Fixed Bond Angles Research Articles

Structure determination of alkali trimers on helium nanodroplets through laser-induced Coulomb explosion.

Alkali trimers, Ak3, located on the surface of He nanodroplets are triply ionized following multiphoton absorption from an intense femtosecond laser pulse, leading to fragmentation into three correlated Ak+ ions. Combining the information from threefold covariance analysis of the emission direction of the fragment ions and their kinetic energy distributions P(Ekin), we find that Na3, K3, and Rb3 have an equilateral triangular structure, corresponding to that of the lowest lying quartet state A2'4, and determine the equilibrium bond distance Req(Na3) = 4.65 ± 0.15Å, Req(K3) = 5.03 ± 0.18Å, and Req(Rb3) = 5.45 ± 0.22Å. For K3 and Rb3, these values agree well with existing theoretical calculations, while for Na3, the value is 0.2-0.3Å larger than the existing theoretical results. The discrepancy is ascribed to a minor internuclear motion of Na3 during the ionization process. In addition, we determine the distribution of internuclear distances P(R) under the assumption of fixed bond angles. The results are compared to the square of the internuclear wave function |Ψ(R)|2.

Densest versus jammed packings of bent-core trimers.

We identify putatively maximally dense packings of tangent-sphere trimers with fixed bond angles (θ=θ_{0}), and contrast them to the disordered jammed states they form under quasistatic and dynamic athermal compression. Incommensurability of θ_{0} with three-dimensional (3D) close packing does not by itself inhibit formation of dense 3D crystals; all θ_{0} allow formation of crystals with ϕ_{max}(θ_{0})>0.97ϕ_{cp}. Trimers are always able to arrange into periodic structures composed of close-packed bilayers or trilayers of triangular-lattice planes, separated by "gap layers" that accommodate the incommensurability. All systems have ϕ_{J} significantly below the monomeric value, indicating that trimers' quenched bond-length and bond-angle constraints always act to promote jamming. ϕ_{J} varies strongly with θ_{0}; straight (θ_{0}=0) trimers minimize ϕ_{J} while closed (θ_{0}=120^{∘}) trimers maximize it. Marginally jammed states of trimers with lower ϕ_{J}(θ_{0}) exhibit quantifiably greater disorder, and the lower ϕ_{J} for small θ_{0} is apparently caused by trimers' decreasing effective configurational freedom as they approach linearity.

Densest versus jammed packings of two-dimensional bent-core trimers

We identify the maximally dense lattice packings of tangent-disk trimers with fixed bond angles ($\ensuremath{\theta}={\ensuremath{\theta}}_{0}$) and contrast them to both their nonmaximally-dense-but-strictly-jammed lattice packings as well as the disordered jammed states they form for a range of compression protocols. While only ${\ensuremath{\theta}}_{0}=0,\phantom{\rule{4pt}{0ex}}{60}^{\ensuremath{\circ}},\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}{120}^{\ensuremath{\circ}}$ trimers can form the triangular lattice, maximally-dense maximally-symmetric packings for all ${\ensuremath{\theta}}_{0}$ fall into just two categories distinguished by their bond topologies: half-elongated-triangular for $0l{\ensuremath{\theta}}_{0}l{60}^{\ensuremath{\circ}}$ and elongated-snub-square for ${60}^{\ensuremath{\circ}}l{\ensuremath{\theta}}_{0}l{120}^{\ensuremath{\circ}}$. The presence of degenerate, lower-symmetry versions of these densest packings combined with several families of less-dense-but-strictly jammed lattice packings act in concert to promote jamming.

Jamming of Semiflexible Polymers.

We study jamming in model freely rotating polymers as a function of chain length N and bond angle θ_{0}. The volume fraction at jamming ϕ_{J}(θ_{0}) is minimal for rigid-rodlike chains (θ_{0}=0), and increases monotonically with increasing θ_{0}≤π/2. In contrast to flexible polymers, marginally jammed states of freely rotating polymers are highly hypostatic, even when bond and angle constraints are accounted for. Large-aspect-ratio (small θ_{0}) chains behave comparably to stiff fibers: resistance to large-scale bending plays a major role in their jamming phenomenology. Low-aspect-ratio (large θ_{0}) chains behave more like flexible polymers, but still jam at much lower densities due to the presence of frozen-in three-body correlations corresponding to the fixed bond angles. Long-chain systems jam at lower ϕ and are more hypostatic at jamming than short-chain systems. Implications of these findings for polymer solidification are discussed.

