A DFT/ab initio study of hydrogen bonding and conformational preference in model cellobiose analogs using B3LYP/6-311++G**

Computerized Molecular Modeling of Carbohydrates

Computerized molecular modeling continues to increase in capability and applicability to carbohydrates. This chapter covers nomenclature and conformational aspects of carbohydrates, perhaps of greater use to computational chemists who do not have a strong background in carbohydrates, and its comments on various methods and studies might be of more use to carbohydrate chemists who are inexperienced with computation. Work on the intrinsic variability of glucose, an overall theme, is described. Other areas of the authors' emphasis, including evaluation of hydrogen bonding by the atoms-in-molecules approach, and validation of modeling methods with crystallographic results are also presented.

Initial pyrolysis mechanism and product formation of cellulose: An Experimental and Density functional theory(DFT) study

In this paper, analytical pyrolyzer coupled with a gas chromatography-mass spectrometry set-up (Py-GC/MS) and density functional theory(DFT) theory was used to reveal the initial pyrolysis mechanism and product formation mechanism of cellulose pyrolysis. We demonstrated an experimentally benchmarked molecular simulation approach that delineates pyrolysis process of cellulose. Experimental results indicated that the cellulose pyrolysis products mostly incorporate levoglucosan (LG), glycolaldehyde (HAA), 5-hydroxyfurfural (5-HMF), and the like. The constituents of fast pyrolysis products of cellulose and cellobiose demonstrated the identical trend, although the contents of certain products are different. Laying the foundation of experimental analysis, the reaction pathways of four categories of cellulose pyrolysis were outlined using DFT theory; the pathways are those of generating LG, HAA, and 5-HMF and the dehydration reaction in the process of cellulose pyrolysis. Also, by comparing the energy barriers of various reactions, the optimal pathway of different reactions were summarized. The deduced cellulose pyrolysis reaction pathway opened up new ideas for studying the pyrolysis behavior of cellulose.

Multi-level Quantum Mechanics and Molecular Mechanics Study of Ring Opening Process of Guanine Damage by Hydroxyl Radical in Aqueous Solution

Combining multi-level quantum mechanics theories and molecular mechanics with an explicit water model, we investigated the ring opening process of guanine damage by hydroxyl radical in aqueous solution. The detailed, atomic-level ring-opening mechanism along the reaction pathway was revealed in aqueous solution at the CCSD(T)/MM levels of theory. The potentials of mean force in aqueous solution were calculated at both the DFT/MM and CCSD(T)/MM levels of the theory. Our study found that the aqueous solution has a significant effect on this reaction in solution. In particular, by comparing the geometries of the stationary points between in gas phase and in aqueous solution, we found that the aqueous solution has a tremendous impact on the torsion angles much more than on the bond lengths and bending angles. Our calculated free-energy barrier height 31.6 kcal/mol at the CCSD(T)/MM level of theory agrees well with the one obtained based on gas-phase reaction profile and free energies of solvation. In addition, the reaction path in gas phase was also mapped using multi-level quantum mechanics theories, which shows a reaction barrier at 19.2 kcal/mol at the CCSD(T) level of theory, agreeing very well with a recent ab initio calculation result at 20.8 kcal/mol.

Pyranose ring conformations in mono- and oligosaccharides: a combined MD and DFT approach

A two-step computational protocol is proposed to efficiently study the conformational properties of hexopyranoses with a special emphasis on their ring-inversion-properties. By applying it, the errors resulting from overestimating the contribution of the hydrogen bond-rich, low-energy structures that are not abundant in aqueous solutions are avoided.

The electronic nature of the 1,4-β-glycosidic bond and its chemical environment: DFT insights into cellulose chemistry

The molecular understanding of the chemistry of 1,4-β-glucans is essential for designing new approaches to the conversion of cellulose into platform chemicals and biofuels. In this endeavor, much attention has been paid to the role of hydrogen bonding occurring in the cellulose structure. So far, however, there has been little discussion about the implications of the electronic nature of the 1,4-β-glycosidic bond and its chemical environment for the activation of 1,4-β-glucans toward acid-catalyzed hydrolysis. This report sheds light on these central issues and addresses their influence on the acid hydrolysis of cellobiose and, by analogy, cellulose. The electronic structure of cellobiose was explored by DFT at the BB1 K/6-31++G(d,p) level. Natural bond orbital (NBO) analysis was performed to grasp the key bonding concepts. Conformations, protonation sites, and hydrolysis mechanisms were examined. The results for cellobiose indicate that cellulose is protected against hydrolysis not only by its supramolecular structure, as currently accepted, but also by its electronic structure, in which the anomeric effect plays a key role.

