Stepwise hydration of cellobiose by DFT methods: 1. Conformational and structural changes brought about by the addition of one to four water molecules

Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19 www.elsevier.com/locate/theochem

Stepwise hydration of cellobiose by DFT methods: 1. Conformational and structural changes brought about by the addition of one to four water molecules Wayne B. Bosma a, Michael Appell b, J.L. Willett c, Frank A. Momany

c,*

a Department of Chemistry and Biochemistry, Bradley University, Peoria, IL 61625, USA Mycotoxin Research Unit, 1USDA, ARS, National Center for Agricultural Utilization Research, 1815 N. University St., Peoria, IL 61604, USA Plant Polymer Research Unit, 1USDA, ARS, National Center for Agricultural Utilization Research, 1815 N. University St., Peoria, IL 61604, USA b

c

Received 23 May 2006; received in revised form 26 July 2006; accepted 26 July 2006 Available online 10 August 2006

Abstract Previous density-functional theory (DFT) calculations found that the anti (or ‘‘flipped’’) form of cellobiose (with the H1 and H4 0 hydrogen atoms on opposite sides of the pseudo-plane formed by the sugar rings) is more stable in vacuo than the syn (or ‘‘normal’’) conformation most often observed in crystalline- and solution-phase experiments. In order to understand the reason for this conformational preference, cellobiose–water complexes were optimized at the B3LYP/6-311++G** level of theory. Ten different anhydrous cellobiose structures were used as starting points, and the results of calculations on 30 monohydrates, 20 dihydrates, 12 trihydrates, and 5 tetrahydrates are presented. The syn form of the molecule was stabilized relative to the anti form as more water molecules were added, with the two conformers being approximately equal in stability at the dihydrate level. Addition of more than two water molecules further increased the relative stability of the syn conformer. One reason for the increase in stability of the syn form upon hydration is the ability of that conformational class to better accommodate a water molecule between the two rings. Changes in bond lengths, bond angles, and dihedral angles that occur due to the interactions with water molecules are described in detail. These hydration induced structural changes are largely localized near the water molecule(s), and the effects of the addition of subsequent water molecules can be predicted based upon the structure differences between the monohydrates and the corresponding anhydrous cellobiose conformers. Published by Elsevier B.V. Keywords: Density functional; B3LYP; Cellobiose; Carbohydrate–water complexes; Hydrogen Bonding

1. Introduction Understanding the effects of the molecular environment on the conformational stability of a bio-active molecule is crucial to understanding the in situ activity of the molecule. Most high-level DFT or MO calculations on large molecules do not represent a realistic model for the molecule’s *

Corresponding author. Tel.: +1 309 681 6362; fax: +1 309 681 6362. E-mail address: [email protected] (F.A. Momany). 1 Names are necessary; to report factually on available data; however, the USDA neither guarantees nor warrants the standard of the product, and the use of the name by USDA implies no approval of the product to the exclusion of others that may also be suitable. 0166-1280/$ - see front matter Published by Elsevier B.V. doi:10.1016/j.theochem.2006.07.024

structure in its natural surroundings; in many cases, the results of these calculations do not agree with the experimental results on the molecule of interest in a solvent environment. This was recently found to be the case in b-cellobiose, where DFT calculations predicted the anti form (in which the H1 and H4 0 hydrogen atoms are on opposite sides of the plane perpendicular to the corresponding C–H bonds) to be more stable in the isolated molecule than the syn form2 (with the / dihedral rotated 180 relative to the anti form, so that the H1 and H4 0

2 In reference [1], the syn and anti conformers were referenced to as ‘‘normal’’ and ‘‘flipped’’, respectively.

2

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

hydrogen atoms are on the same side of the molecule) [1]. This result contrasts with experimental findings on crystalline cellobiose [2,3] and cellobiose in water and DMSO solutions [4,5]. In crystalline cellobiose, the anti form has not been observed [6], while NMR experiments in solution have found anti cellobiose to be present in relatively small amounts (5%) [5]. However, experiments on a very similar carbohydrate in the gas phase [7] reveal a predominately anti conformation in the gas phase isolated molecules. Cellulose is the most abundant naturally occurring polymer and the major structural component of higher plants. Any large-scale structural variations observed in the conformation of this biopolymer must arise from flexibility about the glycosidic linkages that join the glucose rings. b-Cellobiose (b-D-glucopyranosyl-(1 fi 4)-b-D-glucopyranose) is the fundamental disaccharide structural unit in cellulose; i.e., the smallest fragment of cellulose that contains a glycosidic linkage. It is therefore a convenient model compound on which to study variances in energies and internal coordinates associated with conformational isomerism in cellobiose. Previously [1], calculations were performed on 27 conformers of b-cellobiose, with different glycosidic, hydroxyl, and hydroxymethyl orientations, using the B3LYP density functional method and a large basis set (6-311++G**), in order to establish the conformational preference of the isolated molecule. The results showed that several of the anti structures were more stable than the lowest energy syn conformer, contrary to the predictions of most previous molecular mechanics [8] and (less sophisticated) quantum calculations [1]. It has been shown that accurate modeling of hydrogen bonded complexes requires the use of a large basis set, along with some treatment of electron correlation [9]. The B3LYP density functional method [10], using the 6-311++G** basis set, has been shown to give good structures and energies in the modeling of both hydrogenbonded complexes [9,11] and carbohydrates[12–15]. DFT methods have the advantage of being less computationally demanding than MP2 calculations (as well as having a lower basis set superposition error), while giving a more complete electronic description than Hartree–Fock calculations. At this level of theory, one cannot model a cellobiose molecule with 2–3 solvation shells; rather, the onset of the energetic preference of the syn-form can be studied by examining mono-, di-, tri-, and tetra-hydrate cellobiose clusters, and tracking the structural and energy changes associated with the addition of explicit water molecules. This methodology has been used to explain the anomeric preference in glucose [14–16]. This work presents B3LYP/6-311++G** calculations of a systematic stepwise hydration of the cellobiose molecule, considering both anti and syn conformers. The changes in internal coordinates and relative energy upon the addition of one to four molecules are presented, and the onset of the energetic preference for the syn form is examined. We examine the relative stabilities of the various hydrates as a function of water placement, cellobiose conformer, and

number of water molecules. We also examine the extent to which the most stable dihydrates, trihydrates, etc. can be predicted based upon the relative monohydrate stabilities. 2. Methodology To perform our calculations efficiently, most of the systems studied were initially optimized using the AMB02C empirical force field [17]. In some cases, only part of the molecule was optimized in this way, while the rest of the molecule was based on a previous DFT-optimized geometry. The empirical optimization was followed by optimization at the B3LYP/6-31+G* level, and calculations (energies and internal coordinates) reported here were those structures obtained from continuing the optimization using B3LYP/6-311++G**. The hardware and software employed for the calculations described here were from Parallel Quantum Solutions [18]. Calculations were performed on PQS software version 3.0 and 3.1, using four-processor workstations, with processor clock speeds ranging from 1.0 to 2.4 GHz. The convergence criteria for gradient and energy were 3 · 104 au and 1 · 106 Hartree, respectively. The presence of a local minimum was confirmed for each structure by the lack of negative eigenvalues in the Hessian matrix. The cellobiose–water complexes are based on a few selected anti and syn vacuum cellobiose structures. During the course of our studies, some new cellobiose geometries were explored; accordingly, there are anhydrous cellobiose structures presented here that were not a part of the earlier work [1]. Monohydrate starting structures were generated in a systematic way, so that all reasonable hydrogen-bonding sites were studied with both the anti and syn cellobiose structures. The complexes with 2–4 water molecules were designed by considering the relative stabilities of the monohydrates. Throughout this paper, an arrow will be used to denote both water position and direction of hydrogen bonding. For example, a water molecule in the 3 fi 2 position means that the water molecule accepts a hydrogen bond from the HO3 group on cellobiose and donates a hydrogen bond to O2. 3. Results and discussion 3.1. Anhydrous cellobiose conformers Fig. 1 gives the atom numbering convention employed here: the carbons are labeled with their number (the primed atoms are on the reducing sugar), and the attached hydrogen and oxygen atoms are given the same number, with, e.g., HO3 referring to the hydroxyl hydrogen attached to oxygen #3, which is itself bonded to C3. A conformer is designated syn or anti based upon whether the H1 and H4 0 atoms are on the same or opposite sides of the plane perpendicular to the C1–H1 and C4 0 –H4 0 bonds. The dihedral angles /H and wH, defined by H1–C1–O–C4 0

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

Fig. 1. Schematic diagram illustrating the atom numbering convention employed.

and C1–O–C4 0 –H4 0 , respectively, define the orientation of the two rings relative to one another. Syn conformers typically have /H in the range from 10–60, while wH varies from approximately 40 to 0, while anti conformers have either /H or wH close to 180 and the other dihedral angle close to 0. All figures are in approximately the same orientation as shown in Fig. 1. The 10 vacuum (i.e., anhydrous) cellobiose structures shown in Fig. 2 were considered in detail. Tables 1 and 2 give the values of selected internal coordinates for the vacuum cellobiose conformers. Since structural and energetic details of anhydrous cellobiose structures were the focus of reference [1], Table 1 includes only ranges of values for the geometric parameters of interest here. Table 2 gives the values of some internal coordinates associated with the glycosidic region and hydroxymethyl groups for each conformer, as well as a cross-reference to the structure numbers used in reference [1]. The structures are organized by conformer type (anti, then syn) and in order of increasing energy for each conformer type. The vacuum cellobiose conformer energies given are relative to the lowest energy cellobiose conformer (conformer A), which has a B3LYP/6-311++G** electronic energy of 814,729.147 kcal/mol.

