Consequences of Strain for the Structure of Aliphatic Molecules

The chemist is accustomed to deriving structures and preferred conformations of organic compounds from rigid molecular models and standard values for bond lengths, bond angles, and torsional profiles. In the case of strained compounds, this rigid structural model has to be abandoned and replaced by a flexible one which takes individual conditions of strain into consideration. It is shown, on the basis of new experimental structure data, that the force field method is suitable and highly reliable for the calculation of structural parameters and preferred conformations of strained compounds. It is, therefore, capable of replacing the rigid molecular model. Furthermore, the systematic analysis of strain induced angle and bond deformation gives a new pivot for the development of a qualitative discussion of deformation in strained molecules and hence for improved conformational analysis. — In the course of this work we were able to isolate two rotamers of D,L -3,4-di(1-adamantyl)-2,2,5,5-tetramethylhexane; this is the first isolation of a rotamer pair of an aliphatic hydrocarbon.     

A New Method for Molecular Mechanics

A promising new method for optimizing molecular structures is described. In place of the terms involving bond angles and torsion angles, used in the force fields of conventional molecular mechanics, two-body central forces between atoms are used exclusively, resulting in a considerable computational advantage. The program STRFIT, using this method has been tested by comparing geometries obtained with those found using the popular molecular mechanics program MM2 (Allinger) for a variety of cyclic and acyclic molecules. For unstrained molecules, the difference in steric energy between geometries refined by STRFIT and MM2 is only a few tenths of a kilocalorie and up to about a kilocalorie for strained molecules. Geometry optimization with STRFIT, to a structure that is slightly higher in energy than the structure arrived at by MM2 starting from the same initial starting geometry, is three to eight times faster. A complete new package of programs for conveniently and rapidly doing molecular mechanics calculations is described. It includes a convenient algorithm for the input of approximate molecular structures, a rapid structure-optimizing module using a pure Central force-field approach, and a drawing program designed for use with a dot-matrix printer or a laser printer.     

A new method for fast and accurate derivation of molecular conformations

During molecular simulations, three-dimensional conformations of biomolecules are calculated from the values of their bond angles, bond lengths, and torsional angles. In this paper we study how to efficiently derive three-dimensional molecular conformations from the values of torsional angles. This case is of broad interest as torsional angles greatly affect molecular shape and are always taken into account during simulations. We first review two widely used methods for deriving molecular conformations, the simple rotations scheme and the Denavit-Hartenberg local frames method. We discuss their disadvantages which include extensive bookkeeping, accumulation of numerical errors, and redundancies in the local frames used. Then we introduce a new, fast, and accurate method called the atomgroup local frames method. This new method not only eliminates the disadvantages of earlier approaches but also provides lazy evaluation of atom positions and reduces the computational cost. Our method is especially useful in applications where many conformations are generated or updated such as in energy minimization and conformational search.     

Ab initio and equilibrium bond angles. Structures of HNO and H2O2

The possibility of calculating accurate ab initio bond angles is examined using a sample of 29 molecules (35 independent angles) containing only first row atoms and whose equilibrium structures are known. Three different correlated methods are compared: MP2, CCSD(T), and DFT, using the hybrid functional B3LYP. The convergence of Dunning's correlation consistent polarized valence basis sets, cc-pVnZ is also studied. It is found that the CCSD(T) method is consistently the most accurate; the DFT/B3LYP being slightly less reliable than MP2. It is shown that when convergence of the basis set is achieved (which is dependent on the kind of bonding) and when the effect of diffuse functions on electronegative atoms is taken into account, a high accuracy may be obtained: 0.03° for the median of absolute deviations or 0.07° for the mean absolute deviation. It does not exclude the possibility that the ab initio method may fail in some particular case, for instance when a large amplitude motion is involved. The MP2/cc-pVQZ method gives a mean absolute deviation of 0.22° to be compared with the 0.07° of the CCSD(T) method. To obtain these results, it was necessary to reanalyze the structure of a few molecules, particularly, a new and more accurate structure is proposed for nitroxyl, HNO and hydrogen peroxide, H₂O₂.     