Relaxation of backbone bond geometry improves protein energy landscape modeling

A key issue in macromolecular structure modeling is the granularity of the molecular representation. A fine-grained representation can approximate the actual structure more accurately, but may require many more degrees of freedom than a coarse-grained representation and hence make conformational search more challenging. We investigate this tradeoff between the accuracy and the size of protein conformational search space for two frequently used representations: one with fixed bond angles and lengths and one that has full flexibility. We performed large-scale explorations of the energy landscapes of 82 protein domains under each model, and find that the introduction of bond angle flexibility significantly increases the average energy gap between native and non-native structures. We also find that incorporating bonded geometry flexibility improves low resolution X-ray crystallographic refinement. These results suggest that backbone bond angle relaxation makes an important contribution to native structure energetics, that current energy functions are sufficiently accurate to capture the energetic gain associated with subtle deformations from chain ideality, and more speculatively, that backbone geometry distortions occur late in protein folding to optimize packing in the native state.

Incorporation of Fluorene-containing Pyridyl Ligand into Discrete Supramolecules via Coordination-Driven Self-Assembly

During the past decade, coordination-driven self-assembly with Pt or Pd acceptors has drawn much attention and been successfully applied for the production of various discrete 2D or 3-D supramolecules. Well-matched pre-designed donors and metal-containing acceptors have provided discrete self-assembles in an almost quantitative yield. Exclusive production of discrete ensembles rather than oligomeric or polymeric structures has been unique and interesting outcome in that similar result can not be expected with other synthetic methodologies. This result could be ascribed to the fact that the coordination between metal and ligand is thermodynamically controlled and the formation of discrete entities favors in enthalpy over that of oligomeric forms. Thus, the right combination of donor and acceptor in the type of their reacting elements and bond angles was crucial for the effective production of discrete selfassemblies. Most of the reactions required specific donor and acceptors with fixed-bond angles, and the shape of supramolecular product was decided by the fixed-bond angles used. Only a few flexible ligands in the presence of template molecules self-assembled into discrete entities. Recently, ligands with variable bond angles were successfully applied without assistance of any template for the synthesis of discrete supramolecules via coordination-driven self-assembly. The important and challenging next question might be their applicability of self-assembled supramolecules. Some of their useful functions were reported as an optical sensor, reaction catalyst or molecular switch. However, their known applicability to date is rather restricted and needs to be searched for further uses. In this sense, we are interested in the synthesis of discrete supramolecules containing a fluorene moiety since fluorene-based compounds are regarded as excellent fluorescent materials and often used as emitting materials in eletroluminescent devices. Herein, we report the preparation of fluorene-substituted pyridyl ligand 1 (Scheme 1) then describe the non-templated self-assembly of this ligand into discrete supramolecules 2-3 upon reaction with platinum or palladium acceptors 4-5 (Scheme 2). The synthesis of bidentate ligand 1 was achieved in a moderate yield (43%) by palladium-mediated coupling of commercially available 2,7-dibromofluorene with an excess of 4-ethynyl pyridine using the reported conditions. The self-assembly of supramolecules 2-3 was performed in NMR solvents for the facile monitor by NMR analysis. An acetone-d6/D2O solution of 1 and organoplatinum acceptor 4 was heated at 60 C for 4 h. Anion exchange with KPF6

Flexible Bidentate Pyridyl Ligands in the Coordination-Driven Self-Assembly of Discrete Pd-Macrocycles

Their fixedbond angles and the reversibility of dative bond formationhave been ascribed to the unusual quantitative formation ofdiscrete supramolecules instead of infinite network. On thecontrary, conformationally-flexible ligands have been rarelyused for the self-assembly of discrete supramolecules.Template guest molecules or ions were required for theformation of discrete supramolecules self-assembled withflexible ligands.