Density functional conformational study of 2-O-sulfated 3,6 anhydro-α-D-galactose and of neo-κ- and ι-carrabiose molecules in gas phase and water

We examined the conformational preferences of the 2-O-sulfated-3,6-α-D-anhydrogalactose (compound I) and two 1,3 linked disaccharides constituting-κ or ι-carrageenans using density functional and ab initio methods in gas phase and aqueous solution. Systematic modifications of two torsion angles leading to 324 and 144 starting geometries for the compound I and each disaccharide were used to generate adiabatic maps using B3LYP/6-31G(d). The lower energy conformers were then fully optimized using B3LYP, B3PW91 and MP2 with several basis sets. Overall, we discuss the impact of full relaxation on the energy and structure of the dominant conformations, present the performance comparison with previous molecular mechanics calculations if available, and determine whether our results are impacted, when polarization and diffuse functions are added to the 6-31G(d) basis set, or when the MP2 level of theory is used.

Computerized molecular modeling of carbohydrates

Computerized molecular modeling continues to increase in capability and applicability to carbohydrates. This chapter covers nomenclature and conformational aspects of carbohydrates, perhaps of greater use to carbohydrate-inexperienced computational chemists. Its comments on various methods and studies might be of more use to computation-inexperienced carbohydrate chemists. New work on intrinsic variability of glucose, an overall theme, is described.

DFTMD studies of β-cellobiose: conformational preference using implicit solvent

Previous DFT in vacuo studies on the conformational preferences for cellobiose showed that upon optimization the φ(H)-anti conformations were of lower energy than the syn forms. Upon optimization using an implicit solvation method, COSMO, the syn or observed form was still not predicted to be of lower energy than the φ(H)-anti form, even though optimization after addition of several explicit water molecules did show a relative energy difference favoring the syn form. In order to examine the predictive ability of COSMO on this carbohydrate, constant energy dynamics, DFTMD, simulations were carried out on low energy syn and φ(H)-anti conformations with and without COSMO included during the dynamics. The resulting analysis confirmed that when COSMO is included in the dynamics, the syn conformations become energetically favored over the φ(H)-anti forms suggesting that both solvent and entropy play roles in dictating the solution conformation of cellobiose. Analysis of the dynamic runs includes distributions of selected dihedral angles versus time, conformational transitions, and populations of some quasi-planar, boat, skew forms during the simulations.

Conformational properties of glucose-based disaccharides investigated using molecular dynamics simulations with local elevation umbrella sampling

