Spatial Arrangement of a-Cyclodextrins in a Rotaxane. Insights from Free-Energy Calculations (original) (raw)
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Reconsidering the conformational flexibility of �-cyclodextrin
J Mol Struc Theochem, 1997
Conformational analysis of @-cyclodextrin in vacua has been carried out using two complementary searching techniques to answer the question: what is the relationship between the conformational changes in the @,\k torsional angles around the glycosidic bonds and the fluctuations of the hydroxyl pendant groups? Because of the large number of local minima on the conformation and potential energy surface of cyclodextrin, a standard systematic search involving molecular mechanics minimization at points on a regular, fixed torsional angle space grid would generate so many points as to be impractical for conformational sampling. Instead the RAMM (RAndom Molecular Mechanics) procedure, a molecular mechanics calculation based on a random walk within torsional angle space, is used here and is compared to the results of nanosecond molecular dynamics simulation. The RAMM procedure is a semi-automatic calculation of the n-dimensional potential energy surface of a molecule which combines a grid-based conformation and search for one pair of bonds with random generation of a conformational ensemble of rotatable bonds and optimization of molecular geometry. Results are presented for six conformers of low symmetry and three conformers with higher symmetry. For all cases, random sampling of the 287-dimensional hydroxy and hydroxymethyl pendant group torsional angle conformational space improved the molecular energy. Torsional angles involving the primary hydroxyl groups exhibited larger conformational freedom than those involving secondary hydroxyls. The secondary hydroxyls of the symmetric forms are involved in a homodromic 02.. .03 hydrogen bonding network. The results of the RAMM modeling agree with results from molecular dynamics simulations at 300 K (I ns), 400 K (2 ns), and at 1000 K (I ns) with dielectric constant I. At the two lower temperatures, the molecule fluctuates within the 9,\k space at values around O",O". The occupancy profile, drawn in two-dimensional %,\k plots, is similar for each of the seven combinations of +,,P, and has a characteristic half-moon shape. A stabilizing hydrogen bond network between 02(i). ..03(i-I) is present during the entire simulation with a consequent decrease in the mobility of HO2 and HO3 (oscillating around x(2 =-60", XL3 =-60"). No conformational transitions of these groups were observed at 300 K and the first and only reorientation (x,? = I 80", x13 = 180") occurred at approximately I .7 ns at 400 K. At 1000 K, the molecule explores regions beyond G,\k equal to O",O" and the chair conformer of the pyranose rings is not preserved. An additional 2 ns molecular dynamics simulation at 400 K with dielectric constant 4 revealed the "flip-flop" character of 02...03 hydrogen bonding between adjacent glucose residues.
Reconsidering the conformational flexibility of β-cyclodextrin
Journal of Molecular Structure: THEOCHEM, 1997
Conformational analysis of @-cyclodextrin in vacua has been carried out using two complementary searching techniques to answer the question: what is the relationship between the conformational changes in the @,\k torsional angles around the glycosidic bonds and the fluctuations of the hydroxyl pendant groups? Because of the large number of local minima on the conformation and potential energy surface of cyclodextrin, a standard systematic search involving molecular mechanics minimization at points on a regular, fixed torsional angle space grid would generate so many points as to be impractical for conformational sampling. Instead the RAMM (RAndom Molecular Mechanics) procedure, a molecular mechanics calculation based on a random walk within torsional angle space, is used here and is compared to the results of nanosecond molecular dynamics simulation. The RAMM procedure is a semi-automatic calculation of the n-dimensional potential energy surface of a molecule which combines a grid-based conformation and search for one pair of bonds with random generation of a conformational ensemble of rotatable bonds and optimization of molecular geometry. Results are presented for six conformers of low symmetry and three conformers with higher symmetry. For all cases, random sampling of the 287-dimensional