ERCC1 and Clinical Resistance to Platinum-Based Therapy

Praz and colleagues report in this issue on the relationship between the occurrence of a polymorphism of ERCC1 in tumor tissues of patients with colorectal cancer and the rate of disease response to the combination of oxaliplatin and 5-fluorouracil ([1][1]). This polymorphism is associated with

A density functional study on magnetic exchange interaction between Mn(II) ion and nitronyl nitroxide radical in trans- and cis-metal-radical complexes

The magneto-structural correlation between a Mn(ll) ion, coordinated in an octahedral environment, and two nitronyl nitroxide radical ligands in trans- and cis-metal-radical complexes is investigated by the broken symmetry (BS) approach within density functional theory (DFT). The dependences of coupling constants J on three structural parameters: (i) bond angle θ (Mn-O-N (nitroxide)); (ii) rotating angle ψ, defined by the nitronyl nitroxide radical plane rotating around the axial Mn-O (nitroxide); (iii) bond distance R (Mn-O (nitroxide)) are directly calculated. Our calculations showed that both trans- and cis-Mn(ll)-radical complexes behave a stronger antiferromagnetic interaction, consistent with experiments. In view of molecular orbital theory, the direct exchanges, including σ-type and π-type exchanges, are responsible for the magnetic exchange pathways. There is a preferable linear correlation between the calculated coupling constants J and the overlap integral squares S b between the local magnetic orbitals at the various rotating angle ψ at the fixed bond angle θ and bond distance R, in both trans- and cis-Mn(ll)-radical complexes.

Monte Carlo Backbone Sampling for Nucleic Acids Using Concerted Rotations Including Variable Bond Angles

An efficient concerted rotation algorithm for use in Monte Carlo statistical mechanics simulations of nucleic acids is reported. The corresponding algorithm “concerted rotations with flexible bond angles” (CRA) for sampling polypeptides was found to be superior to local moves that included only flexible dihedral angles by allowing exploration of a larger conformational space as well as facilitating backbone transitions. The performance of the present CRA algorithm for polynucleotides is compared to two alternatives, a simple update of main-chain torsion angles and a previously reported, concerted rotation algorithm with fixed bond angles and a mix of flexible and rigid main-chain dihedral angles. The test system is a 12 base-pair duplex B-form DNA helix, and the performance comparisons are made for the system both in a vacuum and with continuum GB/SA solvation. The results demonstrate the superior efficiency of the CRA method over the alternatives.

Molecular modeling of flexible molecules. Vapor–liquid and fluid–solid equilibria

We consider recent applications of Wertheim's first order perturbation theory (TPT1) to the description of the critical properties and the freezing transition of chain molecules. Firstly we consider an extension of TPT1 which allows one to describe the equation of state of atomistic molecular models which incorporate fine chemical details such as overlap between the sites, fixed bond angles and torsional potentials. The theory is applied to the description of the critical properties of all isomers ranging from butane to octane and good qualitative agreement is found. We then show how TPT1 may be applied to the description of the freezing transition of chain molecules. We apply the theory to chains of tangent hard spheres and Lennard–Jones chains and find good agreement for the equation of state and free energies of the fluid and solid phases. Fluid–solid coexistence properties predicted by the theory are in close agreement with simulation results. It is shown that for hard sphere and Lennard–Jones dimers the stable solid structure is a disordered one, with the atoms forming a close packed arrangement, but with the bonds distributed randomly within the solid.

On the Relationship between the Characteristic Ratio of a Finite Chain, Cn, and the Asymptotic Limit, C∞

Often experiments with chains containing a finite number of bonds, n, are interpreted with the assumption that the characteristic ratio, Cn, is determined completely by C∞ and n. This assumption is supported by some, but not all, textbook models for simple flexible chains. The freely jointed chain, freely rotating chain with fixed bond angle, and simple wormlike chain predict Cn = f(C∞,n). These three models share the feature that the stiffness of the chain is specified by no more than one parameter. However, when more than one parameter affects the stiffness of the chain, as in the model with fixed bond angle and symmetric hindered rotation about independent bonds, Cn is no longer determined by C∞ and n alone, Cn ≠ f(C∞,n). Since virtually all real chains have hindered rotation, they cannot be expected to have the dimensions given by Cn = f(C∞,n). This conclusion is supported by numerical calculations using previously published rotational isomeric state models for polyethylene, polyisobutylene, and poly(...

