J. Phys. Chem. 1994, 98, 9477-9485
9477
Ab Initio Molecular Orbital Calculation of Carbohydrate Model Compounds. 2. Conformational Analysis of Axial and Equatorial 2-Methoxytetrahydropyrans Igor Tvaroska'9t and Jeremy P. Carver' Institute of Chemistry, Slovak Academy of Sciences, SK-842 38 Bratislava Slovakia, Centre de Recherches sur les MacromolCcules Vkgttales, CNRS, B.P. 53, F-38041 Grenoble Cedex 9, France, and University of Toronto, Faculty of Medicine, Department of Molecular and Medical Genetics, Toronto, Ontario M5SIA8, Canada Received: May 2, 1994; In Final Form: July 11, 1994@
An ab initio study of the conformational behavior of a-and ,!%glycosidic linkages has been carried out on axial and equatorial 2-methoxytetrahydropyrans as models. The geometry of the conformers about the glycosidic C - 0 bond was determined by gradient optimization at the SCF level using the 4-21G and 6-31G* basis sets and at the second-order Moller-Plesset level using the MP2/6-31G* basis set. The potential of rotation has been calculated using 4-21G, 6-31G*, 6-31+G*, MP2/6-31G*, and 6-31 l++G** basis sets. At all levels of theory, both axial and equatorial forms prefer the GT conformation around the C - 0 glycosidic bond. Conformational changes in bond lengths and angles at the anomeric center also display significant variations with computational methods, but structural trends are in fair agreement with experiment. The correction for the effect of zero-point energy, thermal energy, and entropy on the axial-equatorial energy difference at the 6-31G* level is -0.63 kcal/mol. After these corrections to the energy difference calculated at the 6-31G* level, the axial form is favored by 0.84 kcaymol, in reasonable agreement with experimental values of AG = 0.7-0.9 kcaymol estimated for nonpolar solvents. Solvent effects reduce this energy difference; in the extreme case of water, a value of 0.24 kcal/mol was obtained. Complete torsional profiles have been obtained for rotation about the glycosidic C - 0 bond in eleven solvents, and the calculated energy differences are in fair agreement with experimental data on 2-alkoxytetrahydropyransin solutions. The MM3 (6 = 1.5) force field reproduces the 6-31G* a b initio energy difference reasonably well, but barrier heights are in poor agreement with the ab initio data. The calculated energies and geometries provide an essential set of data for the parametrization of the behavior of acetal fragments in molecular mechanical force fields for carbohydrates.
Introduction The geometry and torsion angles about the glycosidic linkage are the most important geometrical parameters in defining the three-dimensional structure of oligosaccharides. Since the latter determine their biological function, the stereochemistry of this linkage is of crucial importance. Recently we have undertaken ab initio analysis of the stereoelectronic effects on the geometry and the conformational behavior of cyclic model compounds of carbohydrates. In the first paper of this series' we have investigated the halogen derivatives of tetrahydropyran in both the axial and equatorial forms. On the basis of the results of these calculations, using basis sets up to 6-311++G** and geometry optimization up to the 6-31+G* basis set, we suggested that for reliable calculations on carbohydrate molecules it is necessary to used optimized geometries at the 6-31G* level. In this paper we present results of the conformational analysis of 2-methoxytetrahydropyran (MTHP) in both the axial (AMTHF') and equatorial (EMTHP) forms. The conformationalproperties of this molecule are of considerable interest, since it models the glycosidic linkage in oligosaccharides, and the results obtained can be used to improve the parametrization of the behavior of acetal fragments in force fields for molecular mechanics calculations on carbohydrates. It is well-known that
* Author to whom correspondence should be addressed at the Centre de Recherches sur les MacromolCcules VCgCtales. +Slovak Academy of Sciences and Centre de Recherches sur les MacromolCcules VCgCtales. University of Toronto. Abstract published in Advance ACS Abstracts, August 15, 1994.
*
@
0022-365419412098-9477$04.50/0
the dominant factors controlling the conformational behavior of MTHP are the anomeric and exo-anomeric effects.2 The anomeric effect refers to the tendency of an electronegative substituent at the anomeric center of a pyranoid ring to assume the axial rather than the equatorial orientation, in contrast to predictions based solely on steric grounds. The exo-anomeric effect has the same stereoelectronic origin as the anomeric effect, but it influences the orientation of the aglycone; specifically it refers to the preference for a gauche orientation of the aglycone O-R bond with respect to the endocyclic C - 0 bond. The conformational equilibrium of MTHP is illustrated in Figure 1, which shows three staggered orientations for rotation about the glycosidic bond in both the axial and equatorial forms of MTHP. These are referred to as AGT, ATG, AGG, EGT, ETG, and EGG. In this notation, the description of the anomeric form is stated first, then the torsion angle 0 = 0[05-C1Ol-C], and finally the torsion angle 0 = O[C2-C1-01C]. In this way, e.g., AGT means that the methoxy group is in the axial position (A) and the angles CP and 0 are in close to those in the synclinal or gauche (G) and antiperiplanar or trans (T) conformations, respectively. Qualitative conformational analysis is straightforward.2 In AMTHP, the AGG conformer is, on steric grounds, very unstable, since the methyl group lies below the ring in close proximity to the two axial hydrogen atoms on the C5 and C3 atoms. In EMTHP, the EGG conformer suffers from a repulsion between the methyl group and the axial hydrogen atom on C2. The exo-anomeric effect causes a preference for the gauche conformation; therefore, in both anomers, the conformers having the carbon atom of the methyl group in the gauche (synclinal, sc) position with respect to the 1994 American Chemical Society
9478 J. Phys. Chem., Vol. 98, No. 38, 1994
Tvaroska and Carver
Figure 1. Schematic representation of the ACT, ATG, AGG, EGT, ETG, and EGG conformers around the C1-01 glycosidic bond of 2-methoxytetrahydropyran and labeling of atoms.