Explicit-solvent molecular dynamics (MD) simulations of the 11 glucose-based disaccharides in water at 300K and 1bar are reported. The simulations were carried out with the GROMOS 45A4 force-field and the sampling along the glycosidic dihedral angles phi and psi was artificially enhanced using the local elevation umbrella sampling (LEUS) method. The trajectories are analyzed in terms of free-energy maps, stable and metastable conformational states (relative free energies and estimated transition timescales), intramolecular H-bonds, single molecule configurational entropies, and agreement with experimental data. All disaccharides considered are found to be characterized either by a single stable (overwhelmingly populated) state ((1-->n)-linked disaccharides with n=1, 2, 3, or 4) or by two stable (comparably populated and differing in the third glycosidic dihedral angle omega ; gg or gt) states with a low interconversion barrier ((1-->6)-linked disaccharides). Metastable (anti-phi or anti-psi) states are also identified with relative free energies in the range of 8-22 kJ mol(-1). The 11 compounds can be classified into four families: (i) the alpha(1-->1)alpha-linked disaccharide trehalose (axial-axial linkage) presents no metastable state, the lowest configurational entropy, and no intramolecular H-bonds; (ii) the four alpha(1-->n)-linked disaccharides (n=1, 2, 3, or 4; axial-equatorial linkage) present one metastable (anti-psi) state, an intermediate configurational entropy, and two alternative intramolecular H-bonds; (iii) the four beta(1-->n)-linked disaccharides (n=1, 2, 3, or 4; equatorial-equatorial linkage) present two metastable (anti-phi and anti-psi) states, an intermediate configurational entropy, and one intramolecular H-bond; (iv) the two (1-->6)-linked disaccharides (additional glycosidic dihedral angle) present no (isomaltose) or a pair of (gentiobiose) metastable (anti-phi) states, the highest configurational entropy, and no intramolecular H-bonds. The observed conformational preferences appear to be dictated by four main driving forces (ring conformational preferences, exo-anomeric effect, steric constraints, and possible presence of a third glycosidic dihedral angle), leaving a secondary role to intramolecular H-bonding and specific solvation effects. In spite of the weak conformational driving force attributed to solvent-exposed H-bonds in water (highly polar protic solvent), intramolecular H-bonds may still have a significant influence on the physico-chemical properties of the disaccharide by decreasing its hydrophilicity. Along with previous work, the results also complete the suggestion of a spectrum of approximate transition timescales for carbohydrates up to the disaccharide level, namely: approximately 30 ps (hydroxyl groups), approximately 1 ns (free lactol group, free hydroxymethyl groups, glycosidic dihedral angleomega in (1-->6)-linked disaccharides), approximately 10 ns to 2 micros (ring conformation, glycosidic dihedral angles phi and psi). The calculated average values of the glycosidic torsional angles agree well with the available experimental data, providing validation for the force-field and simulation methodology employed.

Interaction energy and the shift in OH stretch frequency on hydrogen bonding for the H2O --> H2O, CH3OH --> H2O, and H2O --> CH3OH dimers

The ability to use calculated OH frequencies to assign experimentally observed peaks in hydrogen bonded systems hinges on the accuracy of the calculation. Here we test the ability of several commonly employed model chemistries--HF, MP2, and several density functionals paired with the 6-31+G(d) and 6-311++G(d,p) basis sets--to calculate the interaction energy (D(e)) and shift in OH stretch fundamental frequency on dimerization (delta(nu)) for the H(2)O --> H(2)O, CH(3)OH --> H(2)O, and H(2)O --> CH(3)OH dimers (where for X --> Y, X is the hydrogen bond donor and Y the acceptor). We quantify the error in D(e) and delta(nu) by comparison to experiment and high level calculation and, using a simple model, evaluate how error in D(e) propagates to delta(nu). We find that B3LYP and MPWB1K perform best of the density functional methods studied, that their accuracy in calculating delta(nu) is approximately 30-50 cm(-1) and that correcting for error in D(e) does little to heighten agreement between the calculated and experimental delta(nu). Accuracy of calculated delta(nu) is also shown to vary as a function of hydrogen bond donor: while the PBE and TPSS functionals perform best in the calculation of delta(nu) for the CH(3)OH --> H(2)O dimer their performance is relatively poor in describing H(2)O --> H(2)O and H(2)O --> CH(3)OH.

Comparison of different force fields for the study of disaccharides

Eighteen empirical force fields and the semi-empirical quantum method PM3CARB-1 were compared for studying beta-cellobiose, alpha-maltose, and alpha-galabiose [alpha-D-Galp-(1-->4)-alpha-D-Galp]. For each disaccharide, the energies of 54 conformers with differing hydroxymethyl, hydroxyl, and glycosidic linkage orientations were minimized by the different methods, some at two dielectric constants. By comparing these results and the available crystal structure data and/or higher level density functional theory results, it was concluded that the newer parameterizations for force fields (GROMOS, GLYCAM06, OPLS-2005 and CSFF) give results that are reasonably similar to each other, whereas the older parameterizations for Amber, CHARMM or OPLS were more divergent. However, MM3, an older force field, gave energy and geometry values comparable to those of the newer parameterizations, but with less sensitivity to dielectric constant values. These systems worked better than MM2 variants, which were still acceptable. PM3CARB-1 also gave adequate results in terms of linkage and exocyclic torsion angles. GROMOS, GLYCAM06, and MM3 appear to be the best choices, closely followed by MM4, CSFF, and OPLS-2005. With GLYCAM06 and to a lesser extent, CSFF, and OPLS-2005, a number of the conformers that were stable with MM3 changed to other forms.