3

The structures shown in Fig. 2 represent only about 1/3 of the total number of cellobiose structures presented in reference [1]; however, the bond lengths, angles, etc. in the conformers considered here are fairly typical of the full-data set. Each of the structures considered here is the basis for at least one of the hydrates studied, and the lowest two anti and the lowest three syn conformers of reference [1] are included in the present subset. For a monohydrate based on a higher energy vacuum cellobiose structure to be more stable than one based on a lower energy conformer, some other contribution(s) to the energy of complexation must compensate for the higher cellobiose conformer energy [19]. Accordingly, one would expect the lowest-energy cellobiose hydrates to be based upon low-energy cellobiose conformers. The lowest-energy syn structure (conformer G) is considerably higher in energy (by 3.8 kcal/mol) than the lowest-energy anti structure (conformer A), so the experimentally observed preference for the syn form in aqueous solution indicates that a considerable stabilization of the syn form (relative to the anti form) must occur due to interactions with water. Fig. 3 gives the H  O distances for all of the intramolecular hydrogen bonds in the lowest-energy anti and syn conformers of cellobiose. In each cellobiose conformer, there are only two or three intramolecular hydrogen bonds with lengths similar to those intermolecular hydrogen bonds seen in complexes of small molecules; the rigidity of the ring structure constrains the intra-ring hydrogen bonds to be relatively long. Accordingly, there are ample opportunities for cellobiose–water interactions to stabilize the system via the replacement of longer hydrogen bonds ˚ range) with shorter (and thus stronger) (in the 2.3–2.7 A ones. It was previously determined [1,20] that the source of the anti form stability lies in a synergism that arises from the length of continuous chain of intramolecular hydrogen bonds, on the left side of the molecule as displayed in Fig. 3. In addition to the syn/anti distinction, there are two other features that distinguish the various cellobiose conformers. A particular cellobiose conformer can be classified first by the orientation of the hydroxyl groups, i.e., whether they point clockwise or counterclockwise. In reference [1] it was found that those conformers with counter-clockwise donor–acceptor orientations on the two rings dominated the low-energy structures; accordingly, all but one (structure J) of the conformers studied here have that arrangement. A second characteristic of a given cellobiose structure is the orientation of the two hydroxymethyl groups, characterized by considering if O6 (or O6 0 ) is trans or gauche to O5 (O5 0 ) (first g or t) and C4 (C4 0 ) (second g or t). The three possibilities for each hydroxymethyl group are thus gg (giving rise to an O5–C5–C6–O6 dihedral angle of approximately 60), gt (O5–C5–C6–O6 dihedral 60), and tg (180). It is experimentally observed that both hydroxymethyl groups are in the gt orientation in crystalline cellobiose [2,3], while in aqueous solution the gg and gt rotamers are approximately equally populated,

4

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

Fig. 2. Vacuum cellobiose conformers used as the basis for cellobiose–water complexes studied here.

with little or no contribution from the tg rotamer [21]. The isolated molecule is a different situation, as any hydrogen bonding by the hydroxymethyl groups must be intramolecular. As a result, tg rotamers are present in several relatively stable vacuum cellobiose conformers; for example, in the lowest-energy syn conformer, both hydroxymethyl groups are tg. All of these quantities, as well as the values of the glycosidic dihedral angles /H and wH, are listed for the individual vacuum cellobiose conformers in Table 2. The variation in the hydroxyl and hydroxymethyl orientations, as well as the glycosidic dihedrals, gives rise to different hydrogen bonding arrangements in the various cellobiose conformers. Fig. 2 indicates (dashed lines) the inter-ring hydrogen bonds, as well as any other intramolec˚ in length. ular hydrogen bonds which are less than 2.20 A These shorter hydrogen bonds are typical of inter-ring and HO6–O4 hydrogen bonds (Fig. 3). At least one short, inter-residue hydrogen bond is present in each of the vacuum cellobiose structures presented here, with the exception of conformer F, which is the highest-energy conformer studied. In the 33 cellobiose structures considered here and in reference [1], there are only four conformers without

˚ , and all inter-residue hydrogen bonds shorter than 2.20 A of these are relatively high in energy. 3.2. Cellobiose monohydrates The monohydrate complexes are ordered in the same way as the vacuum cellobiose conformers: first the anti conformers, from lowest to highest energy, then the syn conformers, from lowest to highest energy. Fig. 4 displays the energy-minimized geometries of the 15 anti cellobiose monohydrate structures that were studied; below each figure is the monohydrate (mh) number, followed in parentheses by the letter corresponding to the vacuum cellobiose structure on which the monohydrate is based. Table 3 gives the numerical values of the changes in some relevant geometrical parameters upon hydration of the vacuum cellobiose structure for the monohydrates displayed in Fig. 4. Fig. 5 displays the corresponding structures, and the geometry changes in the syn monohydrate structures are presented in Table 4. The DE values in Figs. 4 and 5 and Tables 3 and 4 are relative to the lowest-energy monohydrate structure (mh #1), which has a B3LYP/6-311++G**

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19 Table 1 Ranges of selected geometric parameters for vacuum cellobiose Anti conformers

Syn conformers

Bond lengths rOH(2) rOH(3 0 ) rOH(6) rOH(6 0 ) Other rOH rCO(2) rCO(1 0 ) rCO(3 0 ) rCO(6) rCO(6 0 ) Other rCO C5–C6 C5 0 –C6 0

0.965  0.973 0.965  0.966 0.963  0.97 0.964  0.968 0.964  0.965 1.414  1.421 1.395  1.396 1.419  1.432 1.413  1.421 1.411  1.425 1.422  1.428 1.524  1.531 1.522  1.536

0.963  0.975 0.964  0.972 0.965  0.967 0.963  0.965 0.964  0.966 1.415  1.422 1.394  1.396 1.419  1.422 1.416  1.421 1.420  1.431 1.422  1.427 1.525  1.531 1.525  1.536

Sum of ring bond lengths Non-reducing ring Reducing ring

8.964  8.995 8.971  8.987

8.967  8.988 8.966  8.975

Bond angles hCOH(2) hCOH(1 0 ) hCOH(3 0 ) hCOH(6) hCOH(6 0 ) Other hCOH C6–C5–O5 C6 0 –C5 0 –O5 0 hrCO(1 0 ) hrCO(3 0 ) hrCO(6 0 ) Other hrCO

106.1  108.5 109.1  109.4 107.0  107.3 107.5  109.0 107.4  108.6 107.2  108.4 105.2  107.8 104.9  106.6 108.9  109.2 109.5  111.3 111.4  113.9 106.5  113.1

108.4  111.3 107.1  109.3 107.6  109.0 106.9  107.9 107.4  109.6 107.3  108.3 105.8  107.9 103.8  109.3 105.7  108.7 106.4  110.5 112.2  115.1 105.7  113.6

Dihedral angles /rCOH(2) /rCOH(3) /rCOH(4) /rCOH(1 0 ) /rCOH(2 0 ) /rCOH(3 0 ) /OCCx(1,2) /OCCx(2,3) /OCCx(3,4) /OCCx(4,6) /OCCx(1 0 ,2 0 ) /OCCx(2 0 ,3 0 ) /OCCx(3 0 ,1)

55.4  78.4 56.0  50.9 49.7  54.9 68.3  62.5 61.5  62.9 50.8  47.1 71.7  57.3 60.0  64.2 65.3  61.5 60.5  70.6 66.6  64.7 61.1  64.3 71.4  54.8

47.6  69.4 58.3  53.3 49.2  54.1 159.2  165.4a 175.7  174.2a 164.9  178.2a 73.5  65.8 63.4  68.1 65.5  6 0.8 59.6  67.1 64.7  61.2 63.4  67.2 75.6  64.3

Ring dihedrals C4–C5–O5–C1 C5–O5–C1–C2 C4 0 –C5 0 –O5 0 –C1 0 C5 0 –O5 0 –C1 0 –C2 0

53.8  62.0 63.1  54.4 57.8  63.9 64.6  60.9

59.6. . .63.6 64  56.8 58.9  65.6 64.6  61.9

˚ , bond angles are in degrees. Distances are in A a Values exclude conformer J, for which the three dihedrals are 64.7, 62.9, and 59.3, respectively.

calculated energy of 862717.036 kcal/mol. That each monohydrate is based on the vacuum cellobiose structure listed has been verified by carefully comparing the cellobiose geometries in the complexes with the vacuum structures. In Figs. 4 and 5, the lengths of the short hydrogen bonds are indicated, as well as all intermolecular hydrogen bonds.