ring oxygen, that is the AGT and EGT conformers, are expected to be preferred over those having the methyl group in the trans (antiperiplanar, up) position. Due to the anomeric effect, that is, preference for the axial position of polar substituents at the anomeric center, the AGT conformer is expected to be more stable than the EGT conformer. Conformations of the MTHP molecule have been investigated by semiempirical meth~ds,~-lO by molecular mechanics methods,11.12and recently by the ab initio method.13J4 Ab initio calculations of three conformers, namely AGT, EGT, and EGG, using the 3-21G basis set gave energy differences with respect to the AGT conformer of 3.70 and 6.73 kcdmol, whereas energy differences calculated using the 6-3 1G*//3-21G basis set were 1.33 and 4.15 kcal/mol. Calculations with the 6-31G* basis set gave corresponding differences of 1.47 and 4.38 kcal/ mol. An NMR study of the pure liquid 2-metho~ytetrahydropyran~~ at 38 "C gave a free energy difference of 0.58 f 0.3 kcal/mol. The recent thermodynamic study14 on 4,6-dimethyl-2-methoxytetrahydropyran found an enthalpy difference between the axial and equatorial anomers of 1.21 kcal/mol in the gas phase and 0.98 kcdmol in pure liquid. Analysis of the NMR coupling constants of various 2-alkoxytetrahydropyran derivatives has that the free energy difference between the axial and equatorial conformers of MTHP ranges from 0.7-0.9 kcal/ mol in low-dielectric media to 0.07 kcal/mol in water, which corresponds respectively to 77-83% and 52% occurrence of AMTHP. In contrast, however, it has recently been also suggestedz1 that the free energy difference is almost entirely due to the entropic term and that the enthalpic difference between the axial and equatorial conformers is negligible. Despite the earlier ab initio calculations reported for MTHP, a careful study of the internal potential rotation energy curves around the C-0 glycosidic bond using an extended basis set has not been carried out. In this paper, we have performed such calculations in order to ascertain the energy differences between conformers as well as the rotational barriers. To compare our results with experimental data, we have estimated vibrational corrections and solvent effects. The influence of solvents was explored by computing rotational energy curves in 11 solvents for both anomers. Finally, molecular mechanics calculations employing several popular force fields have been carried out and the results are compared to the ab initio data. An additional goal of this study is to establish, at a high level of theory, the relative energy and geometry of conformers about the C-0 glycosidic bond for the purpose of providing molecular mechan-
ics studies with vjlues for an improved parametrization of the force field for carbohydrates. Calculations The calculations were carried out using GAUSSIAN 9OZ2and GAUSSIAN 9223using standard basis setsz4 The optimizations of the geomeCry were performed at the SCF level with the 4-21G and 6-3 lG* basis sets and at the second-order Moller-Plesset perturbation leve1z5-26using the MP2/6-3 lG* basis set. The geometries were fully optimized using the gradient optimization routines in the program without any symmetry constraints, except for the dihedral angle Q, which was kept fixed. First, a 30" grid for the dihedral angle Q [Q = Q(05-Cl-01C6)] was used; then in the vicinity of the minima a 10" grid was used, and the final refinement was carried without freezing the dihedral angle Q in order to locate the minimum on the rotational curve. Next, single-point calculations were performed for each point on the potential energy curve using the 6-3 1+G* and 6-311++G** basis sets. Calculations of the effect of solvent upon the conformational energy differences in dilute solution were based on the model which has successfully been used to predict solvent effects on the conformational properties of carbohydrates and has been described in detail in our previous paper^.^^^^ Molecular mechanics calculations were carried out using the MM328,29and CHARMm30 force field as implemented in Quanta.31 The calculations were carried out at the University of Toronto on an HP 735 computer and at CERMAV on an Indigo 2 station.
Results and Discussion Conformational Energies. The locations and energies of the final minima are given in Table 1, and relative energies of these minima calculated at different ab initio levels are listed in Table 2. For comparison we have included in these tables the relative energies for the conformers ATG, AGG, and ETG, although they are not real minima with the 4-21G and 6-31G* basis sets. Examination of the tables indicates that, regardless of the method, the sc orientation (Q = 60", AGT) of the methyl group with respect to the ring oxygen in the axial form is the most stable. The next most stable conformer is the -sc orientation (Q = -60", EGT) in the equatorial form. This feature has been observed previously2 and may be attributed to the presence of the anomeric and exo-anomeric effects. The calculated conformational energy profiles are shown in Figure 2. The absolute energies of the optimized conformers
Axial and Equatorial 2-Methoxytetrahydropyrans
J. Phys. Chem., Vol. 98, No. 38, 1994 9479
TABLE 1: Ab Initio Calculated Energies (hartrees) and Dipole Moments (0)and the Position of the Conformational Minima of 2-Methoxytetrahydropyran @ 6-3 1G energy CI @ MP2/6-31G* energy p conformer @ 4-21 G energy P AGT ATG AGG EGT ETG EGG a
63.7 150.0" 270.0" 303.4 210.0" 43.1
-383.061 -383.054 -383.044 -383.056 -383.046 -383.053
914 8 245 3 012 3 067 6 284 2 242 0
0.41 2.11 3.34 2.15 3.26 2.44
64.2 150.0" 270.0" 296.5 210.0" 54.3
-383.910 -383.903 -383.983 -383.907 -383.900 -383.903
024 2 652 8 240 0 683 7 414 1 042 3
0.33 1.76 3.03 1.86 2.71 2.10
61.1 158.3 260.2 297.5 206.0 61.6
-385.043 -385.036 -385.027 -385.040 -385.032 -385.035
840 8 557 6 114 1 287 3 671 6 719 3
0.38 2.06 3.05 2.02 2.98 2.37
Conformer is not a minimum on the internal rotation potential energy curve.