hydroxy and hydroxymethyl pendant group torsional angle conformational space improved the molecular energy. Torsional angles involving the primary hydroxyl groups exhibited larger conformational freedom than those involving secondary hydroxyls. The secondary hydroxyls of the symmetric forms are involved in a homodromic 02.. .03 hydrogen bonding network. The results of the RAMM modeling agree with results from molecular dynamics simulations at 300 K (I ns), 400 K (2 ns), and at 1000 K (I ns) with dielectric constant I. At the two lower temperatures, the molecule fluctuates within the 9,\k space at values around O",O". The occupancy profile, drawn in two-dimensional %,\k plots, is similar for each of the seven combinations of +,,P, and has a characteristic half-moon shape. A stabilizing hydrogen bond network between 02(i). ..03(i-I) is present during the entire simulation with a consequent decrease in the mobility of HO2 and HO3 (oscillating around x(2 =-60", XL3 =-60"). No conformational transitions of these groups were observed at 300 K and the first and only reorientation (x,? = I 80", x13 = 180") occurred at approximately I .7 ns at 400 K. At 1000 K, the molecule explores regions beyond G,\k equal to O",O" and the chair conformer of the pyranose rings is not preserved. An additional 2 ns molecular dynamics simulation at 400 K with dielectric constant 4 revealed the "flip-flop" character of 02...03 hydrogen bonding between adjacent glucose residues.
Multiple Weak C-H Intramolecular Hydrogen Bonding as an Aid to Minimizing Bond Rotation Flexibility
Crystal Growth & Design, 2016
Supplementary Data Table S1: X-Ray crystallographic and DFT functional comparison of important bond distances (Å), bond angles (o) and separations (Å). Supplementary Data Table S2: NBO donor-acceptor properties for energy minimised structure and the single point calculation of the X-ray structure. Supplementary Data Table S3: Close contact distances (Å) and NCI iso-surface colour comparisons for the calculated X-ray (X-rayC) and PBE-D3 energy minimised (Emin) structures. Supplementary Data Table S4: Close contact distances (Å) and bond critical point (bcp) data comparisons for the calculated X-ray (X-rayC) and PBE-D3 energy minimised (Emin) structures. Supplementary Data Table S5: Atomic charge [q(A), q(B) partner] comparisons for the calculated X-ray (X-rayC) and PBE-D3 energy minimised (Emin)structures. Supplementary Data Table S6: Cartesian coordinates and total energies for the energy minimised and single point calculation versions of [Mo(NC 6 H 4 CMe 3-2)(O)Cl 2 (bipy)]. Supplementary Date Table S7: Comparison of structural and QTAIM parameters of Energy minimised (Emin), X-ray (xray), and the complexes (a-d), structures. Supplementary Figures S1-S10: Comparison of energy minimised (EM) and single point (SP) iso-surfaces. Supplementary Figure S11: Molecular graphs for the calculated X-ray (X-rayC) and PBE-D3 energy minimised (Emin) structures. Supplementary Figure S12: Unit cell obtained from the X-ray crystal structure. Supplementary Figure S13: Molecular graphs showing intermolecular bond critical points with dicholoromethane solvent molecules for complexes ad. Supplementary Figure S14: Geometries of the complexes (a-d) containing CH 2 Cl 2. Supplementary Data Table S1: X-Ray crystallographic and DFT functional comparison of important bond distances (Å), bond angles (o) and separations (Å). Parameter X-Ray 3σ PBE-D3 diff BP86 diff B3LYP diff Mo=O(1) 1.686(2)
Journal of Computational Chemistry, 2011
Accurate estimation of individual intramolecular hydrogen bond (H-bond) energies is an intricate task for multiply Hbonded systems. In such cases, the hydrogen bond strengths could be highly influenced by the cooperative interactions, for example, those between hydroxyl groups in sugars. In this work, we use the recently proposed molecular tailoring approach-based quantification (Deshmukh, Gadre, and Bartolotti, J Phys Chem A 2006, 110, 12519) to the extended systems of cyclodextrins (CDs). Further, the structure and stability of different conformers of a-, b-, and c-CDs are explained based on the energetics and cooperative contribution to the strength of these H-bonds. The estimated OAHÁÁÁO H-bond energies in the various CD conformers are found to vary widely from 1.1 to 8.3 kcal mol À1 . The calculated energy contributions to cooperativity toward the Hbond strengths fall in the range of 0.25-2.75 kcal mol À1 .