5

As is evident from Fig. 4 and Table 3, the lowest five anti monohydrates found were all based on the lowest energy anti (vacuum) cellobiose structure, conformer A. The lowest four of these, monohydrates 1–4, have electronic energies within 0.55 kcal/mol of one other. Each of these monohydrates was formed by placing a water molecule between two adjacent hydroxyl groups on one of the rings of the cellobiose molecule. In monohydrate #5, the water donates a hydrogen bond to the 5 0 oxygen. This structure is noticeably higher in energy than the first four monohydrates, reflecting the relative weakness of the hydrogen bond from the water molecule to the ether oxygen. The lowest energy anti monohydrate has the water molecule bridging from 3 fi 2; this serves to move the 2-hydroxyl group closer to the reducing ring, resulting in a shorter (and presumably stronger) HO2  O3 0 hydrogen bond. While monohydrate #4, with the water molecule in the 3 0 fi 2 0 position, shows the same shortening of the interring hydrogen bond, structure #4 also brings about larger changes in the cellobiose geometry than does #1; this larger strain in the cellobiose molecule destabilizes monohydrate #4 relative to monohydrate #1. Inter-ring placements of the water molecule, either bridging from 6 fi 6 0 (mh #8 and #12) or from 2 fi 3 0 (mh #13 and #14), do not result in particularly stable cellobiose–water complexes, because of the relatively large amount of energy required to distort the conformation of the cellobiose molecule to accommodate the water molecule [19]. In contrast to the anti case, the lowest energy syn monohydrate is not based on the lowest energy syn cellobiose structure (conformer G). Instead, the lowest-energy syn monohydrate is based upon cellobiose conformer I, in which the hydroxymethyl group on the reducing sugar is in the gg rotamer. When a water molecule is placed between the 2 and 6 0 groups to form mh #16, a new (albeit weak) hydrogen bond forms between HO6 0 and O5 0 ˚ versus 2.93 A ˚ in the vacuum conformer). Fur(r = 2.38 A thermore, the addition of the water molecule changes both glycosidic dihedral angles by 10, so that they are very close to the values of the most stable syn cellobiose structure (conformer G); these values are also very close to the experimentally observed solution-phase dihedral angles[4]. In addition, the distortion of the molecule about the glycosidic linkage brings about a shorter inter-ring (HO3 0 fi O5) hydrogen bond on the other side of the mol˚ in the monohydrate, versus 2.03 A ˚ in the vacecule (1.91 A uum cellobiose conformer). In conformer G, where the hydroxymethyl group on the reducing ring is in the tg orientation, a new hydrogen bond also forms upon adding a water molecule in the same location (to form mh #20); in this case, the new H-bond is between HO6 0 and O2 (Fig. 5). Despite the fact that this newly formed hydrogen bond is shorter than the one formed in mh #16, mh #20 is less stable than mh #16, since the new H-bond in mh #20 does not extend the hydrogen bond network in the same way that the HO6 0 fi O5 0 one does. In mh #16 a synergistic hydrogen bonding network is established, as was found

6

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

Table 2 Internal coordinates and energies of ten vacuum cellobiose conformers Conformer

A

B

C

D

E

F

G

H

I

J

Structure in reference [1] Conformers type DEvaca

XIX Anti 0.00

XVIII Anti 1.87

n/a Anti 3.17

n/a Anti 3.52

XXI Anti 3.78

n/a Anti 7.36

X Syn 3.84

n/a Syn 4.11

VI Syn 4.41

n/a Syn 6.63

Bond lengths C1–O1 C4 0 –O1

1.408 1.431

1.407 1.429

1.395 1.437

1.402 1.435

1.402 1.431

1.404 1.440

1.389 1.431

1.388 1.446

1.396 1.428

1.404 1.426

Bond angles O5–C1–O1 C1–O1–C4 0 C3 0 –C4 0 –O1

107.9 118.9 108.4

108.6 118.2 109.4

108.5 120.8 107.8

108.9 120.7 107.9

109.0 120.0 108.8

107.2 120.4 114.2

108.3 119.0 110.7

109.0 117.5 109.6

107.3 117.5 113.3

107.5 118.7 111.6

179.4 0.6 59.1 gg 59.0 gg

169.5 3.9 54.2 gt 58.5 gg

177.4 1.2 165.9 tg 162.5 tg

176.6 1.9 166.2 tg 57.1 gg

179.2 3.0 59.0 gg 61.9 gt

48.3 162.4 56.7 gg 161.0 tg

28.5 25.2 166.2 tg 164.5 tg

44.4 14.9 166.6 tg 60.6 gg

17.8 36.7 166.0 tg 81.7 gg

7.0 38.0 56.3 gg 174.7 tg

Dihedral angles /H wH O5–C5–C6–O6 Non-reducing CH2OH O5 0 –C5 0 –C6 0 –O6 0 Reducing CH2OH

˚ , bond angles are in degrees, and energies are in kcal/mol. Distances are in A a Energies are relative to the B3LYP/6-311++G** energy of conformer A, which is 814,729.15 kcal/mol.

We present here only a small fraction of the cellobiose monohydrates that could be imagined, if one considers all of the possible hydrogen-bonding sites on all the viable vacuum cellobiose structures. In deciding on structures to study, however, at least one structure has been considered for each of the possible donor–acceptor sites at which water may be added. In addition, there are monohydrates based on several different low energy cellobiose conformers. Accordingly, it is likely that the structures shown in Figs. 4 and 5 include the lowest-energy monohydrate conformers that would be predicted by this level of theory. 3.3. Geometry changes upon hydration

Fig. 3. The lowest-energy anti and syn cellobiose conformers, in the absence of hydrating water molecules. Intramolecular hydrogen bond ˚ ) are indicated. lengths (A

in the most stable anti cellobiose conformers [1,20]. The intra-ring placements of the water molecules in monohydrates 17–19 do give rise to relatively stable complexes; however, there is a noticeable difference in energy between mh #16 and mh #17. In mh #16, one can see the beginnings of the stabilization of the syn form in solution relative to the anti form: The energy gap has decreased from 3.84 to 0.83 kcal/mol upon the addition of the first water molecule. Even in the case of the 2nd lowest syn structure, which has a water in the 3 fi 2 position (the same as in the lowest energy anti form), there has been a greater stabilization of the syn form than the anti form, as evidenced by a closing of the anti–syn energy gap by 1.0 kcal/mol. The reasons for this change in relative energy are discussed in reference [19].

Most of the noticeable geometry changes in cellobiose upon hydration occur in the immediate vicinity of the water molecule. Elsewhere in the molecule, the various bond lengths and angles are extremely close to their vacuum cellobiose values. In designing the data tables presented here (Tables 1–8), this fact was taken into account, and the relevant changes in geometry are indicated at the cellobiose hydrogen bond donor (D) or acceptor (A) sites, or at the site neighboring the donor (nD) group. At sites other than those listed in the Tables, most changes in bond lengths ˚ , while bond angles and dihedral were less than 0.002 A angles not listed in the Tables typically changed by less than 1. 3.3.1. Bond length changes upon addition of a water molecule The O–H bond lengths (denoted rOH(j) in Table 1, and the change in this quantity is denoted DrOH(j) in Tables 3 and 4, where j is the index of the hydroxyl group) in vacuum cellobiose conformers fall into three main categories. In the vacuum cellobiose conformers (Table 1), the longest ˚ , are those in which bonds, ranging from 0.967–0.975 A

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

7

Fig. 4. Structures of the anti water monohydrates, arranged in order of increasing relative energy (in kcal/mol). Cellobiose–water hydrogen bonds and ˚ ) are indicated. The letter in parentheses is the vacuum cellobiose conformer upon which the monohydrate short cellobiose intramolecular bond lengths (A is based.

Table 3 Geometry changes relative to vacuum cellobiose, in the anti monohydrates mh #

1

2

3

4

H2O (D fi A) DErel Vac. CB DrOH(D) DrCO(D) DrCO(A) Drnonred_ring Drred_ring DhCOH(D) DhCOH(A) DhrCO(D) DhrCO(A) D/rCOH(D) D/rCOH(A) D/rCOH(nD) D/OCCx(D,A)

3fi2 0.00 A 0.009 0.006 0.010 0.008 0.00 2.3 0.3 1.8 2.5 24.2 0.7 3.2 4.8

4fi3 0.22 A 0.010 0.008 0.011 0.007 0.00 2.0 0.6 1.2 2.5 20.6 2.9 n/a 5.7

20 fi 10 0.28 A 0.012 0.009 0.011 0.001 0.005 0.8 0.7 1.2 1.8 14.7 4.6 1.7 2.7

30 fi 20 10 fi 50 0.54 1.43 A A 0.013 0.010 0.008 0.011 0.010 n/a 0.00 0.001 0.010 0.021 2.1 1.0 1.2 n/a 1.5 0.3 2.9 n/a 22.7 0.6 9.4 n/a 1.4 3.6 4.4 n/a

5

6

7

8

9

10

11

12

13

14

15

4fi3 2.06 B 0.010 0.007 0.011 0.008 0.00 1.7 0.8 1.2 2.5 24.0 7.0 n/a 5.2

3fi2 2.74 C 0.011 0.006 0.010 0.008 0.00 1.4 0.1 1.6 2.3 25.0 0.9 3.3 4.2

6 fi 60 3.18 B 0.002 0.004 0.008 0.008 0.003 0.4 1.0 1.5 2.1 47.3 11.7 n/a n/a

3fi2 3.23 D 0.010 0.005 0.010 0.008 0.00 1.5 0.0 1.7 2.3 25.7 1.3 3.3 4.3

30 fi 20 3.37 C 0.014 0.008 0.011 0.00 0.010 2.2 1.3 1.5 3.1 23.6 9.3 2.6 5.3

30 fi 20 3.98 D 0.013 0.008 0.010 0.001 0.010 2.1 1.2 1.5 2.9 23.8 9.4 3.6 5.2

6 fi 60 4.65 A 0.004 0.005 0.004 0.013 0.009 1.9 1.2 1.3 1.0 14.9 10.4 n/a n/a

2 fi 30 5.50 A 0.006 0.009 0.010 0.002 0.005 5.4 0.5 0.8 0.7 11.0 18.3 2.6 n/a

2 fi 30 6.66 F 0.014 0.009 0.010 0.009 0.001 3.5 0.6 1.2 1.0 7.9 1.8 3.4 n/a

6.91 E n/a n/a 0.011 0.007 0.001 n/a 0.6 n/a 0.3 n/a 12.9 n/a n/a

˚ , bond angles are in degrees, and energies are in kcal/mol. Distances are in A a The water molecule is not in a single-donor, single-acceptor configuration; see Fig. 4.

a

8

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

Fig. 5. Structures of the syn water monohydrates, arranged in order of increasing relative energy.