TABLE 2: Comparison of the ab Initio Relative Energies (kcaymol) of 2-Methoxytetrahydropyran Conformers Calculated by Different Methods method conformers geometry energy AGT ATG AGG EGT ETG EGG 4-21G 6-31G*
4-21G 6-31G* 6-31+G* 6-311++G** MP2/6-31G* MP2/6-31G* 6-311++G**
0.0 0.0 0.0 0.0 0.0 0.0
4.81 4.00 3.82 3.68 4.57 3.56
11.23 10.53 10.10 10.11 10.50 9.96
3.67 1.47 1.08 0.94 2.23 0.65
9.81 6.03 5.58 5.48 7.01 5.24
5.44 4.38 4.05 3.93 5.10 3.66
around the C - 0 glycosidic bond are reported in Tables IS and 11s in the supplementary material. In the case of AMTHP (Figure 2a), the deepest minimum appears at Q, = 60" (AGT conformer), and the second, at Q, = 300" (AGG conformer). All the methods give similar results, except that, on the MP2/ 6-31G* surface, a shallow minimum appears at Q, = 150" (ATG conformer) whereas at the 4-21G and 6-31G* levels only a plateau is observed. The rotational barrier between the AGT and AGG conformers is approximately 10.5 kcal/mol at the 6-31G* level. The relative energies calculated with the 4-21G basis set are consistently larger than with other methods. For the equatorial form, a deep minimum appears at Q, = -60" (EGT conformer). This minimum corresponds to placing the methyl group sc to the ring oxygen and up to the C2 atom, in agreement with the exo-anomeric effect. The second minimum appears at Q, = 60" (EGG conformer). However, due to steric interactions of the methyl group with pyranoid ring atoms, this conformer loses much of the exo-anomeric stabilization. In the region near Q, = 180" (ETG conformer), once again only MP2/ 6-31G* predicts a shallow minimum. There are rotational barriers separating the EGT and EGG conformers; the lower syn barrier at Q, = 0" is approximately 4.5 kcaYmo1, while the trans barrier at Q, = 120" is somewhat higher, 7.5 kcaymol at the 6-31G* level. As was found for the axial form, the relative energies calculated with the 4-21G basis set are considerably higher than with other methods. The profiles calculated using different basis sets are similar, though they are differently shifted on the energy scale with respect to the lowest energy conformer AGT. A comparison of the relative energies (Table 2) shows that an increase of the basis set from 4-21G to 6-31G* decreases the energy differences by 2 kcal/mol. A similar effect has been observed in going from the 3-21G basis set to the 6-31G* basis set.13 This feature is also consistent with our recent investigation of the effect of basis set on the calculated axial-equatorial energy differences in fluorine and chlorine derivatives of tetrahydropyran,' which showed that inclusion of polarization functions is of crucial importance for a reliable estimation of energy differences between axial and equatorial conformers in these compounds. Single-point calculations revealed that inclusion of a diffuse function into the basis set, Le. the 6-31G* basis set versus the 6-31+G* basis set, decreases the energy difference between the AGT and EGT conformers from 1.47 to 1.08 kcaYmo1. A further increase of the basis set to
6-31 l++G** has only a small effect on this energy difference (decreased to 0.94 kcal/mol). An inclusion of electron correlation at second order into the minimization of energy increases this energy difference by 0.76 kcaYmo1 to give 2.23 kcal/mol. It is a disappointing aspect of the MP2 calculations that the energy difference between the AGT and EGT conformers, 2.23 kcdmol, is not closer to the experimental values of 0.7-0.9 kcal/mol than the 6-31G* results. However, the MP2 energy difference may be decreased (i.e. approach the experiment value) by using larger basis sets and by inclusion of the correlation energy at a higher level. However, such calculations are too time consuming with computational resources available for this study. In the case of halogen derivatives,' such effects were observed and we may expect the same here. It is interesting to note that, within a given anomer, the energy differences are similar, except for the 4-21G results. Geometries. Conformational differences between structural parameters obtained at different computational levels are given in Tables 3 and 4 for the GT, TG, and GG conformers. It is seen from the values in these tables that the absolute values of bond lengths and bond angles vary with basis set. Among the structural parameters which are particularly variable are those than contain atoms of an acetal C-0-C-0-C segment and especially those around the anomeric center. The C1-01 bond length in the EGT conformer, for example, is 1.405 8, at 4-21G, 1.372 A at 6-31G*, and 1.392 8, at MP2/6-31G*. Similarly, the C1-05 bond length in EGT is 1.432 A at 4-21G, 1.398 8, at 6-31G*, and 1.426 A at MP2/6-31G*. Similar features are noticed in the geometries of other MTHP conformers describing the significant dependence of absolute values on computational methods. A comparison of differences between bond lengths and bond angles for different conformers shows that, like the absolute values, they also vary with the method of calculation. In spite of these variations, the geometric parameters display some clear and important structural trends. For the axial anomer, there is a relatively small difference in magnitude between the ring and anomeric C-0 bonds but the anomeric C1-01 bond is the shortest C-0 bond. The 01-C1-05 bond angle is significantly smaller in the ATG conformer than in the AGT and AGG conformers. In the equatorial form, the anomeric C1-01 bond is shorter than that in the axial form and also significantly shorter than the ring C1-05 bond. This difference is smallest in the ETG conformer, where the acetal segment of atoms is in the all-antiperiplanar conformation. On the contrary, the C1-H1 bond is longer in the equatorial form than in the axial form. The 01-C1-05 bond angle is smaller than in the axial form with the lowest value occurring for the ETG conformer. Unfortunately, there are no direct experimental values for MTHP available to compare with the calculated parameters. However, a comparison with the results of a statistical treatment of saccharide structure^^^-^^ reveals that they show patterns similar to those calculated for MTHP. These characteristic patterns of bond lengths and bond angles associated with particular conformations constitute a convincing manifestation
J. Phys. Chem., Vol. 98, No. 38, 1994
Tvaroska and Carver 1.433
1 2
1
113.3 \ 1.414
1.399
1113.5
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.
