHTHP), (e) 2-methylthiotetrahydropyran (STHP), and (f) 2-methoxytetrahydropyran calculated at 6-31G* (2, b) and 6-31+G*//6-31G* (4, O) levels.

MO Calculation of Carbohydrate Model Compounds

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TABLE 3: Ab Initio Calculated Geometrical Parameters of Axially 2-Substituted Tetrahydropyran Conformersa CH2CH3 parameter C-X C1-X C1-O5 C5-O5 C4-C5 C3-C4 C2-C3 C1-H1

AGT

ATG

1.5280 1.5329 1.4114 1.4029 1.5233 1.5298 1.5317 1.0843

1.5300 1.5347 1.4119 1.4027 1.5233 1.5297 1.5317 1.0841

OCH3 AGG 1.5311 1.5383 1.4126 1.4023 1.5211 1.5274 1.5323 1.0837

AGT

ATG

Bond Lengths 1.3993 1.3879 1.3928 1.4105 1.5228 1.5304 1.5302 1.0852

1.3939 1.3976 1.3818 1.4109 1.5231 1.5305 1.5304 1.0849

SCH3 AGG 1.3963 1.3938 1.3934 1.4055 1.5214 1.5286 1.5335 1.0785

AGT

ATG

1.8100 1.8335 1.3940 1.4096 1.5225 1.5299 1.5308 1.0804

1.8101 1.8469 1.3896 1.4103 1.5220 1.5296 1.5295 1.0808

AGG 1.8131 1.8422 1.3929 1.4034 1.5218 1.5300 1.5340 1.0797

C1-X-C X-C1-O5 C1-O5-C5 C4-C5-O5 C3-C4-C5 C2-C3-C4 H1-C1-O5

112.9 112.5 116.6 111.7 110.0 109.6 104.0

113.6 111.4 116.6 111.6 110.0 109.7 104.0

120.0 113.1 119.4 112.0 109.5 109.6 102.9

Bond Angles 115.2 116.1 111.9 108.7 115.5 115.7 111.4 111.2 110.0 110.1 109.6 109.7 104.7 105.5

122.9 112.8 119.4 111.6 109.7 109.8 103.8

99.5 113.2 116.7 111.5 110.0 109.6 104.9

100.3 109.5 116.8 111.5 109.9 109.6 105.6

108.7 113.5 116.7 110.7 109.8 110.5 104.3

φ C5-O5-C1-X C5-O5-C1-H1 C4-C5-O5-C1 C3-C4-C5-O5 C2-C3-C4-C5

54.4 73.1 188.8 58.0 -55.1 52.6

162.9 73.3 188.5 58.2 -54.8 52.4

280.8 87.9 200.0 53.5 -56.4 54.7

Torsional Angles 64.2 150.0 64.7 64.5 183.3 181.8 58.0 58.9 -54.8 -54.3 52.7 52.3

270.0 85.1 195.9 55.3 -56.1 52.9

58.4 71.6 187.1 57.0 -55.1 53.0

161.4 73.0 186.5 57.4 -54.8 52.8

260.1 80.3 188.8 61.0 -57.1 50.7

a

Lengths in angstroms, angles in degrees.

TABLE 4: Ab Initio Calculated Geometrical Parameters of Axially 2-Substituted Tetrahydropyran Conformersa S-NHCH3 parameter C-N C1-N C1-O5 C5-O5 C4-C5 C3-C4 C2-C3 C1-H1

AGT

ATG

1.4500 1.4344 1.4143 1.4020 1.5236 1.5302 1.5326 1.0816

1.4497 1.4507 1.3975 1.4105 1.5225 1.5300 1.5295 1.0895

NH2+CH3

R-NHCH3 AGG 1.4472 1.4475 1.4026 1.4019 1.5220 1.5285 1.5334 1.0811

AGT

ATG

Bond Lengths 1.4500 1.4447 1.3989 1.4087 1.5232 1.5304 1.5308 1.0892

1.4491 1.4475 1.4003 1.4023 1.5243 1.5305 1.5328 1.0814

AGG 1.4488 1.4390 1.4148 1.4033 1.5210 1.5279 1.5335 1.0809

AGT

ATG

1.4963 1.5436 1.3572 1.4313 1.5178 1.5285 1.5310 1.0796

1.4931 1.5459 1.3591 1.4319 1.5174 1.5284 1.5311 1.0791

AGG 1.4926 1.5495 1.3566 1.4361 1.5153 1.5263 1.5314 1.0806

C1-X-C N-C1-O5 C1-O5-C5 C4-C5-O5 C3-C4-C5 C2-C3-C4 H1-C1-O5

115.3 114.7 115.3 111.5 110.0 109.8 103.6

115.5 108.7 116.1 111.5 110.1 109.5 104.5

122.7 112.9 119.0 111.6 109.7 109.8 103.4

Bond Angles 114.4 115.1 110.2 111.6 115.7 115.9 111.3 111.2 110.1 110.0 109.5 109.9 103.8 104.6