Table 4 Geometry changes relative to vacuum cellobiose, in the syn monohydrates mh #

16

17

18

19

20

21

22

23

24

H2O (D fi A) DErel Vac. CB DrOH(D) DrCO(D) DrCO(A) Drnonred_ring Drred_ring DhCOH(D) DhCOH(A) DhrCO(D) DhrCO(A) D/rCOH(D) D/rCOH(A) D/rCOH(nD) D/OCCx(D,A)

2 fi 60 0.83 I 0.006 0.003 0.005 0.018 0.000 1.5 1.6 2.0 2.4 93.3 17.9 10.1 n/a

3fi2 2.89 G 0.012 0.007 0.010 0.008 0.001 1.1 0.1 1.5 2.1 21.0 1.8 3.3 3.8

20 fi 30 3.38 G 0.012 0.007 0.011 0.002 0.010 2.1 0.1 1.7 2.0 18.1 0.7 1.7 5.6

4fi3 3.50 G 0.013 0.006 0.011 0.006 0.000 1.6 1.0 1.5 2.8 23.4 8.0 2.7 4.7

2 fi 60 3.89 G 0.005 0.007 0.007 0.008 0.002 0.3 1.0 0.3 0.5 48.9 144.0 3.3 n/a

20 fi 30 3.95 I 0.012 0.006 0.010 0.003 0.011 1.2 0.1 1.3 2.1 21.9 3.0 0.6 3.9

10 fi 20 4.03 G 0.010 0.009 0.010 0.000 0.006 1.4 0.8 0.6 2.0 40.4 5.6 n/a 5.1

4fi3 4.16 I 0.012 0.005 0.011 0.005 0.000 1.6 1.0 1.5 2.8 24.8 8.2 2.4 4.5

3fi2 a 2 fi 1 6 fi 4 30 fi 5 6 fi 5 a 4.28 4.98 4.99 6.81 7.20 7.60 8.30 H H H G G J G 0.011 n/a 0.010 0.006 0.002 0.006 n/a 0.007 n/a 0.008 0.006 0.001 0.006 n/a 0.010 0.009 n/a 0.007 n/a n/a 0.005 0.006 0.004 0.003 0.003 0.006 0.009 0.000 0.001 0.004 0.001 0.000 0.011 0.001 0.006 0.9 n/a 0.0 1.5 0.9 1.5 n/a 0.9 0.2 n/a 1.9 n/a n/a 0.5 1.4 n/a 0.8 0.8 0.1 1.6 n/a 2.2 0.5 n/a 2.5 n/a n/a 0.2 20.7 n/a 13.9 43.8 42.3 25.2 n/a 7.8 8.6 n/a 9.7 n/a n/a 2.7 3.2 n/a 3.0 n/a 1.8 n/a n/a 3.1 n/a 0.6 n/a n/a 7.1 n/a

25

26

27

28

29

30

˚ , bond angles are in degrees, and energies are in kcal/mol. Distances are in A a The water molecule is not in a single-donor, single-acceptor configuration; see Fig. 5.

the hydrogen atom is a hydrogen-bond donor in a ‘‘short’’ ˚ ) hydrogen bond. The shortest O–H bonds, all at (<2.20 A ˚ ˚ in the 0.963 A in structures A–J (but as short as 0.961 A

full-data set of 33 cellobiose structures studied here and in reference [1]), are those in which the hydrogen atom does not participate in a hydrogen bond. In the middle, ranging

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

9

Table 5 Monohydrate geometry changes related to the glycosidic region and hydroxymethyl groups mh #

Anti

H2O (D fi A) DErel Vac. CB

6 fi 60 3.18 B

8

Syn 12 6 fi 60 4.65 A

13 2 fi 30 5.50 A

14 2 fi 30 6.66 F

15

16

a

20

25

2 fi 60 3.89 G

26

a

6.91 E

2 fi 60 0.83 I

0.004 0.003 0.000 0.003

0.002 0.005 0.003 0.000

0.008 0.005 0.000 0.004

0.005 0.010 0.000 0.000

0.006 0.002 0.000 0.000

27

4.98 H

2fi1 4.99 H

6fi4 6.81 G

0.010 0.005 0.000 0.000

0.001 0.000 0.009 0.000

28 30 fi 5 7.20 G

29 6fi5 7.60 J

Changes in bond lengths C1–O1 0.001 C4 0 –O1 0.000 C5–C6 0.008 C5 0 –C6 0 0.000

0.000 0.002 0.001 0.004

Changes in bond angles C1–O1–C4 0 2.1 O5–C1–O1 0.9 C3 0 –C4 0 –O1 0.5 C6–C5–O5 2.3 C6 0 –C5 0 –O5 0 1.5

2.7 1.8 1.1 2.9 0.5

0.5 0.7 0.9 0.8 1.5

0.6 0.9 0.6 0.8 0.7

0.1 0.6 0.4 0.3 0.3

0.5 0.7 1.7 0.3 3.2

0.1 0.9 0.6 0.2 0.9

0.1 0.2 0.0 0.0 0.7

1.0 1.4 0.5 0.0 0.5

0.0 0.1 0.0 1.6 0.0

0.6 0.0 1.0 0.4 0.9

0.0 0.5 0.2 2.2 0.1

Changes in dihedral angles 7.2 D/H 1.2 DwH O5–C5–C6–O6 12.3 O5 0 –C5 0 –C6 0 –O6 0 7.6 C4–C5–O5–C1 5.4 C5–O5–C1–C2 2.3 C4 0 –C5 0 –O5 0 –C1 0 3.1 C5 0 –O5 0 –C1 0 –C2 0 0.1

2.3 9.5 15.7 13.2 5.2 8.3 2.4 2.3

19.4 5.4 2.8 3.5 2.7 6.2 3.0 1.3

2.0 7.4 0.6 0.7 2.6 0.7 0.7 1.8

2.5 0.8 9.1 0.9 3.8 4.9 0.9 0.5

12.0 10.7 0.8 22.4 2.0 4.2 3.7 0.7

9.2 3.1 0.2 1.7 1.2 2.8 0.1 1.1

0.3 0.7 0.9 6.3 0.8 1.7 0.9 1.0

0.2 6.1 0.0 1.1 0.3 0.0 0.7 0.4

0.1 0.2 15.3 0.2 0.1 0.9 0.1 0.0

14.7 7.5 1.5 5.2 2.9 2.6 0.2 0.4

0.1 2.4 7.1 1.4 0.2 0.3 0.1 0.3

0.015 0.002 0.000 0.001

0.003 0.006 0.000 0.001

0.001 0.003 0.004 0.000

˚ , bond angles are in degrees, and energies are in kcal/mol. Distances are in A a The water molecule is not in a single-donor, single-acceptor configuration; see Figs. 4 and 5. Table 6 Geometry changes relative to vacuum cellobiose, in the anti dihydrates dh #

1

2

3

4

5

6

7

8

9

10

DErel H2O #1 (D fi A) H2O #2 (D fi A) Vac. CB DrCO(D1) DrCO(A1) DrCO(D2) DrCO(A2) Drnonred_ring Drred_ring D/rCOH(D1) D/rCOH(A1) D/rCOH(D2) D/rCOH(A2) D/OCCx(D1,A1) D/OCCx(D2,A2)

0.11 4fi3 3fi2 A 0.007 0.004 0.004 0.012 0.015 0.000 26.4 23.1 23.1 0.3 5.2 4.0

0.12 3fi2 20 fi 10 A 0.006 0.010 0.008 0.011 0.009 0.005 23.9 0.6 17.1 9.7 4.7 2.3

0.15 3fi2 30 fi 20 A 0.006 0.008 0.007 0.010 0.008 0.010 23.2 1.2 21.4 9.5 4.8 4.2

0.34 4fi3 20 fi 10 A 0.008 0.011 0.007 0.012 0.007 0.004 20.4 3.5 16.9 9.5 5.5 2.1

0.45 4fi3 3fi2 A 0.007 0.006 0.006 0.011 0.016 0.001 25.4 24.9 24.9 1.6 5.2 3.4

0.47 4fi3 20 fi 10 A 0.007 0.011 0.008 0.012 0.008 0.004 22.2 7.1 16.7 9.6 4.5 2.1

1.23 3fi2 10 fi 50 A 0.007 0.010 0.012 n/a 0.009 0.020 24.2 0.9 0.6 n/a 4.9 n/a

2.33 3fi2 20 fi 10 C 0.007 0.010 0.008 0.012 0.008 0.004 21.7 0.6 16.9 11.9 4.9 2.5

2.36 4fi3 3fi2 C 0.006 0.005 0.005 0.012 0.015 0.000 26.2 23.4 23.4 1.4 4.9 3.2

2.44 4fi3 60 fi 50 A 0.007 0.011 0.006 n/a 0.005 0.010 22.6 6.3 22.4 n/a 4.6 4.4

11 5.81 3fi2 a

C 0.008 0.008 n/a n/a 0.008 0.000 24.1 0.5 n/a n/a 4.1 n/a

˚ , bond angles are in degrees, and energies are in kcal/mol. Distances are in A a The water molecule is not in a single-donor, single-acceptor configuration; see Fig. 6.