360
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Figure 3. Comparison of the (a) mean valence geometry parameters for aldopyrano~ides~~ with values calculated for the AGT and EGT conformers using (b) the ab initio method at the 6-31G* level and (c) the MM3 ( E = 1.5) method.
-
4-21G
0
60
120
100
246
300
360
0
Figure 2. Ab initio potential energy of rotation about the C1-01 glycosidic linkage (a)for (a, top) axial and (b, bottom) equatorial 2-methoxytetrahydropyran calculated at the 4-21G (A),6-3lG* (e), 6-31+G*//6-31G* (0),6-31l++G**//6-31G* (A), MP2/6-31G* (W), and 6-31l++G**//MP2/6-3lG*(0)levels.
of the anomeric and exo-anomeric effects. Marked differences in molecular geometry between the two anomeric forms, both in both lengths and bond angles, are illustrated in Figure 3, where mean values of key geometric parameters for aldopyrano side^^^ are compared with the ab initio (6-31G*) and MM3 ( E = 1.5) results for the AGT and EGT conformers. The effect of the more complex structure of saccharides compared to MTHP and the effect of packing forces on the crystal-derived geometric parameters are not known. A comparison of average values of bond lengths showed35that averages obtained from data on methyl pyranosides are smaller than those from more complex oligosaccharides. This tendency might be a result of more serious steric interactions between two saccharide residues than between the methyl group and the saccharide residue. On the basis of this observation we might expect smaller values in MTHP than in pyranosides. For further comparison of experimental and calculated parameters, it is noteworthy that computed bond lengths correspond to equilibrium distances (re)whereas diffraction experiments do not provide these data but rather rg, which corresponds to a real intemuclear distance averaged over molecular vibration^.^^ Therefore, the calculated values (re) should be smaller than the experimental distance-averaged bond lengths (rg). The values calculated at the 4-21G and MP2/631G* levels are consistently larger than the values shown in Figure 3. A similar problem with the MP2/6-31G* method has been observed in the case of halogen derivatives of tetrahydropyran.' The above comparison suggests that the geometry of MTHP conformers is reliably represented at the 6-31G* level. The analysis above shows that MP2 energies and geometries are less reliable in this case than SCF geometries and energies. We have obtained similar results for 2-chloro- and 2-fluorotetrahydropyran.' These results suggest that the perturbation series expansion in these calculations is terminated too early.
J. Phys. Chem., Vol. 98, No. 38, 1994 9481
Axial and Equatorial 2-Methoxytetrahydropyrans
TABLE 3: Ab Initio Calculated Geometrical Parameters of Axial 2-MethoxytetrahydropyranConformer@ 4-21G parameter
6-31G*
AGT
ATG
AGG
c-01 c1-01 C1-05 C5-05 c4-c5 c3-c4 C2-C3 C1-H1
1.4432 1.4229 1.4263 1.4526 1.5311 1.5420 1.5339 1.0811
1.4367 1.4326 1.4158 1.4532 1.5323 1.5431 1.5405 1.0816
1.4372 1.4237 1.4260 1.4455 1.5295 1.5401 1.5443 1.0755
c1-01-c 0 1 -C1-05 C1-05-C5 C4-C5-05 c3-c4-c5 c2-c3-c4 H1-C1-05
115.2 111.1 114.7 110.7 109.8 109.4 104.9
116.6 108.4 114.2 110.1 110.0 109.6 106.0
123.2 113.2 118.8 110.3 109.5 109.9 103.7
@ C5-05-C1-01 C5-05-C1 -H1 C4-C5-05-C1 C3-C4-C5-05 c2-c3-c4-c5
63.7 61.6 181.2 57.0 -55.4 55.6
150.0 59.2 177.7 59.3 -54.8 54.5
270.0 82.8 193.8 56.4 -57.4 55.1
a
MP2/6-31G*
ATG
AGG
AGT
ATG
AGG
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
1.3963 1.3938 1.3934 1.4055 1.5214 1.5286 1.5335 1.0785
1.4266 1.4115 1.4196 1.4376 1.5203 1.5283 1.5279 1.1003
1.4199 1.4243 1.4041 1.4384 1.5208 1.5284 1.5276 1,1004
1.4223 1.4196 1.4184 1.4313 1.5199 1.5278 1.5319 1.0935
Bond Angles 115.2 111.9 115.5 111.4 110.0 109.6 104.7
116.1 108.7 115.7 111.2 110.1 109.7 105.5
122.9 112.8 119.4 111.6 109.7 109.8 103.8
112.3 112.0 112.4 111.3 110.0 109.5 103.8
113.4 107.7 112.7 111.1 110.0 109.4 105.2
120.7 112.3 115.1 110.9 109.7 110.0 103.0
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
61.1 61.9 180.6 59.4 -57.0 53.9
158.3 62.7 179.3 59.7 -56.0 53.6
260.2 79.2 189.5 60.6 -58.7 52.0
AGT
Lengths in angstroms; angles in degrees.