Fluidic assembly and packing of microspheres in confined channels

We study fluidic assembly and packing of spherical particles in rectilinear microchannels that are terminated by a flow constriction. First, we introduce a method for active assembly of particles in the confined microchannels by triggering a local constriction in the fluid channel using a partially closed membrane valve. This microfluidic valve allows active, on-demand particle assembly as opposed to previous passive assembly methods based on terminal channels and weirs. Second, we study the three-dimensional assembly and packing of particles against a weir in confined rectilinear microchannels. The packings result in achiral particle chains with alternating (zigzag) structure. This structure is characterized by a single, repeated bond angle whose components projected into the frame of the channel are quantified by confocal microscopy and image processing. Brownian dynamics simulation of the packing comprehensively delineates the range of bond angles possible in narrow, rectilinear microchannels as well as the complex dependence of these angles on the relative dimensions of the channel and particles. The simulations of the three-dimensional packings are accurately modeled by a compact theory based on trigonometric relationships. The experimentally measured bond angles show excellent agreement with the simulations, thereby validating the functional dependence of the achiral packing bond angles on channel dimensions. This functional relationship is immediately useful for the design of anisotropic particles by microfluidic synthesis.     

X–ray absorption fine structure (XAFS) of Si wafer measured using total reflection X–rays

Extended X–ray absorption fine structure (EXAFS) and X–ray absorption near edge structure (XANES) spectra of a Si wafer are measured using grazing incidence X–rays. The spectra are measured using the total electron yield method. Fourier transform of the measured EXAFS oscillation is compared among different glancing angles. It is concluded that the XANES spectra are more sensitive to the surface Si–O bond than the EXAFS spectra. The source of probing depth difference of XAFS spectroscopy estimated by different researchers are discussed.     

Parametrization in the AM 1 method

Parameter definition is considered for the AM 1 method, which is a new modification of MNDO incorporating better correction for atomic-core repulsion, so the promising approach can be used to calculate energy and structural characteristics for molecules and adducts. Calculations have been performed on heats of formation, ionization potentials, and dipole moments for various compounds, as well as structure parameters (bond lengths and bond and torsion angles), which are close to the standard ones and reproduce experimental values satisfactorily.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 6, pp. 713–717, November–December, 1988.     

Molecular conformation of bilirubin from semiempirical molecular orbital calculations

Semiempirical methods were utilized in the computation of a fully optimized structure of bilirubin. Bond lengths and bond angles obtained using either AM1 or PM3 calculations showed excellent agreement with those obtained by X-ray diffraction. This indicated that molecular orbital methods satisfactory reproduced the complex conjugation found in bilirubin. Dihedral angles of the crucial “hinge” and the dihedral angles of the propionic acid side chains agreed well with those found by X-ray diffraction. Calculated hydrogen- bond parameters (distance and angles) showed substantial differences from experimental values, probably due to inherent weakness in the parameterization of the molecular orbital techniques. Conformational studies were carried out using AM1 by rotating the C9? C10 bond in 5° increments showed that the most stable structure exhibited a minimum at about 125° and exhibited a structure similar to those postulated from X-ray and NMR experiments. The hydrogen bonds showed remarkable tenacity during rotation of the C9? C10 bond and resisted breaking until the molecule was under extreme strain. © 1992 John Wiley & Sons, Inc.     

Conformational memories with variable bond angles

Conformational Memories (CM) is a simulated annealing/Monte Carlo method that explores peptide and protein dihedral conformational space completely and efficiently, independent of the original conformation. Here we extend the CM method to include the variation of a randomly chosen bond angle, in addition to the standard variation of two or three randomly chosen dihedral angles, in each Monte Carlo trial of the CM exploratory and biased phases. We test the hypothesis that the inclusion of variable bond angles in CM leads to an improved sampling of conformational space. We compare the results with variable bond angles to CM with no bond angle variation for the following systems: (1) the pentapeptide Met-enkephalin, which is a standard test case for conformational search methods; (2) the proline ring pucker in a 17mer model peptide, (Ala)(8)Pro(Ala)(8); and (3) the conformations of the Ser 7.39 chi(1) in transmembrane helix 7 (TMH7) of the cannabinoid CB1 receptor, a 25-residue system. In each case, analysis of the CM results shows that the inclusion of variable bond angles results in sampling of regions of conformational space that are inaccessible to CM calculations with only variable dihedral angles, and/or a shift in conformational populations from those calculated when variable bond angles are not included. The incorporation of variable bond angles leads to an improved sampling of conformational space without loss of efficiency. Our examples show that this improved sampling leads to better exploration of biologically relevant conformations that have been experimentally validated.     