DFT conformation and energies of amylose fragments at atomic resolution. Part 1: Syn forms of alpha-maltotetraose

DFT optimization studies of 90 syn alpha-maltotetraose (DP-4) amylose fragments have been carried out at the B3LYP/6-311++G** level of theory. The DP-4 fragments studied include V-helix, tightly bent conformations, a boat, and a (1)C(4) conformer. The standard hydroxymethyl rotamers (gg, gt, tg) were examined at different locations in the residue sequence, and their influence on the bridge conformations phi/psi values and conformer energy is described. Hydroxyl groups were considered to be homodromic, that is, they are either in the all clockwise, 'c', or all counterclockwise, 'r'. Energy differences between conformations are examined in order to assess the stability of the different conformations and to identify the sources of energy that dictate amylose polymer formation. A small nearly cyclic compact structure is of low energy as one would expect when these flexible molecules are studied in vacuo. Many conformations in which the only differences are a single hydroxymethyl variation in the residue sequence show similar energies and bridge conformations, with trends being a result of the hydroxymethyl as well as hydroxyl orientation. In general the 'c' structures are of lower energy than the 'r' structures, although this is only true for the in vacuo state. The solvent dependence on conformational preference of several low-energy DP-4 structures was investigated via the continuum solvation method COSMO. These results suggest that the 'r' structures may be favored for fully solvated molecules.

DFT studies of the disaccharide, α-maltose: relaxed isopotential maps

The disaccharide, alpha-maltose, forms the molecular basis for the analysis of the structure of starch, and determining the conformational energy landscape as the molecule oscillates around the glycosidic bonds is of importance. Thus, it is of interest to determine, using density functionals and a medium size basis set, a relaxed isopotential contour map plotted as a function of the phi(H) and psi(H) dihedral angles. The technical aspects include the method of choosing the starting conformations, the choice of scanning step size, the method of constraining the specific dihedral angles, and the fitting of data to obtain well defined contour maps. Maps were calculated at the B3LYP/6-31+G( *) level of theory in 5 degrees intervals around the (phi(H),psi(H))=(0 degrees ,0 degrees ) position, out to approximately +/-30 degrees or greater, for gg-gg'-c, gg-gg'-r, gt-gt'-c, gt-gt'-r, tg-tg'-c, and tg-tg'-r conformers, as well as one-split gg(c)-gg'(r) conformer. The results show that the preferred conformation of alpha-maltose in vacuo depends strongly upon the hydroxyl group orientations ('c'/'r'), but the energy landscape moving away from the minimum-energy position is generally shallow and transitions between conformational positions can occur without the addition of significant energy. Mapped deviations of selected parameters such as the dipole moment; the C1-O1-C4', H1-C1-O1, and H4'-C4'-O1 bond angles; and deviations in hydroxymethyl rotamers, O5-C5-C6-O6, O5'-C5'-C6'-O6', C5-C6-O6-H, and C5'-C6'-O6'-H', are presented. These allow visualization of the structural and energetic changes that occur upon rotation about the glycosidic bonds. Interactions across the bridge are visualized by deviations in H(O2)...O3', H(O3')...O2, and H1...H4' distances and the H(O2)-O2-C2-C1 and H'(O3')-O3'-C3'-C4' hydroxyl dihedral angles.