TABLE 4: Ab Initio Calculated Geometrical Parameters of Equatorial 2-MethoxytetrahydropyranConformers9 4-21G parameter
EGT
ETG
6-3 lG* EGG
EGT
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
1.4279 1.3918 1.4261 1.4295 1.5221 1.5289 1.5302 1.1112
1.4208 1.4058 1.4126 1.4302 1.5220 1.5278 1.5299 1.1108
1.4294 1.3986 1.4262 1.4295 1.5221 1.5280 1.5305 1.1024
116.1 105.5 114.3 111.4 109.8 109.9 109.0
118.3 109.2 114.2 111.3 109.9 110.0 109.0
112.7 108.4 111.1 110.7 109.8 110.2 108.0
113.1 104.1 111.3 111.3 109.6 109.7 109.3
115.0 108.4 111.5 111.3 109.6 109.8 109.1
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
297.5 178.0 58.5 62.9 -57.1 52.1
206.0 177.2 59.7 62.4 -57.0 52.2
61.6 171.2 58.0 61.9 -56.5 52.9
c-01 c1-01 C1-05 C5-05 c4-c5 c3-c4 C2-C3 C1-H1
1.4445 1.4058 1.4341 1.4451 1.5320 1.5424 1.5409 1.0895
1.4382 1.4167 1.4234 1. 4 6 4 1.5317 1.5415 1.5410 1.0901
1.4458 1.4120 1.4331 1.4455 1.5321 1.5419 1.5420 1.OS33
Bond Lengths 1.4005 1.3720 1.3983 1.4030 1.5239 1.5312 1.5318 1.0946
c1-01-c 01-C1-05 C1-05-C5 C4-C5-05 c3-c4-c5 c2-c3-c4 H1 -C1-05
115.6 108.7 113.9 110.2 109.8 109.9 108.3
116.4 105.5 114.1 110.5 109.7 109.6 109.6
117.3 108.9 114.2 110.3 109.7 109.8 109.8
Bond Angles 115.6 109.0 114.0 110.9 110.0 110.2 108.1
@ C5-05-C1-01 C5-05-C1-H1 C4-C5-05-C1 c 3 -c4-c5 - 0 5 c2-c3-c4-c5
303.4 181.7 61.4 60.0 -55.8 554.0
210.0 180.4 61.4 60.0 -55.8 53.9
43.1 175.4 60.1 60.1 -55.2 54.1
a
MP2/6-31G*
ETG
Lengths in angstroms; angles in degrees.
However, for a final explanation of these deficiencies it is necessary to have a more extensive body of MP2 calculations on complex molecules. The key parameters, the C1-01 and C1-05 bond lengths, are plotted as a function of torsion angle @ in Figure 4a, and the 01-C1-05 and C1-01-C bond angles are plotted as a function of torsion angle @ in Figure 4b. It is clear that there are pronounced geometric changes as rotation occurs, with bond angles varying by up to 11" and bond lengths varying by up to 0.04 A. This result demonstrates that the rigid approximation leads to considerable errors in this case. The geometric variations between the a-and &glycosides were attributed to
the lone-pair interactions associated with the anomeric effect. Our results show that the exo-anomeric effect has similar consequences. However, from our results the influence of steric interactions on these variations is also evident. Inspection of Figure 4 shows that these variations are consistent with the structural pattem of bond lengths and bond angles observed in the MTHP minimum energy conformers and the trends observed in acyclic acetal m o d e l ~ . ~ JFor ~ , both ~ ~ anomeric forms, the C1-01 bond length decreases starting with 0" conformations and going through a minimum at 60", and then increases to a maximum at 150" and again decreases to another minimum at 300". A reversed trend is observed for the C1-05 bond lengths
9482
Tvaroska and Carver
J. Phys. Chem., Vol. 98, No. 38, 1994
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-
(E) 01-C1-05 (E)
--C C1-01-C
100 0
6 0
120
360
@
Figure 4. Ab initio 6-31G*-calculated (a, top) C1-01 (0, 0 )and C1-05 (A, A) bond lengths and (b, bottom) 01-C1-0 (0,0 )and C1-01-C (A, A) bond angles in axial (A) and equatorial (E) 2-methoxytetrahydropyran as a function of dihedral angle
a.