Geometric and electronic structure of clusters

The interplay between electronic and geometric structure is investigated for covalently bonded phosphorus clusters. We use a modification of the molecular dynamics/ density functional (MD/DF) method of Car and Parrinello, describing the electronic structure by a simplified linear combination of atomic orbitals (LCAO) approach. The results show clearly the tendency of phosphorus to threefold coordination, and substantial variations in bond angles lead to a large variety of isomers.     

Programmable fluidic production of microparticles with configurable anisotropy

We report a technique for continuous production of microparticles of variable size with new forms of anisotropy including alternating bond angles, configurable patchiness, and uniform roughness. The sequence and shape of the anisotropic particles are configured by exploiting a combination of confinement effects and microfluidics to pack precursor colloids with different properties into a narrow, terminal channel. The width and length of the channel relative to the particle size fully specify the configuration of the anisotropic particle that will be produced. The precursor spheres packed in the production zone are then permanently bonded into particles by thermal fusing. The flow in the production zone is reversed to release the particles for collection and use. Particles produced have linear chain structure with precisely configured, repeatable bond angles. With software programmable microfluidics, sequence and shape anisotropy are combined to yield synthesized homogeneous (type "A"), surfactantlike (type "A-B") or triblock (type "A-B-A") internal sequences in a single device. By controlling the dimensions of the microfluidic production zone, triangular prisms and particles with controlled roughness and patchiness are produced. The fabrication method is performed with precursors spheres with diameter as small as 3.0 microm.     

The molecular structure of tetra-tert-butyldiphosphine: an extremely distorted, sterically crowded molecule

The molecular structure of tetra-tert-butyldiphosphine has been determined in the gas phase by electron diffraction using the new DYNAMITE method and in the crystalline phase by X-ray diffraction. Ab initio methods were employed to gain a greater understanding of the structural preferences of this molecule in the gas phase, and to determine the intrinsic P-P bond energy, using recently described methods. Although the P-P bond is relatively long [GED 226.4(8) pm; X-ray 223.4(1) pm] and the dissociation energy is computed to be correspondingly small (150.6 kJ mol(-1)), the intrinsic energy of this bond (258.2 kJ mol(-1)) is normal for a diphosphine. The gaseous data were refined using the new Edinburgh structure refinement program ed@ed, which is described in detail. The molecular structure of gaseous P(2)Bu(t)(4) is compared to that of the isoelectronic 1,1,2,2-tetra-tert-butyldisilane. The molecules adopt a conformation with C(2) symmetry. The P-P-C angles returned from the gas electron diffraction refinement are 118.8(6) and 98.9(6) degrees, a difference of 20 degrees, whilst the C-P-C angle is 110.3(8) degrees. The corresponding parameters in the crystal are 120.9(1), 99.5(1) and 109.5(1) degrees. There are also large deformations within the tert-butyl groups, making the DYNAMITE analysis for this molecule extremely important.     

Efficient Monte Carlo trial moves for polypeptide simulations

A new move set for the Monte Carlo simulations of polypeptide chains is introduced. It consists of a rigid rotation along the (C(alpha)) ends of an arbitrary long segment of the backbone in such a way that the atoms outside this segment remain fixed. This fixed end move, or FEM, alters only the backbone dihedral angles phi and psi and the C(alpha) bond angles of the segment ends. Rotations are restricted to those who keep the alpha bond angles within their maximum natural range of approximately +/-10 degrees. The equations for the angular intervals (tau) of the allowed rigid rotations and the equations required for satisfying the detailed balance condition are presented in detail. One appealing property of the FEM is that the required number of calculations is minimal, as it is evident from the simplicity of the equations. In addition, the moving backbone atoms undergo considerable but limited displacements of up to 3 A. These properties, combined with the small number of backbone angles changed, lead to high acceptance rates for the new conformations and make the algorithm very efficient for sampling the conformational space. The FEMs, combined with pivot moves, are used in a test to fold a group of coarse-grained proteins with lengths of up to 200 residues.     