˚ , are those OH groups in which the from 0.963–0.969 A ˚ ) hydrogen hydrogen atom is a donor to a ‘‘long’’ (>2.20 A bond. The largest ranges of O–H bond lengths in Table 1 are present in the 2, 3 0 , 6, and 6 0 hydroxyl groups, because these groups can donate to either ‘‘short’’ or ‘‘long’’ hydrogen bonds, or to no hydrogen bond at all. Since HO6 0 only acts as a donor in short hydrogen bonds in the anti form, the range of OH values for the 6 0 group is smaller in the syn conformers than in the anti conformers (similarly,

HO3 0 donates to short H-bonds only in the syn conformers). For the most part, the cellobiose O–H bond lengths change in a predictable way upon hydration (Tables 3, 4). The O–H bond at the hydrogen bond donor (to water) ˚ when the water is placed site typically increases by 0.01 A between two hydroxyl groups on the same ring; this change is the same magnitude as was found in monohydrates of glucose[15]. The increase in O–H bond length is somewhat

10

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

Table 7 Geometry changes relative to vacuum cellobiose, in the syn dihydrates dh #

12

13

14

15

16

17

18

19

20

DErel H2O #1 (D fi A) H2O #2 (D fi A) Vac. CB DrCO(D1) DrCO(A1) DrCO(D2) DrCO(A2) Drnonred_ring Drred_ring D/rCOH(D1) D/rCOH(A1) D/rCOH(D2) D/rCOH(A2) D/OCCx(D1,A1) D/OCCx(D2,A2)

0.00 2 fi 60 20 fi 30 I 0.003 0.006 0.006 0.008 0.020 0.010 95.2 18.3 20.5 10.3 n/a 3.5

0.02 2 fi 60 3fi2 I 0.009 0.005 0.007 0.009 0.026 0.001 90.3 18.6 8.4 90.3 n/a 0.6

0.15 2 fi 60 4fi3 I 0.001 0.005 0.004 0.009 0.025 0.000 92.6 18.0 23.9 16.5 n/a 5.1

0.63 2 fi 60 10 fi 20 I 0.003 0.005 0.010 0.010 0.019 0.007 92.5 19.1 35.2 7.4 n/a 3.4

2.23 3fi2 20 fi 30 G 0.007 0.010 0.007 0.011 0.011 0.011 21.3 1.5 18.7 1.2 3.9 5.6

2.44 4fi3 3fi2 G 0.006 0.004 0.004 0.012 0.015 0.001 26.0 18.8 18.8 3.0 5.5 3.2

3.48 4fi3 10 fi 20 G 0.006 0.011 0.009 0.010 0.006 0.005 23.5 8.1 40.3 5.7 4.7 5.1

3.61 4fi3 3fi2 H 0.006 0.002 0.002 0.012 0.014 0.001 26.1 17.8 17.8 5.7 4.5 2.8

4.19 3fi2 10 fi 20 H 0.008 0.010 0.009 0.010 0.007 0.006 18.2 4.3 40.4 5.5 3.7 5.4

˚ , bond angles are in degrees, and energies are in kcal/mol. Distances are in A

Table 8 Dihydrate geometry changes in the glycosidic region dh # DErel H2O #1 (D fi A) H2O #2 (D fi A) Vac. CB Changes in glycosidic bond lengths C1–O1 C4 0 –O1 Changes in dihedral angles D/H DwH Changes in ring dihedrals C4–C5–O5–C1 C5–O5–C1–C2 C4 0 –C5 0 –O5 0 –C1 0 C5 0 –O5 0 –C1 0 –C2 0

12

13

0.00 2 fi 60 2 fi 30 I

14

0.02 2 fi 60 3fi2 I

0.15 2 fi 60 4fi3 I

15 0.63 2 fi 60 10 fi 20 I

0.009 0.007

0.006 0.006

0.007 0.005

0.009 0.005

11.5 13.5

13.2 9.9

12.3 9.3

11.8 10.5

1.9 3.8 3.0 1.6

3.4 4.5 3.8 0.8

2.4 4.7 3.6 0.7

2.0 4.3 3.4 1.6

˚ , bond angles are in degrees, and energies are in kcal/mol. Distances are in A

smaller when the donor is a hydroxymethyl group, and also smaller for inter-ring water placement (since the O–H bond in question is already lengthened by its participation in a short H-bond in the vacuum cellobiose conformer). There is sometimes a slight increase in the O–H bond length on the acceptor group as well, but these increases are generally ˚ or less, so they have not been included in Tables 0.002 A 3 and 4. Most of the calculated C–OH bond lengths (denoted rCO (j) in Table 1, and DrCO(j) in Tables 3 and 4) in vacuum cel˚ . The exceplobiose are in the range from 1.411 to 1.432 A tions to this are at the anomeric site on the reducing ˚ . That residue, where the C–O bonds are all less than 1.4 A the C–O bond is shorter at the anomeric site has been observed experimentally in cellobiose [2,3] and in glucose [3]. Among the other C–OH bond lengths, there is typically a shortening of the C–O bond when the hydrogen atom

attached to the oxygen is a donor in a short hydrogen bond, and a lengthening when the OH group is not donating to a hydrogen bond at all. In addition, the C–O bond tends to be somewhat longer in conformers where the oxygen atom accepts a short hydrogen bond. These trends cause the larger ranges of C–O bond lengths at those molecular sites (2, 4, 6, 3 0 , and 6 0 ) where the hydroxyl groups participate in the shorter hydrogen bonds. When cellobiose forms a monohydrate complex, the ˚ C–OH bond lengths typically decrease by 0.005–0.010 A at the hydrogen bond donor site, and increase by ˚ at the acceptor site (see Tables 3 and 4). Here 0.010 A again, the exceptions tend to be either those structures with water in the inter-ring region or those with the water molecule at the 6 or 6 0 group. The additional flexibility afforded by the hydroxymethyl groups and by rotation about the glycosidic linkage tends to decrease the magnitude of

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

the bond length changes. Exceptions to this arise in mh #13 and #14, where the water molecule is in the 2 fi 3 0 position. In these conformers, the addition of the water molecule causes a large strain on the glycosidic region of the cellobiose molecule [19], so the relatively large changes in the glycosidic dihedrals alone are not sufficient to accommodate the water molecule. Consequently, in both mh #13 and mh #14, the changes in C–O bond lengths near the water molecule are approximately as large as in the structures with intra-ring water molecules. The individual ring bond lengths vary in rather complicated ways; however, the overall structural changes in the rings can be quantified by summing the changes in the C–C and C–O bonds around the ring, as has been done in Table 1. Upon adding a water molecule, the sum of the bond length changes generally amounts to an increase ˚ in whichever ring is interacting with of 0.005–0.010 A the water molecule, and not much change in the sum of bonds around the other ring. Two interesting exceptions are mh #5 and #8, where the water bridges from 1 0 fi 5 0 . For these structures, the increase is in the sum of bond ˚ , essentially all due to a lengthening lengths is 0.020 A of the C5 0 –O5 0 bond by that amount. Also interesting in this respect are conformers mh #15 and #25, in which the water molecule is an H-bond donor to a hydroxymethyl group on the cellobiose but is not an H-bond acceptor. In mh #15, the non-reducing ring actually decreases in size, ˚ in the C5–O5 bond length; this due to a decrease of 0.007 A is likely due to a decrease in the hydrogen bonding interaction between HO6 and O5 upon addition of the water molecule near the non-reducing hydroxymethyl group. In mh #25, the water is hydrogen bonded to O6 0 , but the proximity of the water molecule to the non-reducing ring results in the two rings being increased in size by approximately the ˚ ). Another interesting case arises for same amount (0.004 A mh #16, the most stable syn monohydrate. In this conform˚ ) increase in the size er, there is an unusually large (0.018 A of the non-reducing ring, but no net change in the size of the non-reducing ring (although there are significant bond length changes, they sum to zero). 3.3.2. Changes in bond angles upon hydration Most cellobiose C–O–H bond angles (denoted hCOH(j) in Table 1, with changes denoted DhCOH(j) in Tables 3 and 4) fall in the 107–109 range. If an OH group is not an H-bond donor, the corresponding C–O–H angle will be near the bottom of that range, while non-H-bond accepting OH groups give rise to C–O–H angles near the top of that range. In addition, there is a pronounced difference between the C–O–H bond angles in the 2 position, depending on whether the molecule is anti or syn. In the anti conformers, the 2-hydroxyl group typically donates to O3 0 , resulting in hCOH(2)  106.6 (conformer F does not have such an H-bond, so its bond angle is 2 larger than in all of the other anti conformers). In most of the syn conformers, the 2-hydroxyl group donates to the 6 0 group, resulting in a bond angle greater than 109. Similar-