with two maxima at 60" and 300", respectively, and a minimum at 180". Although from our results it is not possible to
discriminate quantitatively between various stereoelectronic effects, some qualitative conclusions can be made. It has been shown by perturbation molecular orbital analysis38 that the hyperconjugation model requires the methyl group to be rotated 60"-120" out of the 0-C-0 plane for the maximal delocalization of glycosidic oxygen lone pairs into the antibonding orbitals of the C1-05 bond. The observed minima are consistent with this model. The trend of variations of C1-01 in the axial and equatorial forms of MTHP exhibits a symmetrical character with respect to @ = 180". This might be explained by a dominance of delocalization interactions which are accompanied by steric interactions. For AMTHP, more serious steric interactions between the methyl group and ring atoms occur between 240" and 300". These are relieved during the optimization of geometry by an elongation of the C1-01 bond as well as by an increase in the C1-01-C bond angle. For EMTHP, similar trends are observed in the region 60"120", where more serious steric interactions occur. Clearly, these results show that steric interactions influence the magnitude of the geometrical parameters around the anomeric center. If only delocalization interactions were present, the C1-01 bonds would be the same in both sc conformers of a particular anomer. The above bond length variations seem to be superimposed on a general C1-0 bond shortening. This is charact e r i ~ t i cof~ any ~ CX, grouping where X is an electronegative atom. The 01-C1-05 bond angle decreases when going from 0" to 180". The 01-C1-05 angle variation has been rationalized by a perturbation molecular analysis38focused on the stabilizing interactions between lone-pair orbitals on oxygen atoms. This analysis showed that maximum overlap between these lonepair orbitals is found in an all-trans arrangement of the C-OC-0-C segment of atoms. As a consequence, the 01-C10 5 bond angle should decrease and the 01-C1-H1 angle increase in comparison with other conformations. These trends are clearly seen in Figure 4b; the 01-C1-05 angle is smaller at @ = 180". This angle is also larger in the axial form, where the ring C1-05 bond is in the sc orientation, whereas in the equatorial form it is in an up orientation. Thus these results imply that the variations of bond lengths and bond angles around the anomeric center in carbohydrates are a result of the mutual interplay of steric, electrostatic, and stereoelectronic effects with a dominant role for delocalization interactions of lone pairs. Zero-Point Energy Correction. In order to evaluate the zero-point energy and entropy effects on the conformational energies and rotational barriers of 2-methoxytetrahydropyran, the vibrational frequencies for six MTHP conformations and for the structures at barriers were calculated using the 6-31G* basis set with GAUSSIAN 92.23 These were used to estimate zero-point energies, thermal energies, and entropies, and the results are shown in Table 5. The zero-point vibrational energies and thermal energies are found to be slightly higher for the AGT conformer. The differences in zero-point energy between the AGT and EGT conformers and between the AGT and EGG conformers are -0.28 and -0.24 kcal/mol, respectively. The corresponding differences in the thermal energies are -0.25 and -0.15 kcal/mol. Then entropy of the AGT conformer is lower than in the two equatorial EGT and EGG conformers, and the corresponding entropy differences are 0.32 and 0.90 cal/(mol deg). It appears that these differences are larger than those calculated using the 3-21G basis set13 and also larger than those calculated using the 6-3 lG* basis set for halogen derivatives of tetrahydropyran.' These differences correspond, at 298 K, to contributions to the free energy of 0.1 and 0.57 kcal/mol
Axial and Equatorial 2-Methoxytetrahydropyrans
J. Phys. Chem., Vol. 98, No. 38, 1994 9483
TABLE 5: Summary of Corrections to the Calculated Free Energy Differences (kcaymol) for the AGT, ATG, AGG, EGT, ETG, and EGG Conformers of 2-Methoxytetrahydropyran Using the 6-31G* Basis Set at 298 K
TABLE 6: Comparison of the Relative Energies (kcaymol) Calculated by Different Molecular Mechanics Methods for 2-Methoxytetrahydropyran Conformers method ACT ATG AGG EGT ETG EGG
AGT ATG zero-point energy 121.47 121.31 relative contribution 0.0 -0.16 thermal energy 126.18 126.08 relative contribution 0.0 -0.10 entropy" 84.96 86.25 entropy contribution 25.33 25.72 relative contribution 0.0 0.39 total correction 222.32 221.67 relative total correction 0.0 -0.65 ab initio relative value 0.0 4.00 corrected value 3.35 0.0
MM3,c = 1.0 M M 3 , r = 1.5 MM3, E = 3.0 MM3, E = 4.0 M M ~ , E =10.0
AGG 121.49 0.02 126.24 0.06 86.20 25.70 0.37 222.03 -0.29 10.53 10.24
EGT
ETG
121.19 -0.28 125.93 -0.25 85.28 25.43 0.10 221.69 -0.63 1.47 0.84
121.00 -0.47 125.83 -0.35 87.09 25.97
EGG
121.23 -0.24 126.03 -0.15 86.86 25.90 0.64 0.57 220.86 221.36 -1.46 -0.96 6.03 4.38 4.57 3.42
In cal/(mol deg). and give total corrections of -0.63 and -0.96 kcdmol. Thus, all the above-mentioned contributions decrease the free energy difference between the axial and equatorial MTHP conformers. The calculated entropy contributions also favor EMTHP and do not support a suggestion based on NMR results*l that the free energy difference of 0.9 kcaYmol found in chloroform (in favor of the axial form) is entirely due to entropic factors. Combining the above corrections with the ab initio AE values of 1.47 and 4.38 kcalJmol leads to a prediction of A G z ~ sof 0.84 kcaYmol for the difference between the AGT and EGT conformers and 3.42 kcalJmo1 for the difference between the AGT and EGG conformers. The calculated difference between the EGT and AGT conformers of 0.84 kcal/mol is in fair agreement with the free energy difference of 0.7-0.9 kcaYmo1 between axial and equatorial MTHP observed in nonpolar solvent^.^^-*^ As reported in Table 5, the calculated total corrections to the energies of the ATG, AGG, and ETG conformers are -0.65, -0.29, and -0.63 kcal/mol, respectively. These contributions have essentially no effect on the barriers to rotation. Molecular Mechanics Calculations. Molecular mechanics calculations provide an inexpensive way to determine conformational energies and geometries for complex carbohydrate systems.40 It is clearly desirable from many points of view that force field calculations on these types of molecules be as accurate as possible.41 Because of the importance of the anomeric and exo-anomeric effects in determining the conformations of carbohydrates, particular care must be used in the parametrization of the behavior of acetal fragments in force fields for oligosaccharides. Recently it has been shown" that molecular mechanics calculations, using the MM2(77) and MM2(85) programs with E = 1.5, predicted 1.22 and 1.16 kcal/ mol for the energy difference between the AGT and EGT conformers. However, MM2(77) failed to describe geometric differences between the axial and equatorial conformers and the MM2(85) method detected only one conformer for each of the anomeric forms, namely AGT and EGT. The OPLS/ AMBER calculations12gave 1.81 kcaYmo1 energy differences between the AGT and EGT conformers. In order to analyze the performance of different molecular methods, we calculated the energies of these conformers using MM3 and CHARMm methods and included the values calculated using the CVFF force field42,43as implemented in DISCOVERu and PEF9 1L.45 Calculated relative energies are shown in Table 6. The results in Tables 2 and 6 indicate that MM3 and CHARMm force fields correctly predict the preference for the AGT conformer. On the contrary, the PEF91L46 and DISCOVER47 force fields erroneously predict the EGT conformer to be the preferred species. As well, the relative
CHARMM AMBER" PEF9 lLb
DISCOVERc a
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3.46 3.17 2.98 2.93 2.83 4.70 5.11 0.98 1.85
8.20 7.75 7.40 7.30 7.13 9.00 12.21 7.20 6.70
1.21 0.88 0.57 0.47 0.33 2.38 1.81 -1.70 -0.75
4.71 4.08 4.56 3.42 3.15 7.59 7.81 -1.26 1.20
4.04 3.72 3.44 3.38 3.24 3.21 4.80 0.40 1.26
Reference 12. Reference 46. Reference 47.