122.7 114.9 119.4 111.7 109.6 109.9 102.4

114.1 108.2 119.3 112.1 110.0 109.1 107.5

116.3 106.8 119.5 112.0 109.9 109.3 107.3

119.5 107.1 122.8 112.5 109.5 109.0 107.1

φ O5-C1-N-H C5-O5-C1-N C5-O5-C1-H1 C4-C5-O5-C1 C3-C4-C5-O5 C2-C3-C4-C5

54.8 286.8 70.3 186.5 59.0 -55.1 52.1

166.0 44.0 67.8 186.4 57.6 -54.4 52.8

270.0 137.5 82.7 195.0 57.2 -55.8 52.5

Torsional Angles 66.5 150.0 191.3 275.8 65.9 69.0 185.4 184.0 58.7 60.6 -55.0 -54.6 52.4 51.3

279.5 50.5 85.8 198.6 54.7 -56.6 53.9

56.0 293.2 80.7 191.9 48.7 -54.2 55.8

155.8 34.6 81.3 191.8 48.6 -54.0 56.0

288.7 163.3 103.4 211.3 37.6 -54.6 59.3

a

Lengths in angstroms, angles in degrees.

used. Calculated energy profiles for the R- and S-NTHP at 6-31G* and 6-31+G* levels are shown in Figure 3b and 3c. The shape of the calculated profiles resembles that calculated for MTHP, though the ap minima are more pronounced in NTHP. The structures of R- and S-NTHP differ only in the relative orientation of the nitrogen proton and nitrogen lone pair (Figure 2). Therefore, it is reasonable to assume that differences in their rotational profiles reflect different conformational dependence of intramolecular interactions associated with the nitrogen proton and nitrogen lone pair. For both configurations, five minima were found on the potential energy curve. The

third axial minimum expected in the ap or sc region for R-NTHP and S-NTHP, respectively, did not occur. The question of whether the amino or methylamino groups exhibit a reverse anomeric effect is still a matter of discussion.34,35 Variable-temperature NMR studies have shown36 that the 2-methylamino group in tetrahydropyran has a strong preference for the equatorial orientation. At 300 K, a population of 6.6% for the axial form of NTHP was estimated, in comparison to 12.3% for N-methylcyclohexylamine. The almost 2-fold difference in populations suggests that NTHP exhibits a reverse anomeric effect. In agreement with these data, the

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TABLE 5: Ab Initio Calculated Geometrical Parameters of Equatorially 2-Substituted Tetrahydropyran Conformersa CH2CH3 parameter C-X C1-X C1-O5 C5-O5 C4-C5 C3-C4 C2-C3 C1-H1

OCH3

EGT

ETG

EGG

1.5277 1.5228 1.4072 1.4008 1.5237 1.5304 1.5316 1.0931

1.5289 1.5243 1.4078 1.4003 1.5233 1.5298 1.5320 1.0930

1.5292 1.5263 1.4076 1.4007 1.5239 1.5305 1.5318 1.0924

EGT Bond Lengths 1.4005 1.3720 1.3983 1.4030 1.5239 1.5312 1.5318 1.0946

SCH3

ETG

EGG

EGT

ETG

EGG

1.3943 1.3823 1.3883 1.4030 1.5239 1.5302 1.5316 1.0941

1.4025 1.3779 1.3972 1.4035 1.5240 1.5306 1.5324 1.0874

1.8094 1.8084 1.3995 1.4059 1.5230 1.5306 1.5326 1.0889

1.8103 1.8218 1.3953 1.4058 1.5231 1.5303 1.5331 1.0894

1.8112 1.8133 1.3985 1.4064 1.5228 1.5299 1.5330 1.0888

C1-X-C X-C1-O5 C1-O5-C5 C4-C5-O5 C3-C4-C5 C2-C3-C4 H1-C1-O5

113.5 107.6 114.4 111.2 110.0 110.1 108.5

114.4 106.3 114.7 111.3 109.8 110.3 108.5

115.3 107.7 114.4 111.4 110.1 110.0 108.3

Bond Angles 115.6 116.1 109.0 105.5 114.0 114.3 110.9 111.4 110.0 109.8 110.2 109.9 108.1 109.0

