Carlos A. Stortz

Evaluation of Density Functionals and Basis Sets for Carbohydrates

Correlated ab initio wave function calculations using MP2/aug-cc-pVTZ model chemistry have been performed for three test sets of gas phase saccharide conformations to provide reference values for their relative energies. The test sets consist of 15 conformers of α- and β-d-allopyranose, 15 of 3,6-anhydro-4-O-methyl-d-galactitol, and four of β-d-glucopyranose. For each set, conformational energies varied by about 7 kcal/mol. Results obtained with the Hartree-Fock method, with pure density functional approximations (DFAs) like LSDA, PBEsol, PBE, and TPSS and with hybrid DFAs like B3PW91, B3LYP, PBEh, and M05-2X, were then compared to the reference and local MP2 relative energies. Basis sets included 6-31G*, 6-31G**, 6-31+G*, 6-31+G**, 6-311+G**, 6-311++G**, cc-pVTZ(-f), cc-pVTZ, and aug-cc-pVTZ(-f). The smallest basis set that gives good DFA relative energies is 6-31+G**, and more converged results can be obtained with 6-311+G**. The optimized geometries obtained from a smaller basis set, 6-31+G*, were useful for subsequent single point energy calculations with larger basis sets. The best agreement with MP2 was shown by M05-2X, but only when using a dense DFT grid. The popular B3LYP functional is not the best for saccharide conformational studies. The B3PW91 functional gives systematically better results, but other hybrid functionals like PBEh or TPSSh are even better. Overall, the nonempirical PBE GGA and TPSS meta-GGA functionals also performed better than B3LYP.

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.

Disaccharide conformational maps: adiabaticity in analogues with variable ring shapes

Relaxed MM3 ϕ, ψ potential energy surfaces (conformational maps) were calculated for analogues of α,α-trehalose, β,β-trehalose, α,β-trehalose, maltose, cellobiose and galabiose based on 2-methyltetrahydropyran. Starting structures included not only 4C1 (sugar nomenclature) geometries, but also combinations with 1C4 conformers, and some flexible (boat or skew) forms. These forms were included as part of continuing efforts to eliminate unwarranted assumptions in modelling studies, as well as to account for new experimental findings. Four to nine maps were obtained for each analogue, and from them adiabatic maps were produced. Although the minimum energy regions always resulted from 4C1–4C1 geometries, moderate to large parts of most maps had lower energies when one or both rings were in the 1C4 conformation. Only the adiabatic surface for the (diequatorial) analogue of β,β-trehalose was covered entirely by 4C1–4C1 conformers. For the cellobiose and α,β-trehalose analogues, these conformers covered 74 and 67% of the surfaces, respectively. The remainder of the cellobiose analogue surface was covered by conformers having a 1C4 conformation at the “reducing” end, and for the α,β-trehalose analogue, by conformers having 1C4 shapes for the α-linked unit. Adiabatic surfaces of the other three analogues were based on all combinations of 4C1 and 1C4 conformers. The “normal” 4C1–4C1 combination only covered 37–41% of those surfaces, whereas each of the other three conformations accounted for 10–31%. Although the “normal” conformation accounted for 97.0–99.8% of the total population, adiabaticity in disaccharide maps is not guaranteed unless variable ring shapes (another manifestation of the “multiple minima problem”) are considered.

Structural analysis of methyl 6-O-benzyl-2-deoxy-2-dimethylmaleimido-α-D-allopyranoside by X-ray crystallography, NMR, and QM calculations: hydrogen bonding and comparison of density functionals.

The crystal structure of methyl 6-O-benzyl-2-deoxy-2-dimethylmaleimido-α-D-allopyranoside was solved in order to gain insight into the hydrogen bond features which can be determining features in the glycosylation regioselectivity observed for this compound. An intramolecular hydrogen bond between the hydroxyl H(O)3 and a carbonyl oxygen from the dimethylmaleoyl (DMM) group was observed. This was in agreement with previous NMR temperature shift determinations and molecular modeling. The determination has also found an intermolecular hydrogen bond between the second hydroxyl H(O)4 and the other carbonyl oxygen (generated by symmetry) from DMM. The crystal structure was optimized by five different functionals, namely the hybrid methods B3LYP, M06-2X, B3PW91, and PBE0, and the pure functional PBE, and the optimized geometries were compared with the crystal geometry and with MM3. An excellent coincidence of the geometries was found with the five quantum methods, with minor details deviating from this coincidence. PBE tends to yield larger bond distances, whereas M06-2X fails slightly to match the exocyclic torsion angles for the sugar moiety. In any case, the differences are small, implying that any of these functionals can accurately emulate the geometries of a complex carbohydrate derivative like this one.

DFT/PCM theoretical study of the conversion of methyl 4-O-methyl-α-d-galactopyranoside 6-sulfate and its 2-sulfated derivative into their 3,6-anhydro counterparts.

Modeling of the conversion of methyl 4-O-methyl-α-d-galactopyranoside 6-sulfate (2) and 2,6-disulfate (1) into methyl 3,6-anhydro-4-O-methyl-α-d-galactopyranoside (4) and its 2-sulfate (3), respectively (Scheme 1) has been carried out using DFT at the M06-2X/6-311 + G(d,p)//M06-2X/6-31 + G(d,p) level with the polarizable continuum model (PCM) in water. The three steps necessary for the alkaline transformation of 6-sulfated (and 2,6-disulfated) galactose units into 3,6-anhydro derivatives were evaluated. The final substitution step appears to be the rate limiting, involving an activation energy of ca. 23 kcal/mol. The other two steps (deprotonation and chair inversion) combined involve lower activation energies (9-12 kcal/mol). Comparison of the thermodynamics and kinetics of the reactions suggest that if the deprotonation step precedes the chair inversion, the reaction should be faster for both compounds. No major differences in reaction rate can be theoretically predicted to be caused by the presence of sulfate on O-2, although one experimental result suggested that O-2 sulfation should increase the reaction rate. The conformational pathways are complex, given the large number of rotamers available for each compound, and the way that some of these rotamers combine into some of the pathways. In any case, the conformation (O)S2 appears as a common intermediate for the chair inversion processes.

Seaweed Polysaccharides: Structure and Applications

Seaweeds represent a widely used source of different polysaccharides, well known in the industry for their food and nonfood applications. Red seaweeds produce carrageenans, agars, and variants, used in a manifold of industries as gelling and thickening agents. Brown seaweeds are a source of alginates, fucoidans, and laminarans; alginates have also wide industrial applications. Green seaweeds produce ulvans and other glycans. Most of the polysaccharides from red, brown, and green seaweeds are highly sulfated polymers; many of them have been investigated for their strong biological activities (antiviral, antitumor, anticoagulant, etc.), thus bringing hopes of promising applications in the biomedical field.