DFT study of α- and β-d-allopyranose at the B3LYP/6-311++G∗∗ level of theory

One hundred and two conformations of alpha- and beta-D-allopyranose, the C-3 substituted epimer of glucopyranose, were geometry optimized using the density functional, B3LYP, and the basis set, 6-311++G **. Full geometry optimization was performed on different ring geometries and on the hydroxymethyl rotamers (gg/gt/tg). Analytically derived Hessians were used to calculate zero point energy, enthalpy, and entropy. The lowest energy and free energy conformation found is the alpha-tg(g-)-4C1-c conformation, which is only slightly higher in electronic (approximately 0.2 kcal/mol) and free energy than the lowest energy alpha-D-glucopyranose. The in vacuo calculations showed a small (approximately 0.3 kcal/mol) energetic preference for the alpha- over the beta-anomer for allopyranose in the 4C1 conformation, whereas in the 1C4 conformation a considerable (approximately 1.6 kcal/mol) energetic preference for the beta- over the alpha-anomer for allopyranose was encountered. The results are compared to previous aldohexose calculations in vacuo. Boat and skew forms were found that remained stable upon gradient optimization although many starting boat conformations moved to other skew forms upon optimization. As found for glucose, mannose, and galactose the orientation and interaction of the hydroxyl groups make the most significant contributions to the conformation/energy relationship in vacuo. A comparison of different basis sets and density functionals is made in the Discussion section, confirming the appropriateness of the level of theory used here.

Conformational and dynamical properties of disaccharides in water: a molecular dynamics study

Explicit-solvent molecular dynamics simulations (50 ns, 300 K) of the eight reducing glucose disaccharides (kojibiose, sophorose, nigerose, laminarabiose, maltose, cellobiose, isomaltose, and gentiobiose) have been carried out using the GROMOS 45A4 force field (including a recently reoptimized carbohydrate parameter set), to investigate and compare their conformational preferences, intramolecular hydrogen-bonding patterns, torsional dynamics, and configurational entropies. The calculated average values of the glycosidic torsional angles agree well with available experimental data, providing validation for the force field and simulation methodology employed in this study. These simulations show in particular that: 1) (1-->6)-linked disaccharides are characterized by an increased flexibility, the absence of any persistent intramolecular hydrogen bond and a significantly higher configurational entropy (compared to the other disaccharides); 2) cellobiose presents a highly persistent interresidue hydrogen bond and a significantly lower configurational entropy (compared to the other disaccharides); 3) persistent hydrogen bonds are observed for all disaccharides (except (1-->6)-linked) and typically involve a hydrogen donor in the reducing residue and an acceptor in the nonreducing one; 4) the probability distributions associated with the glycosidic dihedral angles and psi are essentially unimodal for all disaccharides, and full rotation around these angles occurs at most once or twice for (never for psi) on the 50-ns timescale; and 5) the timescales associated with torsional transitions (except around and psi) range from approximately 30 ps (rotation of hydroxyl groups) to the nanosecond range (rotation of the lactol and hydroxymethyl groups, and around the omega-glycosidic dihedral angle in (1-->6)-linked disaccharides).

Quantum mechanics studies of cellobiose conformations

Three regions of the conformation space that describes the relative orientations of the two glucose residues of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 × 9 grid of 20° increments of the linkage torsion angles ϕ and ψ. Besides these 81 constrained minimizations, we studied two central subregions and two regions at the edges of our maps of complete ϕ,ψ space with unconstrained minimization, for a total of 85 target geometries. HF/6-31G(d) and single-point HF/6-311+G(d) calculations were used to find the lowest energies for each geometry. B3LYP/6-31G+G(d) and single point B3LYP/6-11+G(d) calculations were also used for all unconstrained minimizations. For each target, 181 starting geometries were tried (155 for the unconstrained targets). Numerous different starting geometries resulted in the lowest energies for the various target structures. The starting geometries came from five different sets that were based on molecular mechanics energies. Although all five sets contributed to the adiabatic map, use of any single set resulted in discrepancies of 3–7 kcal/mol (1 cal = 4.184 J) with the final map. For most of the targets, the starting geometry that gave the lowest energy depended on the basis set and whether the HF or B3LYP method was used. However, each of the above four calculations gave the same overall lowest energy structure that was found previously by Strati et al. This global minimum, stabilized by highly cooperative hydrogen bonds, is in a region that is essentially not populated by crystal structures. HF/6-31G(d) energy contours of the mapped central region were compatible with the observed crystal structures. Observed structures that lacked O3···O5′ hydrogen bonds were about 1 kcal/mol above the map's minimum, and observed structures that have a pseudo twofold screw axis ranged from about 0.4 to 1.0 kcal/mol. The HF/6-311+G(d) map accommodated the observed structures nearly as well.Key words: cellulose, carbohydrate, conformation, energy, flexibility, folding, helix, shape.