118.3 109.2 114.2 111.3 109.9 110.0 109.0

100.2 109.2 113.6 111.0 110.0 110.4 108.9

100.6 104.4 114.0 111.3 110.0 109.7 110.1

102.0 109.1 114.0 111.3 109.9 110.2 109.6

φ C5-O5-C1-X C5-O5-C1-H1 C4-C5-O5-C1 C3-C4-C5-O5 C2-C3-C4-C5

298.1 176.1 58.4 61.1 -55.0 51.2

186.6 175.5 58.6 61.1 -55.1 51.3

60.5 173.6 57.5 60.4 -54.7 51.7

Torsional Angles 296.5 210.0 179.2 178.1 59.8 60.3 61.2 60.9 -54.9 -54.7 51.1 51.1

54.3 172.5 58.6 60.5 -54.3 51.7

299.2 177.0 59.2 61.3 -55.1 51.4

192.1 174.9 59.6 60.7 -54.4 51.4

57.0 172.1 59.5 60.8 -54.9 51.6

a

Lengths in angstroms, angles in degrees.

results given in Table 1 show a 2.5 kcal/mol preference of R-NTHP for the -sc orientation (Φ ) 297.7°, EGT) of the methyl group in the equatorial form over the sc orientation (Φ ) 66.5°, AGT) of the axial form. The most stable conformer of S-NTHP is the sc (59.5°, EGG) conformer of the equatorial form. The energy of this conformer lies 1.89 kcal/mol above EGT of R-NTHP. The equatorial-axial energy difference of 2.51 kcal/mol in NTHP is lower than the 3.43 kcal/mol calculated for CTHP. In comparison, calculations at the 6-31G* level showed33 a 0.7 kcal/mol preference for the equatorial form over the axial in aminocyclohexane, also suggesting that the methylamino group exhibits a reverse anomeric effect. Both anomers of NTHP prefer the sc orientation of the methyl group with respect to the ring oxygen, over the ap orientation. For NTHP, the sc - ap energy differences are larger than those in CTHP and similar to differences calculated for MTHP. Based on an NBO analysis it has been suggested33 that the reverse anomeric effect of NTHP is a consequence of a balance between hyperconjugation and steric interactions. However, an interplay of the nitrogen lone pair delocalization and steric interactions can also be used to qualitatively rationalize the stability of conformers around the anomeric C1-N bond. For the axial anomer, a stabilizing delocalization of the nitrogen lone pair into an antibonding C-O orbital (nN f σC-O*) is possible in the AGG (R-) and AGT (S-) cases. However, steric repulsions between the methyl group and ring atoms are large in AGG (R-) and this conformer has a higher energy than AGT (S-). In the AGT (R-), steric interactions are small, but stabilizing delocalization is not possible. Therefore, the AGT (R-) conformer has nearly the same energy as the AGT (S-). In ATG (R-) and AGG (S-), the unfavorable influence from steric interactions and a lack of delocalization are combined. This is probably the reason why minima for these conformers are not found. For the equatorial anomers, EGT (R-) and EGG (S-), the nitrogen lone pair is ap to the C1-O5 bond allowing nN f σC-O* delocalization. However, for the EGG (S-), the methyl group is eclipsed with the hydrogen at C2, which destabilizes this conformer. In ETG (R-) and EGT (S-), such delocalization is not possible but steric interactions are small. The lower