MOLECULAR DYNAMICS SIMULATIONS FOR ICE MODIFICATIONS II AND IX

Molecular vibrations of water (H2O and D2O) in crystals of ice II and ice IX are studied by molecular dynamics in a rigid bond approximation with a fixed bond angle. Using an atom-atomic potential PM for describing the interactions between water molecules in ice II (N = 576 molecules) and ice IX (N = 768) in an NVE ensemble leads to reproduction of the structure of both types of ice. For all water molecules and separately for each system of crystallographically equivalent water molecules in ice crystals, we defined the time dependence of the mean-square displacement of the center of mass of the molecule, the autocorrelation function of velocity for the center of mass, and the autocorrelation function of velocity for hydrogen (deuterium) atoms. The densities of vibrational states are calculated as Fourier integrals of the corresponding autocorrelation functions. In the case of ice II, the densities of states agree well with the experimental incoherent inelastic neutron scattering spectra. In the case of ice IX, agreement is worse. For both polymorphs, the mean-square displacement and the densities of vibrational states of the center of mass of the molecule and the hydrogen (deuterium) atom differ slightly between molecules belonging to different systems of crystallographic positions. This is explained by the difference in their environments.

Equilibrium Partitioning of Flexible Macromolecules in Fibrous Membranes and Gels

A theory was developed to describe the equilibrium partitioning of a flexible polymeric solute between a dilute solution and a medium consisting of a randomly oriented array of fibers (e.g., a fibrous membrane or gel). The fibers were regarded as long, rigid cylinders, and the solute was modeled as a chain consisting of n mass points joined by n − 1 rectilinear segments. Results were obtained for freely jointed chains and for chains with fixed bond angles, using a combination of analytical and computational (e.g., Monte Carlo) techniques. The predicted partition coefficient (Φ, the solute concentration in the fibrous material divided by that in the bulk solution) proved to be sensitive to the number of fibers included; typically, 50 or more nearest-neighboring fibers were needed to obtain a convergent result. The values of Φ decreased as fiber volume fraction, molecular size, or number of mass points was increased selectively. As the bond angle was increased from 0° (a chain folding back on itself) to 180° (a rodlike chain), Φ first decreased and then increased. The model predictions agreed reasonably well with literature partitioning data for various polymeric solutes in hydrogels, especially when the radius of gyration was no more than a few times the fiber radius. With the radius of gyration specified, the model predictions were fairly insensitive to whether the bond angle was fixed or random.

Geometric and computational aspects of molecular reconfiguration

We examine geometric problems of reconfiguring molecules modeled by polygons and polygonal chains in two and three dimensions. The molecule can be continuously reconfigured as long as the edge lengths are maintained and the object does not self-intersect. We begin with a treatment of polygons in chapters 3 and 4. We prove that in two dimensions all convex configurations of a given polygon are reachable from any other and provide an efficient algorithm for convexifying planar monotone polygons. We also describe an algorithm to convexity three-dimensional polygons with simple projections. We further prove that the motions to bring a convex configuration to another can be accomplished in three-dimensions by a series of restrictive moves called pivots, which are widely used in the polymer physics community. A pivot is a motion by which a contiguous subchain of the polygon is rotated about the line through its endpoints. A particular type of pivot on a planar polygon, known as a deflation, splits the polygon into two linearly separable subchains and rotates one by 180°. (A deflation can be thought of as the inverse of a flip as defined by Erdos [49].) Since a rotation of 180° about a line is equivalent to a reflection, a planar polygon remains planar after the deflation. In 1993 [164], Wegner conjectured that a planar polygon could admit only a finite number of deflations before self-intersecting. We disprove this conjecture by exhibiting a counterexample. In chapters 5 through 7, we consider only polygonal chains in three-dimensions. As is consistent with the conventions of the chemistry and physics communities, we augment our model by allowing only those motions which maintain the angles at the vertices of the chain (and which also maintain the edge lengths and do not cause self-intersection). The chain can be reconfigured by only altering the dihedral torsion angles, which better reflects the fixed bond angles of a molecule. We discuss several computational problems on this model. First, we describe an algorithm to determine the feasibility of the simplest possible motion—the alteration of only one dihedral angle—called a dihedral rotation. Since molecular reconfiguration is a complex process, the motion of a chain would involve a vast number of dihedral rotations. We prove lower bounds on the computational complexity of preprocessing a polygonal chain to determine the feasibility of multiple rotations. We continue by demonstrating the intractability of several questions: (1) computing the maximum possible and minimum possible distance between the endpoints of the chain, (2) determining whether a chain can be reconfigured to certain canonical configurations, and (3) determining configurational chirality, that is, whether or not a chain can be reconfigured into its mirror image. This last problem has important implications for drug design, since the two mirror images of a molecule can have radically different properties.