On the structure of aqueous LiCl solutions

The structure of highly concentrated aqueous lithium chloride solutions was investigated by the Reverse Monte Carlo method. Two total structure factors, obtained from neutron and x-ray diffraction experiments, were applied as input information. From the resulting particle configurations, partial pair correlation functions, coordination numbers and cosine distributions of bond angles have been determined. It was found that, in accordance with common-sense expectations, the hydrogen bonded network of water molecules is breaking up continuously as the concentration of the electrolyte increases. The hydration shell of the cations becomes more and more distorted as concentration grows whereas the hydration structure of the anions appears to be nearly invariant. Ion-pairing was not detected even at the highest salt concentration.     

Molecular structure of the macrocyclic copper(II) chelate with 6,7,13,14-tetramethyl-3,10-dithio-1,2,4,5,8,9,11,12-octaazatetradecatetraene-1,5,7,11 according to quantum-chemical DFT calculations

The key parameters of the molecular structure of macrotetracyclic (NNNN)-coordinated chelate of Cu(II) with 6,7,13,14-tetramethyl-3,10-dithio-1,2,4,5,8,9,11,12-octaazatetradecatetraene-1,5,7,11 have been calculated by means of the DFT-based B3LYP6-31G(d) method in GAUSSIAN-09 software. The complex may be formed via self-assembly of Cu(II), thiocarbohydrazide, and diacetyl in the gelatin-immobilized matrix implants. The bond lengths, bond angles, and torsion angles are presented; it has been shown that the metal chelate and the chelating ligand are almost planar.     

Structural aspects of metal–amide complexes

An exhaustive survey of crystal structure data on simple amides and metal complexes containing monodentate amide ligands has been performed. Statistical analysis of structural features are reported as a function of the degree of alkylation of the amide functional group, the type of metal ion in the amide complex, and the type of binding to the metal ion. Average values are reported for bond lengths, bond angles, and torsional angles. Orientational preferences of the coordinated amide ligand are discussed in terms of M–O–C bond angles and M–O–C–N torsion angles.     

Hairpin conformation of a chiral siloxane-based dimesogenic compound by single crystal analysis

A hairpin conformation of a siloxane-based dimesogen was established on atomic resolution by evaluation of a single crystal structure and the fold described by bond lengths and bond angles, as well as by torsion angles. This hairpin conformation can be extended in the crystalline and liquid crystalline states to a homologous series of dimesogenic compounds with a hexamethyltrisiloxane unit connecting the two mesogenic parts of the molecules.     

Hairpin conformation of a chiral siloxane-based dimesogenic compound by single crystal analysis

A hairpin conformation of a siloxane-based dimesogen was established on atomic resolution by evaluation of a single crystal structure and the fold described by bond lengths and bond angles, as well as by torsion angles. This hairpin conformation can be extended in the crystalline and liquid crystalline states to a homologous series of dimesogenic compounds with a hexamethyltrisiloxane unit connecting the two mesogenic parts of the molecules.     

Crystal structure of the complex of trichosanthin with NADPH at 0.172 nm resolution

The orthorhombic crystal structure of the complex of trichosanthin with nicotinamide adenine dinucleotide phosphate has been determined by molecular replacement method using one of the molecules of the monoclinic crystal structure of trichosanthin at 0.27 nm resolution as the search model. The crystallographic refinement at 0.172 nm resolution led to a final R-factor of 17.4% with root-mean-square deviations of 0.0013 nm and 3.8 from the ideal bond lengths and bond angles, respectively. The quality of the structure, the polypeptide chain fold and the comparison of it with that of the monoclinic trichosanthin structure, the location of nicotinamide adenine dinucleotide phosphate, the active site structure as well as the solvent structure are described.