Modeling the interplay of inter- and intramolecular hydrogen bonding in conformational polymorphs
Chemical Physics, 2008
The predicted stability differences of the conformational polymorphs of oxalyl dihydrazide and ortho-acetamidobenzamide are unrealistically large when the modeling of intermolecular energies is solely based on the isolated-molecule charge density, neglecting charge density polarization. Ab initio calculated crystal electron densities showed qualitative differences depending on the spatial arrangement of molecules in the lattice with the greatest variations observed for polymorphs that differ in the extent of inter-and intramolecular hydrogen bonding. We show that accounting for induction dramatically alters the calculated stability order of the polymorphs and reduces their predicted stability differences to be in better agreement with experiment. Given the challenges in modeling conformational polymorphs with marked differences in hydrogen bonding geometries, we performed an extensive periodic density functional study with a range of exchange-correlation functionals using both atomic and plane wave basis sets. Although such electronic structure methods model the electrostatic and polarization contributions well, the underestimation of dispersion interactions by current exchange-correlation functionals limits their applicability. The use of an empirical dispersion-corrected density functional method consistently reduces the structural deviations between the experimental and energy minimized crystal structures and achieves plausible stability differences. Thus, we have established which types of models may give worthwhile relative energies for crystal structures and other condensed phases of flexible molecules with intra-and intermolecular hydrogen bonding capabilities, advancing the possibility of simulation studies on polymorphic pharmaceuticals.
Homodromic hydrogen bonds in low-energy conformations of single molecule cyclodextrins
Journal of Inclusion Phenomena and Macrocyclic Chemistry, 2007
Low-energy conformations of b-cyclodextrin under anhydrous conditions in the gas phase were investigated by DFT calculations. In these conformations, two homodromic hydrogen bond rings are formed with very short hydrogen bonds at the narrow side of the cyclodextrin ring and a second one at the wider side. These hypothetical conformations are not comparable to those conformations, which have been studied experimentally, forming inclusion complexes with small and medium-sized guest molecules, but their energy is significantly lower than the open conformations (DE = 10 kcal/mol).
Cooperative effects in one-dimensional chains of three-center hydrogen bonding interactions
The Journal of Chemical Physics, 2003
Cooperative effects in a one-dimensional network of intermolecular bifurcated hydrogen bonding interactions are investigated by means of ab initio calculations. The trans-trans conformation of the diformamide molecule is used as a basic motif to model a chain of bifurcated H bonds. In this model system, the two proton-acceptor atoms belong to the same molecule. The one-dimensional network is modeled then by periodically stacking up to 12 molecules of the unit motif. Different indicators of H-bond strength such as energetic, structural, dielectric, vibrational frequencies, and isotropic chemicals shifts consistently show significant cooperative effects in the chains. The dissociation energy in the dimer is calculated to be 9.88 kcal/mol, while that of the strongest interaction in the decamer is calculated to be 26.12 kcal/mol ͑164% increase in cooperativity͒. Thus, although three-center H bonds can be viewed as a consequence of proton deficiency, in some cases they may also be viewed as the natural result of an interaction that is itself energetically favorable and capable of competing with the more conventional two-center H bonds. Natural bond orbital analysis reveals substantial charge delocalization within each molecule, and charge transfer along the chains. Interestingly, this charge delocalization makes the system a good candidate for resonance-assisted H bonding which in turn increases the covalent character of this type of bifurcated H-bonding interaction.