DFT study of α- and β-d-galactopyranose at the B3LYP/6-311++G** level of theory

Forty-one conformations of alpha- and beta-d-galactopyranose were geometry optimized using the B3LYP density functional and 6-311++G** basis set. Full geometry optimization was performed on different ring geometries and different hydroxymethyl rotamers (gg/gt/tg). Analytically derived Hessians were used to calculate zero point energy, enthalpy, and entropy. The lowest energy and free-energy conformation found is the alpha-gg-(4)C(1)-c chair conformation, which is of lower electronic and free energy than the lowest energy alpha-d-glucopyranose conformer because of favorable hydrogen-bonding interactions. The in vacuo calculations showed considerable ( approximately 2.2kcal/mol) energetic preference for the alpha over the beta anomer for galactopyranose in both the (4)C(1) and (1)C(4) chair conformations. Results are compared to glucopyranose and mannopyranose calculations in vacuo. Boat and skew-boat forms were found that remained stable upon gradient optimization, although many starting conformations moved to other boat forms upon optimization. As with glucopyranose and mannopyranose, the orientation and interaction of the hydroxyl groups make the most significant contributions to the conformation-energy relationship in vacuo.

DFT study of alpha- and beta-D-mannopyranose at the B3LYP/6-311++G** level

Thirty-five conformations of alpha- and beta-d-mannopyranose, the C-2 substituted epimer of glucopyranose, were geometry optimized using the density functional (B3LYP), and basis set (6-311++G**). Full geometry optimization was performed on the hydroxymethyl rotamers (gg/gt/tg) and an analytical hessian program was used to calculate the harmonic vibrational frequencies, zero point energy, enthalpy, and entropy. The lowest energy conformation investigated is the beta-tg in the (4)C(1) chair conformation. The in vacuo calculations showed little energetic preference for either the alpha or beta anomer for mannopyranose in the (4)C(1) chair conformation. Results are compared to similar glucopyranose calculations in vacuo where the alpha anomer is approximately 1kcal/mol lower in electronic energy than the beta anomer. In the case of the generally higher energy (1)C(4) chair conformations, one low-energy, low-entropy beta-gg-(1)C(4) chair conformation was identified that is within approximately 1.4kcal/mol of the lowest energy (4)C(1) conformation of mannopyranose. Other (1)C(4) chair conformations in our investigation are approximately 2.9-7.9kcal/mol higher in overall energy. Many of the (3,O)B, B(3,O), (1,4)B, and B(1,4) boat forms passed through transitions without barriers to (1)S(3), (5)S(1), (1)S(5) skew forms with energies between approximately 3.6 and 8.9kcal/mol higher in energy than the lowest energy conformation of mannopyranose. Boat forms were found that remained stable upon gradient optimization. As with glucopyranose, the orientation and interaction of the hydroxy groups make a significant contribution to the conformation/energy relationship in vacuo.

B3LYP/6-311++G** geometry-optimization study of pentahydrates of α- and β-d-glucopyranose

Five water molecules were placed in 37 different configurations around alpha- and beta-D-glucopyranose in the gt, gg, and tg conformational states, and the glucose-water complexes were geometry optimized using density functionals at the B3LYP/6-311++G** level of theory. The five water molecules were organized in space and energy minimized using an empirical potential, AMB02C, and then further geometry optimized using DFT algorithms to minimum energy positions. Electronic energy, zero point vibrational energy, enthalpy, entropy, stress energy on glucose and the water cluster, hydrogen-bond energy, and relative free energy were obtained for each configuration using thermodynamic procedures and an analytical Hessian program. The lowest energy complex was that of a clustering of water molecules around the 1- and 6-hydroxyl positions of the beta-gt anomer. Configurations in which the water molecules created a favorable network completely around and under glucose were found to have low energy for both alpha and beta anomers. Calculation of the alpha/beta anomeric ratio using the zero point corrected energy gave, approximately 32/68%, highly favoring the beta anomer in agreement with the experimental approximately 36/64% value. This ratio is better than the approximately 50/50% ratio found in our previous monohydrate study. An approximate hydroxymethyl population was obtained by noting average relative energies among the three conformational states, gt, gg, and tg. In the beta anomer complexes the gt conformation was favored over the gg state, while in the alpha anomer complexes the gg state was favored over the gt conformation, with the tg conformations all being of higher energy making little or no contribution to the rotamer population. Some geometry variances, found between glucose in vacuo and glucose after interaction with water molecules, are described and account for some observed C-5-C-6 bond length anomalies reported by us previously for the vacuum glucose structures.