11

ly, the nature of the inter-residue hydrogen bonding gives rise to differences in hCOH(3 0 ) values between syn and anti conformers. The C–O–H angle at the 6-position is constrained to the very narrow range 107.7–107.9, owing to the relatively strong HO6  O4 hydrogen bond and the flexibility in the hydroxymethyl group. No noticeable trends were found in the 6- and 6 0 - hydroxyl C–O–H bond angles that depended on the rotamer type (gg, tg, or gt). The r–C–OH bond angles [denoted hrCO(j) in Table 1, and DhrCO(j) in Tables 3 and 4, where the ring atom ‘‘r’’ is either O5, in the case of hrCO(1 0 ), or carbon (j  1)] generally depend on the orientation of the hydrogen atom attached to oxygen ‘‘j’’. If the hydrogen atom lies along the r–C bond, the r–C–O bond angle usually falls in the range 110.5–113.0, while if the hydrogen atom points away from the ‘‘r’’ atom, the angle range is approximately 105.0–108.5. Exceptions arise in the hydroxymethyl groups (where the hrCO angle can be somewhat larger), and where r = O5 0 (often giving rise to angles between the two ranges), as well as in the case of hrCO(3 0 ) (where an HO3 0   O5 inter-residue hydrogen bond in the syn conformers can result in an angle between the two ranges). Upon hydration, the hCOH and hrCO angles in the vicinity of the added water molecule change by small amounts, typically 3 or less. Changes in these angles are noticeable at the donor and acceptor sites. The C–O–H angle changes are largest at the donor site, with typical values of 1–2. That the C2–O2–HO2 angles in mh #13 and mh #14 increase by 5.4 and 3.5, respectively, highlights the stress put on the cellobiose molecule by forcing a water molecule to be between the 2 and 3 0 groups in the anti cellobiose conformer. For the r–C–O case, the largest changes are at the acceptor site, with changes of 2–3 typical of those structures with the water molecule placed between two hydroxyl groups on the same ring. 3.3.3. Dihedral angle changes The r–C–O–H dihedral angles [denoted as a range by /rCOH(j) in Table 1, and D/rCOH(j) in Tables 3 and 4, where the r atom is again either O5 0 or C(j  1)] are indicative of the direction that the OH groups point along the ring. Most of these values fall within ranges of 5 for a particular dihedral angle and conformer type (See Table 1). One set of exceptions occurs in the C1–C2–O2–HO2 dihedral: anti conformer F, which is the only anti cellobiose conformer in Fig. 2 without a short HO2  O3 0 hydrogen bond, has a C1–C2–O2–HO2 dihedral angle of 55.4, much less than conformers A–E. Furthermore, the HO2  O6 0 hydrogen bond in the syn conformers studied, combined with a large range of /H and wH values, leads to a large range of /rCOH(2) values. The large range (16.9) of values present in the syn conformers for the C2 0 –C3 0 –O3 0 –HO3 0 dihedral is because the HO3 0 atom serves as a hydrogen bond donor to O5 in most of these conformers, so a small change in the glycosidic linkage will have a noticeable effect in the C2 0 –C3 0 –O3 0 –HO3 0 dihedral.

12

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

Significant changes in the cellobiose /rCOH dihedrals occur upon hydration (See Tables 3 and 4). To accommodate the water molecule, the cellobiose molecule generally ‘‘swings out’’ the donor hydroxyl group, by a rotation about the C–OH bond. This produces dihedral angle changes that are typically in the range 10–50. Smaller changes are observed when the water spans from HO1 0 to O5 0 site (monohydrate 5), and a particularly large change (93.3) in this dihedral occurs in the most stable syn complex (mh #16). In addition to the changes at the donor site, the inclusion of the water molecule, with the concomitant hydrogen bond to the acceptor site, causes the r–C–O–H dihedral to change at the acceptor site as well, generally by 1–10. These changes tend to be small when the H-bond acceptor group is also donating in a (relatively short) inter-ring hydrogen bond (e.g., /rCOH(2), in the case of water in the 3 fi 2 position); the stronger hydrogen bond constrains the hydroxyl group to a narrower range of dihedral angles. There is a very large change (144) observed in /rCOH(6 0 ) in monohydrate #20, relative to vacuum cellobiose conformer G, due to a rearrangement of intramolecular hydrogen bonds upon the addition of the water molecule (Fig. 5, cf. Structure G in Fig. 2). In monohydrate #12, the 1 0 -hydroxyl group has been rotated by 117 relative to cellobiose conformer A, because the HO1 0   O5 0 hydrogen bond has switched to the other lone pair on O5 0 ; this change in hydrogen bonding destabilizes the complex somewhat. A more detailed analysis of the implications of this change is presented in reference [19]. There is also a large change in the C5 0 –C6 0 –O6 0 –HO6 0 dihedral in monohydrate #16, due to the formation of a new hydrogen bond between HO6 0 and O5 0 . The rotation of the hydrogen bond donor group brings about a rotation of the neighboring hydroxyl group (nD, in Tables 3 and 4), with changes of 1–3 (10.7 in the case of monohydrate #16). As with the r–C–O–H dihedrals, most of the individual O–C–C–x dihedral angles (denoted /OCCx(i,j) in Tables 1, 3 and 4, where x = O or C6, and Ci and Cj are two adjacent carbon atoms) on vacuum cellobiose have ranges of 5. Most of the exceptions can be explained in terms of the inter-ring hydrogen bonds. For example, in the anti conformers studied, /OCCx(1,2) lies between 62.0 and 57.3, except in conformer F, where there is no HO2  O3 0 hydrogen bond (for the same reason, conformer F has a O3 0 –C3 0 –C4 0 –O1 dihedral angle of 54.8; the next highest value is 66.1). For the case of the O4–C4– C5–C6 dihedral, the values for both the anti and syn conformers fall between 59.6 and 61.4 when there is a HO6  O4 hydrogen bond, and are in the 66.3–70.6 range if such a hydrogen bond is not present. Conformer I is unusual in the O–C–C–O dihedrals in the glycosidic region, namely O1–C1–C2–O2 (73.5) and O3 0 –C3 0 –C4 0 –O1 (64.3). The values for both of these dihedrals are significantly different from those of the other syn conformers, even when the other structures presented in reference [1] are considered. Interestingly, conformer I forms the basis

for the hydrated structures that stabilize the syn form relative to the anti form; furthermore, adding a water molecule to the glycosidic region brings these two dihedral angles closer to the values characteristic of other syn cellobiose conformers. The addition of the water molecule produces a torsion about the ring bond in between the two hydroxyl groups interacting with the water; this is manifested in a change in the O–C–C–O (or O4–C4–C5–C6) dihedral angle (see Tables 3 and 4). These dihedrals typically change from 3 to 5, with a larger change in monohydrate #29, where the torsion is about C5–C6, rather than a ring bond. The OCCO dihedral angles are clearly not as flexible as the r– C–O–H dihedrals, due to the constraining effect of the ring structures. 3.3.4. Cellobiose–water interactions in the hydroxymethyl and glycosidic regions The various monohydrate conformers in which water molecules are interacting with the glycosidic and hydroxymethyl regions in cellobiose provide insights into the change in relative stability of the syn and anti forms as more water molecules are added. The relevant bond lengths, bond angles, and dihedral angles have been tabulated for vacuum cellobiose in Tables 1 and 2. Table 5 gives the changes for both the anti and syn monohydrate conformers, focusing on those complexes in which the water molecule interacts with cellobiose in the inter-ring region or with the hydroxymethyl groups (or both). With rare exceptions, these are the only monohydrate complexes in which significant changes occur in the intramolecular coordinates listed in Table 5. The glycosidic bond lengths (C1–O1 and C4 0 –O1) for the individual vacuum cellobiose conformers are tabulated in Table 2. In all of the cellobiose conformers, the C1–O1 bonds are shorter than the C4 0 –O1 bonds, as was noted in reference [1]. When a water molecule is placed in the glycosidic region, there are noticeable differences in how the glycosidic bond lengths change, depending on which hydroxyl groups interact with the water molecule. For water placement between HO6 and O6 0 (anti monohydrates 8 and 12 in Table 5), there is very little adjustment in the glycosidic bond lengths; the hydroxymethyl groups readjust to accommodate the water molecule. There is a noticeable difference between the two anti monohydrates with the water molecule bridging from 2 fi 3 0 (mh #13 and #14): For mh #13, which is based upon cellobiose conformer ˚ ) in the C1–O1 bond A, there is a large increase (0.015 A length, to make room for the water. In mh #14, which is based upon cellobiose conformer F, there is already a good deal of space in the region to be occupied by the water molecule, so not as much change in the bond lengths is required; in fact, the C4 0 –O1 bond actually shortens by almost as much as the C1–O1 bond increase in length. For the 2 fi 6 0 syn conformers (mh #16 and #20), there is also a decrease in the C1–O1 glycosidic bond, due to the newly formed hydrogen bonds. Monohydrate 28, where