energies of conformers for a given anomer calculated by these methods are in poor agreement with ab initio results. On the other hand, MM3 seems to be in better agreement both with ab initio and experimental data than CHARMm. For example, the MM3 ( E = 1.5) calculated energy difference of 0.88 kcalJmo1 between the AGT and EGT conformers is in good agreement with experimental data for nonpolar solvents. for a comparison of ab initio data with molecular mechanics values it is important to distinguish between 0 K and room t e m p e r a t ~ r e .Therefore, ~~ the zero-point correction (-0.28 kcdmol) and thermal energy (-0.25 kcaumol) need to be added to the ab initio energy difference. The total correction is -0.53 kcaYmo1, which gives a difference of 0.94 kcaVmol at the 6-31G* level compared to the MM3 value of 0.88 kcal/mol. On the negative side, the MM3 results show a considerable dependence on the dielectric constant used for the calculation of electrostatic contributions. For example, values of the energy difference for E = 3.0 and 4.0 are 0.57 and 0.37 kcaYmo1, respectively. The CHARMm value of 2.38 kcaYmol is too large. Another interesting point about the data in Table 6 is that the relative energies of the other staggered conformations about the C1-01 bond are always higher for the ab initio calculations than with MM3. For the AGG conformer this difference is 3 kcaYmol. The ab initio optimized geometries of MTHP allow an exploration of the exact location of minima in CP dihedral space. The values given in Table 1 show that the dihedral angle CP in the AGT conformer is 64.2" with the 6-31G* geometry and 61.1" in the MP2/6-31G* geometry, but it changes to 72.6" in the MM3 geometry. In the EGT conformer, CP varies from -63.5' at 6-31G* to -62.5" at MP2/6-31G* and -73.6' in the MM3 geometry. Since the dihedral angles around the glycosidic linkage determine the three-dimensional structure of oligosaccharides, a difference of almost 10" is potentially highly significant. For example, a difference of almost 10" in dihedral angle might change the vicinal carbon-proton interglycosidic coupling constant by 1 Hz. Considering values of bond lengths and bond angles, it is seen from Figure 3 that MM3 values describe structural trends observed for both anomers. The absolute values, however, are different from those calculated at the 6-31G* level. For example, the MM3-calculated C10 1 and C1-05 bond lengths are approximately 0.03 A larger than the corresponding 6-31G* values. As well, the C1-01-C bond angle is about 3" larger in MM3 structures. Solvent Effect. Finally we have investigated the effect of the solvent upon the potential of rotation around the glycosidic C1-01 bond and on the energy differences between conformers. A plot of relative energies as a function of the angle @ is given in Figure 5. The ab initio data, obtained at the 6-31+G* level for an isolated molecule are compared to the results calculated for chloroform, dimethyl sulfoxide, and water solutions. These results show that the solvent effects stabilize the regions where the TG and GG conformers occur and lower the
J. Phys. Chem., Vol. 98, No. 38, 1994
1 2
Tvaroska and Carver
4
L
-
6-31 + G * -Chloroform DMSO
, - 2
-Wafer I
0
60
.
l
120
.
I
.
180
1
240
.
I
300
.
3
0
12-
10-
analysis of solvation contributions revealed that the electrostatic term is mainly responsible for this stabilization. The electrostatic term follows approximately the conformational dependence of the dipole moment." Since the highest values of dipole moment are found for TG and GG conformers, these will be the most stabilized and the stabilization will be proportional to the dielectric constant of the solvent. The relative free energies of MTHP conformers in 11 solvents are given in Table 7. These results clearly document that the inclusion of solvent effects decreases the axial-equatorial energy difference. The recent Monte Carlo study12on MTHP gave free energy differences between the AGT and EGT conformers of 1.7, 0.2, and -0.3 kcallmol in carbon tetrachloride, acetonitrile, and water, respectively. The ab initio reaction field method49predicted the EGT conformer to be better solvated than the AGT conformer by 0.6 kcal/mol in carbon tetrachloride and 1.4 kcallmol in water. NMR measurements21found that solvation of the equatorial anomer is larger by 0.5 kcaVmol in acetonitrile than in carbon tetrachloride and by 0.8 kcal/mol in water than in carbon tetrachloride. The relative energy of the EGT conformer calculated with the 6-31G* basis set decreases from 1.47 kcaVmol in vacuum through 1.31 kcallmol in chloroform to 0.85 kcaVmol in water. In the literature there is a relatively large amount of data describing the equilibrium of the axial and equatorial forms of 2-alkoxytetrahydropyransin various solvent^.'^-^^ In order to estimate the reliability of the calculated results, the experimental data are compared with the calculated free energy difference between the AGT and EGT conformers in Table 7. For this purpose the calculated energy difference in solution was corrected using calculated zero-point and thermal energy, and entropy corrections (Table 5). As can be seen, particularly when the scattering and accuracy of the experimental data are taken into account, the calculated values are in very good agreement with the experimental data obtained for a number of solvents of diverse character. The calculated data nicely predict a decreased abundance of axial forms with increasing solvent polarity represented by dielectric constant. It is noteworthy that the marked effect of chloroform as compared to the more polar dimethyl sulfoxide is also obtained.
