Spatial Arrangement of a-Cyclodextrins in a Rotaxane. Insights from Free-Energy Calculations (original) (raw)
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 .
Journal of Molecular Liquids, 2019
Numerous microscopic definitions of hydrogen bonding have been proposed and employed in molecular simulations. They are typically based on various energetic, topological, and geometric criteria and require a specification of the cut-off values. The cut-off values are chosen to yield a reasonable description of hydrogen bonding in a particular molecular system under particular conditions and for a particular molecular model, and they are not thus straightforwardly transferable to different molecular systems or conditions. We propose a general approach to define and quantify the intermolecular bonds in liquids and solutions, including hydrogen bonds, which is free of any cutoff values. The approach is based on finding a continuous bond region in the surroundings of a local maximum of a spatial distribution function, enclosed by an isosurface going through the nearest significant saddle point. Moreover, the general definition of intermolecular bonding can quantify significance of particular intermolecular bonds or can be used locally to quantify and characterise bonds in heterogeneous systems or confinement. Besides the general definition of the intermolecular bonding, the bond region can be further characterised by a number of relevant properties such as the number of bonds per molecule, volume of a bond region per molecule, bond stability/strength or hydration number to provide deep insight into the intermolecular bonding. The approach is demonstrated for pure water and aqueous NaCl solutions under different thermodynamic conditions, and our results on the behaviour and quantification of their intermolecular bonding are compared with results obtained using commonly-used bond definitions.
Localized orbital studies of hydrogen bonding
Journal of Molecular Structure, 1976
INDO localized molecular orbitals (LMO's) are utilized for investigating the nature of intermolecular hydrogen bonding in the fully geometry optimized dimers (HFh, (Hz0)2, (NH3)2, FH-OH 2 , HOH-FH, FH-NH 3 , H 2 NH-FH, H20-HNH2, HOH-NH3, HCN-HF, and HzCO-HF. The results suggest that a reasonable measure of relative hydrogen bond strengths should be the intra bond, two-center, one-electron interference energy connecting the acceptor atom and donated proton. This approach views the net stabilization energy of a hydrogen bonded dimer as arising from a large energy decrease due to formation of the hydrogen bond, modified by smaller energy increases due to internal decreases in monomer bond energies upon formation of the dimer. Hydrogen bond stabilization app.ears to be closely related to the extent of charge transfer within the hydrogen bonded complex. The calculated transfer of charge can largely be explained in terms of electron density shifts within the acceptor lone pairs, while the decrease in electron density on the proton is discussed in terms of the donor XH bond. The approach presented should be particularly useful for analyzing intramolecular hydrogen bonding systems where the hydrogen bond energy is not simply obtainable from monomer-dimer energy differences.
Pex, analytical tools for PDB files. II. H-Pex: Noncanonical H-bonds in ?-helices
Proteins: Structure, Function, and Genetics, 2001
We use the H-Pex (Thomas et al., this issue) to analyze the main chain interactions in 131 proteins. In antiparallel -sheets, the geometry of the NH. .. O bond is: median N. .. O distances, 2.9 Å, CAO. .. N angles at 154 degrees and the C␣OCAO. .. H angles are dispersed around 3 degrees. In some instances, the other side of the CAO axis is occupied by a HC␣. As recently supported by Vargas et al. (J Am Chem Soc 2000;122:4750-4755) C␣H. .. O and NH. .. O could cooperate to sheet stability. In ␣-helices, the main chain CAO interact with the NH of their n ؉ 4 neighbor on one side, and with a CH or C␥H on the other side. The median O. .. N distance (3.0 Å) and CAO. .. N angle (147 degrees) suggest a canonical H-bond, but the C␣OCAO. .. H dihedral angle invalidates this option, since the hydrogen attacks the oxygen at 122 degrees, i.e., between the sp 2 and orbitals. This supports that the H-bond is noncanonical. In many instances, the C␥H or the CH of the n ؉ 4 residue stands opposite to the NH with respect to the oxygen. Therefore, we propose that, in ␣-helices, the C␥H or CH and the NH of the n ؉ 4 residue hold the oxygen like an electrostatic pincher. Proteins 2001;43:37-44.
The Journal of Physical …, 2011
Hydrogen bonds are of crucial relevance to many problems in chemistry biology and materials science. The recently-developed NCI (Non-Covalent Interactions) index enables real-space visualization of both attractive (van der Waals and hydrogen-bonding) and repulsive (steric) interactions based on properties of the electron density It is thus an optimal index to describe the interplay of stabilizing and de-stabilizing contributions that determine stable minima on hydrogenbonding potential-energy surfaces (PESs). In the framework of density-functional theory energetics are completely determined by the electron density Consequently NCI will be shown to allow quantitative treatment of hydrogen-bond energetics. The evolution of NCI regions along a PES follows a well-behaved pattern which, upon integration of the electron density is capable of mimicking conventional hydrogen-bond interatomic potentials. * weitao.yang@duke.edu ‡ ejohnson29@ucmerced.edu Supporting Information Available: Binding energy curves computed at the MP2/Aug-cc-PVTZ level for all the dimers in are available. A plot comparing computed s(ρ) values with results using STO model densities is also provided. These materials can be downloaded free of charge via the Internet at
Molecular Simulation, 2014
2014): Quantum chemical topological analysis of hydrogen bonding in HX…HX and CH 3 X…HX dimers (X = Br, Cl, F), Molecular Simulation, We present a systematic investigation of the nature and strength of the hydrogen bonding in HX···HX and CH 3 X· · ·HX (X ¼ Br, Cl and F) dimers using ab initio MP2/aug-cc-pVTZ calculations in the framework of the quantum theory of atoms in molecules (QTAIM) and electron localisation functions (ELFs) methods. The electron density of the complexes has been characterised, and the hydrogen bonding energy, as well as the QTAIM and ELF parameters, is consistent, providing deep insight into the origin of the hydrogen bonding in these complexes. It was found that in both linear and angular HX· · ·HX and CH 3 X· · ·HX dimers, F atoms form stronger HB than Br and Cl, but they need short (, 2 Å ) X· · ·HX contacts.
Quantification of Hydrogen Bond Strength Based on Interaction Coordinates: A New Approach
The Journal of Physical Chemistry A, 2017
A new approach to quantify hydrogen bond strengths based on interaction coordinates (HBSBIC) is proposed and is very promising. In this research, it is assumed that the projected force field of the fictitious three atoms fragment (DHA) where D is the proton donor and A is the proton acceptor from the full molecular force field of the H-bonded complex characterizes the hydrogen bond. The " interaction coordinate (IC) " derived from the internal compliance matrix elements of this three-atom fragment measures how the DH covalent bond (its electron density) responds to constrained optimization when the HA hydrogen bond is stretched by a known amount (its electron density is perturbed by a specified amount). This response of the DH bond, based on how the IC depends on the electron density along the HA bond, is a measure of the hydrogen bond strength. The inter-and intramolecular hydrogen bond strengths for a variety of chemical and biological systems are reported. When defined and evaluated using the IC approach, the HBSBIC index leads to satisfactory results. Because this involves only a three-atom fragment for each hydrogen bond, the approach should open up new directions in the study of " appropriate small fragments " in large biomolecules.