energy of EGT (S-) can be rationalized by electrostatic interactions between the methyl and the ring oxygen. Delocalization and steric interactions are also reflected in geometrical parameters. Delocalization (nN f σC-O*) elongates a C-O bond and shortens a C-N bond. This is clearly demonstrated in Tables 4 and 6. Conformers AGT (S-), AGG (R-), EGG (S-), and EGT (R-), where this delocalization occurs, have the shortest C1-N bonds, 1.4344, 1.4390, 1.4294, and 1.4247 Å, and the longest C1-O5 bonds, 1.4143, 1.4148, 1.4130, and 1.4127 Å, respectively. In contrast to nN f σC-O*, delocalization of the nitrogen lone pair, delocalization of the ring oxygen lone pairs into C-N antibonding orbitals (nO f σC-N*) seems to be less influential. Differences between the relevant structural parameters in the axial and equatorial forms are observed, but clear trends are difficult to draw. Steric interactions are indicated by the larger C1-N-C bond angles in the AGG and EGG conformers. 2-Methylammoniotetrahydropyranyl Cation. To provide more insight into the reverse anomeric effect, we have carried out calculations on the protonated form of NTHP, 2-methylammoniotetrahydropyran (NHTHP). The results obtained revealed some very interesting features arising from the substitution of the nitrogen lone pair by a proton. Calculated energy profiles for rotation around the C1-N bond in NHTHP (Figure 3d) differ significantly from those calculated for NTHP (Figure 3, b and c) but are very similar (almost identical) to profiles calculated for CTHP. This suggests that the methylammonio group has steric interactions similar to that of the ethyl group. For both anomers of NHTHP, the calculations predict an approximately threefold symmetry for the torsional potential with minima at the staggered conformations. The relative energies of the GT and TG minima are within 0.7 kcal/mol and the minima are separated by an energy barrier of less than 3 kcal/mol. In the equatorial anomer, all three conformers are within 2 kcal/mol. The third minimum of the axial anomer, the AGG conformer, was found to be ∼4.3 kcal/mol above the GT conformer. The transition barrier between the TG and GG conformer is larger for the axial anomer. In the absence of delocalization interactions from the nitrogen to the C1-O5 bond, it is not unexpected that the sc - ap energy difference for the C1-X bond in CTHP

MO Calculation of Carbohydrate Model Compounds

J. Phys. Chem., Vol. 100, No. 27, 1996 11311

TABLE 6: Ab Initio Calculated Geometrical Parameters of Equatorially 2-Substituted Tetrahydropyran Conformersa S-NHCH3 parameter C-N C1-N C1-O5 C5-O5 C4-C5 C3-C4 C2-C3 C1-H1

NH2+CH3

R-NHCH3

EGT

ETG

EGG

1.4498 1.4338 1.4003 1.4007 1.5240 1.5310 1.5317 1.0989

1.4463 1.4362 1.3994 1.4013 1.5236 1.5295 1.5319 1.0911

1.4546 1.4294 1.4130 1.4012 1.5238 1.5304 1.5320 1.0895

EGT Bond Lengths 1.4520 1.4247 1.4127 1.4011 1.5238 1.5305 1.5316 1.0899

ETG

EGG

EGT

ETG

EGG

1.4478 1.4409 1.3991 1.4023 1.5235 1.5304 1.5317 1.0989

1.4504 1.4389 1.3995 1.4013 1.5239 1.5299 1.5319 1.0907

1.4979 1.5069 1.3696 1.4324 1.5202 1.5312 1.5356 1.0863

1.4920 1.5081 1.3712 1.4320 1.5196 1.5306 1.5366 1.0863

1.4994 1.5130 1.3688 1.4327 1.5206 1.5316 1.5370 1.0871

C1-N-C N-C1-O5 C1-O5-C5 C4-C5-O5 C3-C4-C5 C2-C3-C4 H1-C1-O5

114.8 107.1 114.0 111.0 110.0 110.2 107.1

116.3 106.0 114.7 111.5 109.7 110.0 109.4

117.2 110.3 114.4 111.3 109.9 110.1 107.9

Bond Angles 115.2 115.1 110.3 105.6 114.5 114.4 111.1 109.9 109.9 110.1 110.4 110.1 108.2 108.1

117.5 107.1 114.5 111.6 109.9 109.8 109.0

114.9 103.1 114.5 110.5 110.5 110.1 112.0

117.2 101.7 114.9 110.4 110.3 110.5 111.8

116.9 103.3 114.2 110.6 110.6 110.1 111.4

φ O5-C1-N-H C5-O5-C1-N C5-O5-C1-H1 C4-C5-O5-C1 C3-C4-C5-O5 C2-C3-C4-C5

292.8 167.9 177.6 57.3 61.6 -55.0 50.9

189.4 61.5 174.0 58.6 61.4 -54.7 51.1

59.5 295.6 173.6 57.6 60.3 -54.6 54.8

Torsional Angles 297.7 199.9 62.3 323.3 176.4 177.8 58.8 58.4 61.4 60.7 -55.0 -54.7 51.1 51.4

64.1 192.3 172.0 57.5 60.7 -54.5 51.6

294.3 170.2 180.4 66.9 57.9 -53.8 53.2

187.8 62.9 180.0 67.6 57.8 -53.8 53.4

62.3 301.9 176.6 65.1 57.2 -53.4 53.6

a

Lengths in angstroms, angles in degrees.