Conclusion
-C Chloroform -C
Water
- 2 0
6 0
120
160
240
300
3
Q
Figure 5. Ab initio potential energy of rotation about the C1-01 glycosidic linkage (Q) for the (a, top) axial and (b, bottom) equatorial 2-methoxytetrahydropyran calculated for an isolated molecule at the 6-31+G*//6-31G* level (A) and in chloroform (a), dimethyl sulfoxide (m), and water (+) solutions.
barriers of rotation by 2 kcallmol. The stabilization of these regions is so pronounced that in water the ATG and ETG conformers become a minimum on the energetical curve. The
The geometries and energies of conformers around the exocyclic C - 0 bond in axial and equatorial 2-methoxytetrahydropyran have been obtained at various levels of ab initio molecular orbital calculations. Although structural trends in geometrical parameters between axial and equatorial forms are correctly described at all levels, conformational changes in bond lengths and angles are best reproduced using a polarized basis set, 6-31G*. The zero-point energy difference between axial and equatorial conformers calculated at the 6-31G* level is -0.28 kcallmol, the thermal energy correction at 298 K is -0.25 kcaVmo1, and the contribution from the entropy difference is -0.09 kcallmol. This give a AG298 value of 0.84 kcallmol, which compares favorably with the values of 0.7-0.9 kcallmol observed in nonpolar solvents. Calculated solvation energy tends to reduce this difference for more polar solvents; for example, in water this difference is 0.23 kcallmol. The resulting free energy differences are in fair agreement with observed values in 11 solvents. MM3 ( E = 1.5) reasonably reproduces the axial-equatorial energy difference, but the barriers of rotation are found to be too low. Further, the calculated structural parameters at the anomeric center differ from those calculated at the 6-31G* level. The calculated energy values and geometries presented here
J. Phys. Chem., Vol. 98, No. 38, 1994 9485
Axial and Equatorial 2-Methoxytetrahydropyrans
TABLE 7: Effect of Solvents upon the Calculated Relative Energies of 2-MethoxytetrahydropyranConformers solvent
6-31G* corrected valueb dioxan carbon tetrachloride benzene carbon disulfide chloroform acetone ethanol methanol acetonitrile dimethyl sulfoxide water
AGT
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0
ATG
AGG
EGT
ETG
EGG
4.00 3.35 3.36 3.36 3.36 3.35 3.17
10.53 10.24 10.00 10.00
1.47 0.84 0.80 0.80 0.79 0.77 0.68 0.63 0.59 0.5 1 0.55 0.59 0.23
6.03 4.57 4.58 4.58 4.55 4.54 4.25 4.10 3.92 3.56 3.76 3.92 2.00
4.38 3.42 3.46 3.46 3.45 3.45 3.26 3.20 3.13 2.97 3.06 3.14 2.35
3.11
3.02 2.79 2.91 3.01 1.69
10.00
9.88 9.69 9.59 9.49 9.25 9.36 9.50 8.29
AGco~c
0.84 0.80 0.80 0.79 0.77 0.68 0.63 0.59 0.51 0.55
0.59 0.23
AG,,,‘
0.72 0.72-0.93 0.81-0.99 0.81 0.49-0.74 0.55-0.72 0.34-0.45 0.31-0.48 0.33-0.45 0.62-0.69 0.07
a From equilibrium studies of 2-metho~ytetrahydropyran,~~-~~ 6-methyl-2-metho~ytetrahydropyran,~~~~~ 4-methyl-2-methoxytetrahydropyra11,~~~” 2-ethoxytetrahydropyran,” and 4,6-dimethy1-2-metho~ytetrahydropyran.’~ Values calculated using the corrections in Table 5 .
are valuable for the refinement of molecular mechanical potential functions suitable for carbohydrates. 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. Supplementary Material Available: Tables of ab initio calculated absolute energies of conformations around the glycosidic C1-01 bond for axial and equatorial 2-methoxytetrahydropyran ( 2 pages). Ordering information is given on any current masthead page. References and Notes (1) Tvaroska, I.; Carver, J. P. J. Phys. Chem. 1994,98,6452-6458. (2) Tvaroska, I.; Bleha, T. Adv. Carbohydr. Chem. Biochem. 1989,47, 45-123. (3) Kozar, T.; Tvaroska, I. Theor. Chim. Acta 1979,53,1-19. (4) Tvaroska, I.; Kozar, T. J . Am. Chem. Soc. 1980,102,6929-6935. ( 5 ) Tvaroska, I.; Kozar, T. Carbohydr. Res. 1981,90,173-185. (6)Tvaroska, I.; Kozar, T. Int. J. Quatum Chem. 1983,23,765-778. (7)Tvaroska, I.; Kozar, T. THEOCHEM 1985,123,141-154. (8) Tvaroska, I.; Kozar, T. Theor. Chim. Acta 1986,70,99-114. (9)Tvaroska, I.; Carver, J. P. J . Chem. Res., Miniprint 1991,123144. (10) Tvaroska, I.; Carver, J. P. J . Chem. Res., Synop. 1991,6-9. (11) Navio, P. F.; Molina, J. M. J. Mol. Strucr. 1990,222,387-400. (12) Jorgensen, W. L.; Morales de Tirado, P.I.; Severance, D. L. J . Am. Chem. SOC.1994,116,2199-2200. (13) Wiberg, K. B.; Murcko, M. A. J.Am. Chem. SOC.1989,111,4821-
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