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

the water bridges from 3 0 fi 5, shows increases in both glycosidic bonds, as does monohydrate 26, where the water connects the HO2 with the bridging oxygen. In mh #15 and #25, the water molecule is only forming one hydrogen bond with the cellobiose molecule; however, there are changes in the glycosidic region, despite the fact that the hydroxymethyl group that interacts with the water is not involved in an inter-ring hydrogen bond in the corresponding vacuum cellobiose conformer. The C5–C6 and C5 0 –C6 0 bond lengths in vacuum cellobiose (Table 1) show similar behavior in the anti and syn forms, and give a fairly large range of values, owing to the different conformations and hydrogen bonding arrangements available to the 6 and 6 0 groups. With a few exceptions, there are not many significant changes in these bond lengths upon the addition of a water molecule. In mh #8 and #12, there is some adjustment in these bond lengths, as mentioned above. In addition, there is a lengthening of the C5–C6 bond length in mh #27, as the placement of water from 6 fi 4 requires some rearrangement of the hydroxymethyl group. As was found in reference [16], there is no evidence to support the shortening of the C5–C6 (or C5 0 –C6 0 ) bond due to interaction with water. Rather, the differences in C5–C6 bond lengths arise from the different hydroxymethyl rotamers. The values for the glycosidic bond angles (O5–C1–O1, C1–O1–C4 0 , and C3 0 –C4 0 –O1) of the vacuum cellobiose conformers are given in Table 2. These angles fall in fairly narrow ranges of values, and not many significant changes (>2) are observed upon the addition of a water molecule (Table 5). These bond angles, like the r–C–O and C–O–H bond angles discussed previously, are relatively unaffected by the weak interactions of water molecules with cellobiose. There are significant variations in the glycosidic dihedral angles /H and wH among the different vacuum cellobiose conformers (Table 2), depending on the hydroxymethyl conformations and the arrangement of intramolecular hydrogen bonds. As mentioned previously, anti conformers are obtained by a rotation of either /H or wH by 180. The rotation of /H typically produces a more stable anti conformer, so only one structure studied here (conformer F) has the wH dihedral rotated 180 from the syn configuration. When the water molecule is placed in an intra-ring position, the values of the glycosidic dihedrals /H and wH do not change by more than 2 relative to the vacuum cellobiose values. As one would expect, larger changes in /H and wH result from placing the water molecule in an inter-ring location (see Table 5). In particular, mh #13 (with water bridging from 2 fi 3 0 ), mh #16 (2 fi 6 0 ), and mh #28 (3 0 fi 5) show large changes in one or both of the glycosidic dihedrals upon hydration. The largest change /H or wH occurs in mh #13; the fact that no hydroxymethyl groups are involved in the HO2  O3 0 means that significant glycosidic angle rotation is required to accommodate the water molecule in the 2 fi 3 0 location.

13

In the case of mh #16, the relatively large distortions of the cellobiose molecule do not have the same net destabilizing effect, owing in part to the formation of the new intramolecular hydrogen bond in that complex, and in part to synergism in the hydrogen bonding network in this monohydrate [18]. It is interesting to note that the changes in /H and wH caused by the addition of the water molecule in the 2 fi 6 0 location bring the cellobiose dihedrals of conformer I very close to those of conformer G, which is the lowest-energy syn cellobiose conformer. These dihedral angles are also very close to the reported solution-phase values [4]. As mentioned previously, the hydroxymethyl dihedral angles (O5–C5–C6–O6, and the corresponding angle on the reducing sugar) can have values in three different ranges, corresponding to the gg, tg, and gt rotamers; the specific values for these dihedrals are given in Table 2. When a water molecule is added so that it is interacting with the 6 or 6 0 hydroxyl group, there can be a large change in the corresponding dihedral angle, although not enough to change the hydroxymethyl group to a new rotamer. The ring dihedral angles listed in Table 1 quantify the ring puckering of each ring in the cellobiose molecule. The range of these dihedrals is 5 for each type of vacuum cellobiose conformer (syn or anti), with a few outlying values. Numerically, these dihedrals are in the same range as calculated for the glucose molecule [15], with both rings in the 4C1 conformation. Upon hydration, the change in the shapes of the two rings is typically very small, with changes in each ring dihedral of 2 or less, so they are not included in Tables 3 and 4. Larger changes occur for some of the monohydrates with inter-ring water molecules (Table 5). There is again a noticeable difference between mh #13 and mh #14, with the accommodation of the water molecule in mh #13 being accompanied by larger distortions of the two sugar rings than is observed in mh #14. The largest distortions in the ring structures are associated with mh #12, with the water placed between the two hydroxymethyl groups. 3.3.5. Water geometry changes due to cellobiose–water interactions In most of the cellobiose monohydrates, the water molecule interacts with cellobiose in a single-donor, single-acceptor arrangement. Accordingly, the changes to the water geometry are very similar in most of the monohydrates: The OH bond that is interacting with cellobiose ˚ , while the other OH bond increases in length by 0.010 A does not change much in length. The H–O–H angle in water increases by 1–2 in most of the monohydrates. These changes also characterize mh #15 and #25, where the water molecule is acting only as a donor. The only unusual monohydrate is mh #30, in which the water molecule acts as a hydrogen bond donor to both O5 0 and O1 0 . In this conformer, there is a smaller increase in the water ˚ ), and the bond angle bond lengths (0.004 and 0.001 A decreases by 3.3.

14

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

3.4. Cellobiose dihydrates The geometry optimized structures for the cellobiose dihydrates are presented in Figs. 6 and 7, with details of the changes in selected internal coordinates tabulated in Tables 6–8. The dihydrate complexes are based on fewer vacuum cellobiose structures (2 anti and 3 syn) as starting points, and most were generated by adding a second water molecule to one of the more favorable monohydrate structures. The relative energies reported in Figs. 6 and 7 (cf. Figs. 4 and 5 for low energy monohydrates) show that this strategy is effective for predicting the most stable dihydrate structures. The DE values in Figs. 6, 7 and Tables 6, 8 are relative to the lowest-energy dihydrate structure (dh #12), which has a B3LYP/6-311++G** calculated energy of 910704.737 kcal/mol. Figs. 6 and 7 show that the lowest energy anti and syn dihydrate complexes are comparable in stability to each

other. In fact, of the six most stable dihydrates (all of which lie within a 0.15 kcal/mol range of relative energies), three are syn and three are anti. The relative stabilities of the anti dihydrates can be predicted from the relative stabilities of the anti monohydrates. In terms of the monohydrate numbers, the relative ordering of the lowest four anti dihydrates is: 1 + 2, 1 + 3, 1 + 4, and 2 + 3, where the ‘‘+’’ indicates a combination of water locations in the corresponding monohydrates. Interestingly, dh #5 and #6 are very similar to dh #1 and #4, respectively, with the primary difference being which water lone pair is acting as a hydrogen-bond acceptor with cellobiose. An examination of the geometry changes from vacuum cellobiose to dh #1 and #5 (Table 6) reveals only subtle differences in the Dr and D/ values for the two dihydrates. This was confirmed by examining the two structures superimposed on each other (not shown here), revealing only minor geometry differences in the

Fig. 6. Structures of the anti water dihydrates, arranged in order of increasing relative energy.

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

15

Fig. 7. Structures of the syn water dihydrates, arranged in order of increasing relative energy.

cellobiose molecules, localized near the rotated water molecule (3 fi 2). That dihydrates 1 and 5 are separated by 0.34 kcal/mol is a clear indication of the sensitivity of the energy to small differences in the cellobiose geometry. As with the anti form, the lowest energy syn dihydrates are based on the lowest syn monohydrate, with the water molecule bridging from 2 fi 6 0 . As was the case in the monohydrates, having a water molecule in this location makes a significant difference in the stability of the complex, as seen in the energy difference (1.6 kcal/mol) between dh #15 and #16. It is interesting to note that there does not

seem to be an energetic preference for (or against) having the two water molecules in consecutive positions around the molecule: In both the syn and anti forms, the two lowest-energy complexes are very close in energy, and one has ‘‘consecutive’’ water molecules, while the other has the two water molecules on different rings. Many of the local structural changes in the dihydrates are virtually identical to those in the corresponding monohydrates; accordingly, we give fewer details of structural changes (relative to vacuum cellobiose) in Tables 6–8 than were given in Tables 3–5. Of particular interest are those

16

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

Fig. 8. Structures of the anti water trihydrates, arranged in order of increasing relative energy.

instances in which the two water molecules are both interacting with the same hydroxyl group on cellobiose; this occurs in dh #1, #5, #9, #13, #17, and #19. In those complexes, one hydroxyl group on the cellobiose molecule is acting both as a hydrogen bond donor and a hydrogen bond acceptor with water, as is likely the case (with all of the hydroxyl groups) in solution. As with the monohydrates, the cellobiose C–OH bond ˚ at the hydrogen-bond lengths decrease by 0.005–0.010 A (to water) donor site and increase by approximately ˚ at the acceptor site, with the changes being 0.010 A somewhat less for the hydroxyl groups involved in hydrogen bonds with inter-ring water molecules. Where a hydroxyl group acts as both a donor and acceptor to water, there is typically a small increase (0.002– ˚ ) in the C–OH bond length. One exception to 0.006 A this is in dh #13, where the 2-hydroxyl group is acting as a donor to an inter-ring water and an acceptor to an intra-ring water. As one might expect, the increase in bond length is somewhat larger, since the inter-ring water molecules tend to have less effect on the C–OH bond length.

The second water molecule affects the sums of ring bond lengths to the same extent as the first molecule; that is, the effects of the two water molecules are approximately additive. As with the monohydrates, the presence of the water molecule bridging from 2 fi 6 0 has a large effect on the non-reducing ring, and produces no net change on the reducing ring. Putting a water molecule between HO1 0 and O5 0 again corresponds to a very large increase in the size of the reducing ring. The r–C–O–H dihedrals change to the same degree (10–50) in dihydrates as in monohydrates. As mentioned previously, this degree of freedom is likely to be the most easily varied to accommodate the water molecule, so large changes are observed in this dihedral angle at the cellobiose–water interaction sites (see Tables 7 and 8). As observed in the monohydrate cases, the largest change in this quantity is caused by the addition of a water molecule in the HO2 to O6 0 inter-ring position. Dihydrate #13 is somewhat unusual in that the C2–C3–O3–H3 dihedral angle changes by only 8, despite the presence of a water bridging from 3 fi 2. The presence of the 2 fi 6 0 water apparently changes the position of the 2-hydroxyl group

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

17

Fig. 9. Structures of the syn water trihydrates, arranged in order of increasing relative energy.

enough to more easily accommodate the second water molecule. As with the monohydrates, the dihydrate O–C–C–x (x = O, in these complexes) dihedral angles spanned by the water molecules change by ± 2–5. Interestingly, an exception arises in dh #13, where the O2–C2–C3–O3 dihedral increases by only 0.6. Presumably, this represents a partial cancellation of the forces due to the two water molecules both interacting with the 2-hydroxyl group, resulting in a dihedral angle close to the vacuum cellobiose value. Table 8 gives the changes in glycosidic bond lengths and dihedral angles, as well as changes in the ring dihedral angles reported previously. Since the only significant changes in these quantities occur when one water molecule is in the glycosidic region (bridging from 2 fi 6 0 , for the dihydrates presented here), Table 8 gives only results for those complexes. Comparing the values in Table 8 to those seen in mh #16, it is clear that the addition of the second water molecule does not create a significant change in the glycosidic bond lengths or dihedral angles, as would be expected from the previous discussion of monohydrates. The ring dihedrals are somewhat affected by the addition of the second water molecule, but the changes from the vacuum cellobiose structure are still relatively small.