and NHTHP is almost the same. This suggests that the methylammonio group, in contrast to the methylamino group, does not exhibit the exo-anomeric effect. An angular dependence of the geometrical parameters is one of the properties manifested by stereoelectronic effects. The absence of the exoanomeric effect in N-protonated 2-aminotetrahydropyrans is supported by the failure to observe such angular dependence in the C1-N and C1-O5 bond lengths and the N-C1-O5 bond angle. For the methylammonio group in the axial position, the lowest energy conformer, AGT, is for the sc (Φ ) 56.0°) orientation of the methyl group. In the equatorial anomer, the lowest energy conformer lies at the -sc orientation (Φ ) 294.3°). The relative energy of these two conformers shows a 3.5 kcal/mol equatorial preference at the 6-31G* level. This result is qualitatively supported by an experimental study on the axial-equatorial equilibrium of N-protonated alkylglucopyranosylamines34 which showed that the β-anomer (equatorial form) is preferred by an average of 2 kcal/mol in D2O and 1.5 kcal/mol in other solvents. Previous ab initio calculations33,37 predicted an equatorial preference of 1-1.5 kcal/mol for the cyclohexylammonium cation and 2.2-3.0 kcal/mol for the 2-ammoniotetrahydropyranyl cation, depending on the basis set. The calculated equatorial preference in NHTHP of 3.5 kcal/mol is larger than the 1.4 kcal/mol preference found in cyclohexylammonium33 and implies the presence of a reverse anomeric effect in this compound. Though nN f σC-O* delocalization is not possible in NHTHP, it seems that nO f σC-N* delocalization is stronger in NHTHP than in NTHP. This is indicated by changes in the C1-N and C1-O5 bond lengths and the N-C1-O5 bond angle on going from the axial to the equatorial anomer. As expected from the conformational dependence of the nO f σC-N* delocalization, the C1-N bond is shorter in equatorial conformers compared to axial conformers, 1.5069-1.5130 Å vs 1.54361.5495 Å. In contrast, the C1-O5 bond length is longer in the equatorial conformers (1.3696-1.3712 Å vs 1.3566-1.3591 Å) and the N-C1-O5 bond angle is reduced by ∼5°. The C1-N

bond length in NHTHP is significantly larger than that in NTHP where a possible nN f σC-O* delocalization shortens this bond. 2-Methylthiotetrahydropyran. The calculated conformational energy profiles for 2-Methylthioterahydropyran (STHP) are shown in Figure 3e. For the axial anomer, the deepest minimum appears at Φ ) 58.4° (AGT conformer), the second at Φ ) 161.4° (ATG conformer), and the third at Φ ) 260.1° (AGG conformer). The rotational barriers between the AGT and ATG conformers and between the ATG and AGG conformers are similar, ∼3.5 kcal/mol. For the equatorial form, the deepest minimum appears at Φ ) -63.5° (EGT conformer) and the next deepest is at Φ ) 58.3° (EGG conformer). The third minimum is in the ap region at Φ ) 192.1°. The minima for the ATG and ETG conformers correspond to an orientation of the methyl group sc to the ring oxygen and ap to the C2 atom, in agreement with the exo-anomeric effect. A comparison of the relative energies (Table 2) shows that in STHP the energy difference between EGT and AGT conformers is reversed comparing to MTHP, and EGT is preferred by 0.23 kcal/mol. However, the equatorial form is preferred by 0.9 kcal/mol for a thiomethyl group38 in cyclohexane, suggesting the presence in STHP of a 0.7 kcal/mol anomeric effect favoring AGT. The relative energies of the GT and TG conformers indicate that both anomers of STHP exhibit the exo-anomeric effect. The energies of TG conformers are ∼3 kcal/mol higher than the energies of GT conformers. Steric interactions in STHP conformers are not as severe as in MTHP, due to the larger C-S bond lengths. Therefore, the relative energies and barriers of rotation are smaller than those calculated for MTHP. A comparison of the differences between the bond lengths and bond angles for different conformers of STHP revealed that they display some clear and important structural changes. For the axial anomer, the anomeric C1-S bond is longer than that in the equatorial form and significantly longer than the aglycon S-C bond. In contrast, the C1-O5 and C1-H1 bonds are shorter in the axial form than in the equatorial form. The O5C1-S bond angle is smaller in the equatorial form with the

11312 J. Phys. Chem., Vol. 100, No. 27, 1996

Tvarosˇka and Carver

TABLE 7: Ab Initio Thermodynamic Functions (kcal/mol) for the Lowest Energy Minima of 2-Substituted Tetrahydropyrans Calculated Using 6-31G* Basis Set at 298 K