B3LYP/6-311++G** study of alpha- and beta-D-glucopyranose and 1,5-anhydro-D-glucitol: 4C1 and 1C4 chairs, (3,O)B and B(3,O) boats, and skew-boat conformations

Geometry optimization, at the B3LYP/6-311++G** level of theory, was carried out on 4C1 and 1C4 chairs, (3,O)B and B(3,O) boats, and skew-boat conformations of alpha- and beta-D-glucopyranose. Similar calculations on 1,5-anhydro-D-glucitol allowed examination of the effect of removal of the 1-hydroxy group on the energy preference of the hydroxymethyl rotamers. Stable minimum energy boat conformers of glucose were found, as were stable skew boats, all having energies ranging from approximately 4-15 kcal/mol above the global energy 4C1 chair conformation. The 1C4 chair electronic energies were approximately 5-10 kcal/mol higher than the 4C1 chair, with the 1C4 alpha-anomers being lower in energy than the beta-anomers. Zero-point energy, enthalpy, entropy, and relative Gibbs free energies are reported at the harmonic level of theory. The alpha-anomer 4C1 chair conformations were found to be approximately 1 kcal/mol lower in electronic energy than the beta-anomers. The hydroxymethyl gt conformation was of lowest electronic energy for both the alpha- and beta-anomers. The glucose alpha/beta anomer ratio calculated from the relative free energies is 63/37%. From a numerical Hessian calculation, the tg conformations were found to be approximately 0.4-0.7 kcal/mol higher in relative free energy than the gg or gt conformers. Transition-state barriers to rotation about the C-5-C-6 bond were calculated for each glucose anomer with resulting barriers to rotation of approximately 3.7-5.8 kcal/mol. No energy barrier was found for the path between the alpha-gt and alpha-gg B(3,O) boat forms and the equivalent 4C1 chair conformations. The alpha-tg conformation has an energy minimum in the 1S3 twist form. Other boat and skew-boat forms are described. The beta-anomer boats retained their starting conformations, with the exception of the beta-tg-(3,O)B boat that moved to a skew form upon optimization.

B3LYP/6-311++G** study of monohydrates of α- and β-d-glucopyranose: hydrogen bonding, stress energies, and effect of hydration on internal coordinates

Twenty-six monohydrates of alpha- and beta-D-glucopyranose were studied using gradient methods at the B3LYP/6-311++G** level of theory. Geometry optimization was carried out with the water molecules at different configurations around the glucose molecule. A new nomenclature for hydrated carbohydrates was developed to describe the water configurations. Zero-point vibrational energy, enthalpy, entropy, and relative free energy were obtained using the harmonic approximation. Hydrogen-bond energies for the monohydrates range from approximately -5 to -12 kcal/mol, and the average relative free energy is approximately 5 kcal/mol. The 1-hydroxy position is the most energetically favored site for hydration, and the region between the two and three positions is the next-most favored site. A water molecule approaching alpha-D-glucose between the 1- and 2-hydroxy positions pulls the 2-hydroxyl hydrogen atom away from the 1-hydroxy oxygen atom, thus increasing the hydrogen-bond length and also increasing the alpha-D-glucose energy. The increase in energy that occurs with a similar interaction on the beta-anomer is much less effective since the hydrogen bond is much longer. Using the calculated free energies of all 26 configurations, the anomer population (alpha/beta) increases in the beta-anomer population relative to the in vacuo case by approximately 10% at the expense of the alpha-anomer, giving an (alpha/beta) ratio of approximately 50/50. This result arises from entropy contributions favoring the beta-anomer more than the alpha-anomer. From analysis of donor and acceptor hydrogen-bond lengths, excellent correlation is found between the DFT calculated distances and those taken from carbohydrate structures in the Cambridge Crystallographic Data Bank.