3.5. Cellobiose trihydrates and tetrahydrates That the most stable dihydrate complexes can be predicted from the most stable monohydrate complexes means that one can reasonably expect to predict the most favorable water sites in complexes with more than two water molecules. Accordingly, most of the trihydrate calculations are based on the low-lying monohydrate structures. The geometry-optimized trihydrate structures that were studied are presented in Figs. 8 (anti) and 9 (syn). The local changes in internal coordinates are very similar to those seen in the monohydrate and dihydrate calculations, and are not presented here. The relative trihydrate energies are reported in Figs. 8 and 9 are based on absolute energy of trihydrate #6, which has a total B3LYP/6-311++G** energy of 958693.248 kcal/mol. The first four anti trihydrates in Fig. 8 can be thought of as arising from the four possible combinations of the monohydrates 1–4 (cf. Fig. 4). Since there is a large energy gap from mh #4 to mh #5, it was not beneficial to consider water positions characteristic of higher-lying anti monohydrates. Trihydrate #5 has its water molecules placed in the same positions as trihydrate #1, but the cellobiose structure is based on conformer C, which is itself 3.17 kcal/ mol higher in energy than conformer A. The addition of

18

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

Fig. 10. Structures of the water tetra-hydrates studied here. 4w #1 is anti and the rest are syn.

three water molecules to the cellobiose molecules decreases this energy gap to a value of 2 kcal/mol. As expected, the lowest energy syn trihydrates (Fig. 9) all have a water molecule in the 2 fi 6 0 position, as in mh #16. In fact, the lowest three syn trihydrates are extensions of the lowest-energy dihydrate, with water molecules bridging from 2 fi 6 0 and 2 0 fi 3 0 . All of these complexes are calculated to be lower in energy than the lowest energy anti cluster, with the lowest energy syn complex 0.8 kcal/mol more stable than the lowest energy anti trihydrate. Trihydrate #12 is based on dh #20, where a third water molecule has been added in the 2 0 fi 3 0 position. The stability of this complex relative to the most stable syn trihydrate is comparable to the stability of dh #20 relative to the lowest energy dihydrate. Given the results of the previous sections, the most stable anti and syn cellobiose tetrahydrates are predicted to be those shown in Fig. 10. These structures are all based on the cellobiose conformers that give rise to the lowest energy complexes for 1–3 water molecules, with the water molecules placed in sites characteristic of the most stable smaller complexes. Since the anti cellobiose conformers are not stabilized by the presence of a water molecule in the glycosidic region, there is only one anti tetra-hydrate that would be expected to be particularly stable (4w #1 in Fig. 10). This complex has water molecules in all of the possible intra-ring single donor, single acceptor configurations. The bottom row of Fig. 10 gives the four syn tetrahydrates that would be expected to be particularly stable, each of which has one vacant intraring position available for a fifth water molecule. Each

of the syn complexes is more stable than 4w #1, with the lowest energy syn tetra-hydrate being more stable by 1.18 kcal/mol. The addition of the fourth water molecule thus further stabilizes the syn form of cellobiose relative to the anti form, by an additional 0.4 kcal/mol beyond the trihydrates. 4. Conclusions We have presented a subset of the possible cellobiose– (water)n complexes, with n = 1–4. The number of possible combinations of cellobiose conformers and water locations makes it unfeasible to perform high-level quantum calculations on all of the possible cellobiose monohydrates. However, the systematic approach used to generate the clusters is one that we expect to be effective in finding the lowest-energy conformers. For intra-ring placement of the first water molecule, the cellobiose geometry changes generally are localized and predictable. This allows the prediction of the most stable dihydrates and trihydrates based upon the most stable monohydrates. For the B3LYP method at this level of theory, it is likely that the absolute uncertainties in the energies are 1 kcal/mol; however, it is probable that the similarity of the structures under consideration leads to a partial cancellation of error in considering the relative energies of the complexes. Thus, while there may be some uncertainty in which particular structure is lowest in energy, the trend towards the stabilization of the syn form upon hydration is clear. In the absence of water, the lowest-energy anti cellobiose conformers are more stable than the lowest-energy

W.B. Bosma et al. / Journal of Molecular Structure: THEOCHEM 776 (2006) 1–19

syn conformers due to a synergistic hydrogen bonding network in the former that does not exist in the latter [1,20]. The relative stabilities rapidly change as water molecules are added, with the syn and anti forms being comparable in energy at the dihydrate level. The origin of the syn form stability in solution lies in the ability of that conformer to better accommodate a water molecule in the inter-ring region. While both the syn and anti conformers undergo significant changes in geometry for an inter-ring water molecule, the syn conformer achieves a particular stabilization due to the cellobiose–water interaction [19]. Placing a water molecule in the 2 fi 6 0 position also leads to the formation of a new intramolecular hydrogen bond (between HO6 0 and O5 0 ) in the syn form of cellobiose, effectively lengthening the hydrogenbonding network in the cellobiose. This additional stabilization realized represents the formation of a synergistic network of hydrogen bonds similar to that seen in the anti conformers [19]. In addition, the difference in stability for inter-ring water placement means that there is an additional stabilizing site on the syn conformer, so it should be much more stable than the anti conformer in the presence of as few as five water molecules. Acknowledgement W.B. acknowledges the Biotechnology Research and Development Corporation (BRDC) for grant support during a sabbatical leave. References [1] G.L. Strati, J.L. Willett, F.A. Momany, Carbohydr. Res. 337 (2002) 1833. [2] C.J. Brown, J. Chem. Soc. A (1966) 927. [3] S.S.C. Chu, G.A. Jeffrey, Acta Cryst. B24 (1968) 830.

19

[4] N.W.H. Cheetham, P. Dasgupta, G.E. Ball, Carbohydr. Res. 338 (2003) 955. [5] E.A. Larsson, M. Staaf, P. So¨derman, C. Ho¨o¨g, G. Widmalm, J. Phys. Chem. A 108 (2004) 3932. [6] G.A. Jeffrey, Acta Crystallogr. B 46 (1990) 89. [7] R.A. Jockusch, R.T. Kroemer, F.O. Talbot, L.C. Snoek, P. Carcabal, J.P. Simons, M. Havenith, J.M. Bakker, I. Compagnon, G. Meijer, G. von Helden, J. Am. Chem. Soc. 126 (2004) 5709. [8] A.D. French, Carbohydr. Res. 188 (1989) 206; M.K. Dowd, A.D. French, P.J. Reilly, Carbohydr. Res. 233 (1992) 15; S. Mendonca, G.P. Johnson, A.D. French, R.A. Laine, J. Phys. Chem. A 106 (2002) 4115. [9] J.E. Del Bene, W.B. Person, K. Szczepaniak, J. Phys. Chem. 99 (1995) 10705; P.R. Rablen, J.W. Lockman, W.L. Jorgensen, J. Phys. Chem. A 102 (1998) 3782; O. Ga´lvez, P.C. Go´mez, L.F. Pacios, J. Chem. Phys. 115 (2001) 11166; O. Ga´lvez, P.C. Go´mez, L.F. Pacios, J. Chem. Phys. 118 (2003) 4878. [10] A.D. Becke, J. Chem. Phys. 98 (1993) 5648; C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [11] W. Wang, W. Zheng, X. Pu, N.-B. Wong, A. Tian, J. Mol. Struct. (Theochem.) 618 (2002) 235. [12] F.A. Momany, J.L. Willett, J. Comput. Chem. 21 (2000) 1204. [13] J.Y.-J. Chen, K.J. Naidoo, J. Phys. Chem. B 107 (2003) 9558. [14] M. Appell, G.L. Strati, J.L. Willett, F.A. Momany, Carbohydr. Res. 339 (2004) 537. [15] F.A. Momany, M. Appell, G.L. Strati, J.L. Willett, Carbohydr. Res. 339 (2004) 553. [16] F.A. Momany, M. Appell, J.L. Willett, W.B. Bosma, Carbohydr. Res. 340 (2005) 1638. [17] F.A. Momany, J.L. Willett, Carbohydr. Res. 326 (2000) 194; F.A. Momany, J.L. Willett, Carbohydr. Res. 326 (2000) 210. [18] Parallel Quantum Solutions, 2013 Green Acres, Suite A, Fayetteville, AR, 72703. [19] W.B. Bosma, M. Appell, J.L. Willett, F.A. Momany, J. Mol. Struct. 776 (2006) 1–11. [20] G.L. Strati, J.L. Willett, F.A. Momany, Carbohydr. Res. 337 (2002) 1851. [21] L.M.J. Kroon-Batenburg, J. Kroon, B.R. Leeflang, F.G. Vliegenthart, Carbohydr. Res. 245 (1993) 21.