X CH2CH3 R-NHCH3 NH2CH3+ SCH3 OCH3a Fb Clb a

zero point thermal free-energy minimum energy energy entropyc correction AGT EGT AGT EGT AGT EGT AGT EGT AGT EGT A E A E

136.91 136.68 129.80 129.64 139.60 139.71 118.64 118.41 121.47 121.19 94.21 93.95 93.04 92.79

141.76 141.56 134.55 134.42 144.53 144.61 123.70 123.56 126.18 125.93 97.82 97.58 96.86 96.64

85.74 86.00 85.05 85.28 86.64 86.32 89.24 89.36 84.96 85.28 76.48 76.72 79.04 79.36

253.12 252.61 239.01 238.65 258.31 258.59 215.75 215.34 222.33 221.71 169.24 168.67 166.35 165.78

∆corr 0.0 -0.51 0.0 -0.36 0.0 0.28 0.0 -0.41 0.0 -0.62 0.0 -0.57 0.0 -0.57

From ref 19. b From ref 18. c In cal/(mol deg).

lowest value occurring for the ETG conformer. These characteristic patterns of bond lengths and bond angles associated with particular conformations, similar to those calculated for MTHP, are a manifestation of the anomeric and exo-anomeric effects in STHP. Anomeric, Reverse Anomeric, and Exo-Anomeric Effects. The calculated energies at 6-31G* reported above, together with previously published values for the methoxy group19 and fluorine and chlorine,18 showed that the preference for the equatorial position in 2-substituted tetrahydropyrans decreases in the order NH2CH3+ > CH2CH3 > NHCH3 > SCH3 > OCH3 > F > Cl (-3.5, -3.4, -2.5, -0.2, 1.5, 2.6, and 2.7 kcal/mol). For the latter three groups, the axial form is preferred. The most frequently used measure of the anomeric effect (AE) is based on a comparison of the axial-equatorial equilibrium of a given substituent in a heterocyclic system (∆G) and in cyclohexane (A). Recently, it has been suggested39 that the steric interactions in cyclohexanes represented by the A value should be corrected to relate steric effects in cyclohexanes to tetrahydropyrans (Acorr) and a conversion factor was proposed. The magnitude of the anomeric effect is then expressed as

AE ) ∆G - Acorr

TABLE 8: Free Energy Difference (∆G) between the Equatorial and Axial Conformers Calculated Using the 6-31G* Basis Set and the Anomeric Effect (AE) in 2-Subistuted Tetrahydropyran Derivatives at 298 K (kcal/mol) CH2CH3 NHCH3 NH2CH3+ SCH3 OCH3b Fc Clc a

∆E

∆corr

∆G298

Aa

Acorr

AE

-3.43 -2.51 -3.50 -0.23 1.47 2.62 2.67

-0.51 -0.36 0.28 -0.41 -0.62 -0.58 -0.57

-3.9 -2.9 -3.2 -0.6 0.9 2.0 2.1

-1.5 -1.6 -1.3 -0.9 -0.9 -0.2 -0.5

-2.4 -2.5 -2.0 -1.5 -1.5 -0.4 -0.8

-1.5 -0.4 -1.9 2.3 2.4 2.4 2.8

From refs 28, 36, 38, and 40. b From ref 19. c From ref 18.

and those in the entropies from 0.12 to 0.24 cal/(mol deg). These differences, at 298 K, correspond to contributions to the axialequatorial free energy differences between -0.41 and -0.58 kcal/mol. An exception is NHTHP where free-energy contributions destabilize the EGT conformer relative to the AGT by 0.28 kcal/mol. Combining the above corrections with ab initio ∆E values leads to a prediction of ∆G298. Finally, using experimental A values27,35,37,38 converted to Acorr and eq 1 we obtained AE values that are given in Table 8. It follows from these values that the anomeric effect decreases in the order Cl > OCH3 ∼ F > SCH3 and the reverse anomeric effect increases in the order NHCH3 < CH2CH3 < NH2CH3+. The exo-anomeric effect has been defined by analogy with the anomeric effect.41 In this case, the sc - ap energy difference in the 2-ethyltetrahydropyran anomers represents a reference value. This difference is assumed to be entirely steric. According to this definition, the exo-anomeric effect is present if the preference for the sc conformation around C1-X is larger in a given substituent than in CTHP. Using the 0.9 kcal/mol sc - ap energy difference calculated for CTHP, we estimated a 2.5 kcal/mol magnitude for the exo-anomeric effect of the axial anomer and 2.0 kcal/mol for the equatorial form of STHP. For the 2-methylamino group, the corresponding values are 3.9 and 3.2 kcal/mol for the R configuration and 0.3 and 2.5 kcal/ mol for the S configuration. Thus, the exo-anomeric effect in 2-substituted tetrahydropyrans decreases in the order OCH3 > NHCH3 > SCH3. From a comparison of the relative energies for NHTHP conformers (Table 2) it appears that the NH2CH3+ group does not exhibit an exo-anomeric effect.