Density functional theory of polymers: A Curtin-Ashcroft type weighted density approximation

A density functional theory is presented that combines an exact expression for the ideal gas free energy functional with a weighted density approximation for the excess free energy functional. The weighting function required in the theory is obtained from the Curtin-Ashcroft recipe, with a bulk fluid direct correlation function from the polymer reference interaction site model integral equation theory. The theory is in quantitative agreement with computer simulations for the density profiles of freely jointed tangent sphere hard chains at a hard wall, about as accurate as the Curtin-Ashcroft theory is for hard spheres at a hard wall. For a more realistic fused-sphere chain model with fixed bond angles and bond lengths, the theory is in excellent agreement with simulations at low and intermediate densities but overestimates the magnitude of layering at high densities for short chains. The theory becomes more accurate as the chain length is increased.

New model of potential energy functions for atomic solids. Part 2. New potentials of silicon and germanium crystals

A new theoretical model has been developed to determine potential energy functions which take into account the fixed bond angles of covalently bonded systems in atomic solids. In this paper it has been applied to give new empirical potentials fitted to lattice energy, equilibrium geometry and phonon frequencies for silicon and germanium crystals.

Computer simulations of molecular motion in liquid crystals by the method of Brownian dynamics

AbstractComputer simulations of the molecular motion of polymer chains in the presence of a strong nematic field were carried out by the method of Brownian dynamics. Two models were studied: the first model (linear liquid crystal) is a freely jointed chain with rigid bonds, the second model (comb‐like liquid crystal) is a chain with fixed bond angles and rigid side groups. The influence of ordering on chain conformations, orientational and translational mobility and spectra of relaxation times was investigated.

Excited electronic potential energy surfaces and transition moments for the H 3 system

Four electronic states of H 3 have been studied using a multi-reference configuration interaction method and a basis set of 75 AOs. The calculations were carried out at a fixed bond angle of 60°. The four states include the ground state and the Rydberg 2s and 2p z states, as well as the state which in the equilateral triangular geometry is related to the ground state by a conical intersection. Electric dipole transition moments were calculated between all of these states at every geometry. The potential energies obtained for the various states show that the atomic and diatomic asymptotes are accurately described, and that the barriers, wells and energy differences also show good agreement compared to literature values, where available. The ground state and 2p z Rydberg state potential energy surfaces were fitted over the whole geometric configuration space spanned using a rotated Morse curve—cubic spline approach, and show smooth contour maps appropriate for studies in excited-state reaction dynamics.

Site–site correlations in short chain fluids

Intramolecular and intermolecular site–site correlations in short chain fluids are obtained via Monte Carlo simulation for volume fractions ranging between 0.05 and 0.35. The chains are modeled as pearl necklaces of freely jointed hard spheres; chains composed of 4 and 8 beads are studied. The intramolecular distribution between a pair of beads separated by a fixed number of segments along the chain is found to be remarkably independent of the position of the pair along the chain. At low densities the intermolecular site–site pair distribution function at contact is found to be much less than one due to the ‘‘correlation hole’’ effect. The contact value increases as the density is increased, and decreases as the chain length is increased. We use the intramolecular correlations measured to obtain polymer reference interaction site model predictions for the intermolecular site–site distribution function. We find that the theory accurately reproduces the local structure of the fluid, but significantly overestimates the contact value of the distribution function, especially at low densities. A comparison of freely jointed chain results with simulations of chains with fixed bond angles and torsional rotations treated in the rotational isomeric state approximation shows that the correlation hole is more pronounced in freely jointed chains. We test a superposition approximation used to evaluate the three body term in the pressure equation for chain molecules. We find that the three-body term is sizeable, and that the superposition approximation significantly underestimates the three-body contribution.