(1)

In this definition, a positive value of AE means that the anomeric effect is present. In contrast, the reverse anomeric effect is present when the preference for the equatorial form is increased in the tetrahydropyran derivative compared to the “corrected” cyclohexane derivative. In this case, the value of AE is negative. According to this definition, the magnitudes of the anomeric and reverse anomeric effects depend on the A value of the substituent, and on the temperature and solvent used in measurement of the equilibria. We have applied this definition to estimate EA values using the 6-31G* calculated ∆G298 values and experimental A values in nonpolar solvents.28,36,38,40 To convert the ab initio calculated energy differences to free energies, the vibrational frequencies calculated at the 6-31G* level were used to evaluate the zero-point energies, thermal energies, and entropies. The results are shown in Table 7 together with previously reported values for chlorine, fluorine, and the methoxy substituents.18,19 The zero-point vibrational energies are found to be slightly higher for axial forms. Differences between the equatorial and axial conformers range from -0.16 to -0.28 kcal/mol. The corresponding differences in the thermal energies are between -0.13 and -0.24 kcal/mol

Conclusion In this paper we have modeled the conformational properties of the linkages in C-, N-, and S-glycosyl compounds. The geometries and energies of the conformers around the exocyclic C-X bond in the axial and equatorial forms of 2-ethyltetrahydropyran, 2-methylaminotetrahydropyran, 2-methylammoniotetrahydropyranyl cation, and 2-methylthiotetrahydropyran have been obtained at the 6-31G* and 6-31+G* levels of ab initio molecular orbital calculations. The results provide an essential set of data for the parametrization of molecular mechanical force fields for carbohydrates. Calculated conformational equilibria have been used to estimate the magnitudes of the anomeric and exo-anomeric effects. The anomeric effect decreases in the following order: chlorine > methoxy ∼ fluorine > thiomethyl > methylamino > ethyl > methylammonio with the methylamino, ethyl, and methylammonio groups exhibiting reverse anomeric effects. The exo-anomeric effect decreases in the order methoxy > methylamino > thiomethyl. The sc preference of the ethyl and methylammonio groups over the ap orientation around the C1-C bond is assumed to be entirely as a result of steric interactions.

MO Calculation of Carbohydrate Model Compounds Calculated differences between bond lengths and bond angles for different conformers of studied compounds display some interesting structural changes. These differences reflect a delocalization interaction of lone pair into antibonding orbital of the C1-X or C1-O5 linkages. One very obvious conclusion from these calculations is that significant differences must be expected for the extent of flexibility and conformational preferences among the different C1-X-R bonds. As a result, extreme caution must be used in attempts to use as substrate models the noncleavable forms of glycosides generated by substituting C, N, a S for the glycosidic oxygen. Acknowledgment. This investigation was supported by grants from the Canadian Protein Engineering Network of Centres of Excellence and from the Slovak Grant Agency of Sciences. References and Notes (1) Edward, J. T. Chem. Ind. (London) 1955, 1102-1104. (2) Lemieux, R. U. In Molecular Rearrangements, de Mayo, P., Ed.; Interscience: New York, 1964; Vol. 2, pp 709-769. (3) Lemieux, R. U.; Pavia, A. A.; Martin, J. C.; Watanabe, K. A. Can. J. Chem. 1969, 47, 4427-2239. (4) Lemieux, R. U.; Morgan, A. R. Can. J. Chem. 1965, 43, 22052213. (5) deHoog, A. J.; Buys, H. R.; Altona, C.; Havinga, E. Tetrahedron 1969, 25, 3365-3375. (6) Szarek, W. A., Horton, D., Eds. The Anomeric Effect, Origin and Consequences; ACS Symposium Series; American Chemical Society: Washington, DC, 1979; Vol. 87. (7) Kirby, A. J. The Anomeric Effect and Related Stereoelectronic Effects at Oxygen; Springer-Verlag: Berlin, 1983. (8) Deslongchamps, P. Stereoelectronic Effects in Organic Chemistry; Pergamon: Oxford, U.K., 1983. (9) Tvarosˇka, I.; Bleha, T. Chem. Pap. 1985, 39, 805-847. (10) Tvarosˇka, I. In Theoretical Chemistry of Biological Systems; NaraySzabo, G., Ed.; Elsevier: Amsterdam, 1986; pp 283-348. (11) Gorenstein, D. G. Chem. ReV. 1987, 87, 1047-1077. (12) Sinnott, M. L. AdV. Phys. Org. Chem. 1988, 24, 113-204. (13) Tvarosˇka, I.; Bleha, T. AdV. Carbohydr. Chem. Biochem. 1989, 47, 45-123. (14) Box, V. G. S. Heterocycles 1990, 31, 1157-1181. (15) Juaristi, E.; Cuevas, G. Tetrahedron 1992, 48, 5019-5087. (16) Thatcher, G. R. J., Ed.; The Anomeric Effect and Associated Stereoelectronic Effects; ACS Symposium Series; American Chemical

J. Phys. Chem., Vol. 100, No. 27, 1996 11313 Society: Washington, DC, 1992; Vol. 539. (17) Juaristi, E.; Cuevas, G. The Anomeric Effect; CRC Press: Boca Raton, FL, 1994. (18) Tvarosˇka, I.; Carver, J. P. J. Phys. Chem. 1994, 98, 6452-6458. (19) Tvarosˇka, I.; Carver, J. P. J. Phys. Chem. 1994, 98, 9477-9485. (20) Tvarosˇka, I.; Carver, J. P. J. Phys. Chem. 1995, 99, 6234-6241. (21) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92, Revision C; Gaussian, Inc.: Pittsburgh, PA, 1992. (22) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley: New York, 1986. (23) Wu, T.-C.; Goekjian, P. G.; Kishi, Y. J. Org. Chem. 1987, 52, 4823-4825. (24) Goekjian, P. G.; Wu, T.-C.; Kishi, Y. J. Org. Chem. 1991, 56, 6412-6422. (25) Houk, K. N.; Eksterowicz, J. E.; Wu, Y.-D.; Fuglesang, C. D.; Mitchell, D. B. J. Am. Chem. Soc. 1993, 115, 4170-4177. (26) Tvarosˇka, I. Carbohydr. Res. 1984, 125, 155-159. (27) Tvarosˇka, I.; Carver, J. P. J. Chem. Res. (S) 1991, 6-7; J. Chem. Res. (M) 1991, 0123-0144. (28) Eliel, E. L.; Hargrave, K. D.; Pietrusiewicz, K. M.; Manoharan, M. J. Am. Chem. Soc. 1982, 104, 3635-3643. (29) David, S.; Eisenstein, O.; Hehre, W. J.; Salem, L.; Hoffmann, R. J. Am. Chem. Soc. 1973, 95, 3806-3807. (30) Pitzer, K. S. Chem. ReV. 1940, 27, 39-57. (31) Kozˇa´r, T.; Tvarosˇka, I. Biopolymers 1990, 29, 1531-1539. (32) Senderowitz, H.; Aped, P.; Fuchs, B. J. Comput. Chem. 1993, 11, 944-960. (33) Salzner, U.; Schleyer, P. v. R. J. Org. Chem. 1994, 59, 21382155. (34) Perrin, C. L. In The Anomeric Effect and Associated Stereoelectronic Effects; Thatcher, G. R. J., Ed.; ACS Symposium Series 539; American Chemical Society: Washington, DC, 1993; pp 73-96. (35) Pinto, M.; Leung, R. Y. N. In The Anomeric Effect and Associated Stereoelectronic Effects; Thatcher, G. R. J., Ed.; ACS Symposium Series 539; American Chemical Society: Washington, DC, 1993; pp 126-155. (36) Booth, H.; Khedhair, K. A.; Readshaw, S. A. Tetrahedron, 1987, 43, 4699-4723. (37) Cramer, C. J. J. Org. Chem. 1992, 57, 7034-7043. (38) Hoog, d. A. J.; Havinga, E. Recl. TraV. Chim. Pays-Bas 1970, 89, 972-979. (39) Franck, R. W. Tetrahedron 1983, 39, 3251-3252. (40) Anderson, C. B.; Sepp, D. T. J. Org. Chem. 1967, 32, 607-611. (41) Tvarosˇka, I. Carbohydr. Res. 1984, 125, 155-160.

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