Dihedral angle

About: Dihedral angle is a research topic. Over the lifetime, 15718 publications have been published within this topic receiving 174904 citations.

Organic polymers based on aromatic rings (polyparaphenylene, polypyrrole, polythiophene): Evolution of the electronic properties as a function of the torsion angle between adjacent rings

Abstract: We present ab initio Hartree–Fock and valence effective Hamiltonian (VEH) calculations on polyparaphenylene, polypyrrole, and polythiophene dimers and polymer chains. These polymeric materials are among the most studied compounds in the field of conducting polymers. We examine, as a function of the torsion angle between consecutive rings, the evolution of electronic properties such as ionization potential, bandgap and width of the highest occupied bands and of the carbon–carbon bond length between rings. This investigation is motivated by the fact that many derivatives of these compounds have substituents that lead to an increase of the torsion angle between adjacent rings, as a result of steric interactions. As expected, on going from a coplanar to a perpendicular conformation, the ionization potential and bandgap values increase and the width of the highest occupied bands decreases. This makes it more difficult to ionize or reduce the polymer chains and can result in achieving lower maximum conductivities on doping. However, since the evolution of the electronic properties is found to follow a cosine law (related to the decrease of the overlap between the π orbitals on adjacent rings), the modifications up to a ∼40° torsion angle are not very large. For instance, in all three polymers, the ionization potential value for a 40° torsion angle is about 0.4 eV larger than the coplanar conformation value. Therefore, substituents that lead to torsion angles between consecutive rings smaller than 40° are quite acceptable. Finally we discuss the importance, for the substituted compounds, of the possibility of achieving a coplanar conformation upon doping, in order to permit high intrachain mobilities of charge carriers such as bipolarons.

Torsion angle dynamics: reduced variable conformational sampling enhances crystallographic structure refinement

Abstract: A reduced variable conformational sampling strategy for macromolecules based on molecular dynamics in torsion angle space is evaluated using crystallographic refinement as a prototypical search problem. Bae and Haug's algorithm for constrained dynamics [Bae, D.S., Haug, E.J. A recursive formulation for constrained mechanical system dynamics. Mech. Struct. Mach. 15:359-382, 1987], originally developed for robotics, was used. Their formulation solves the equations of motion exactly for arbitrary holonomic constraints, and hence differs from commonly used approximation algorithms. It uses gradients calculated in Cartesian coordinates, and thus also differs from internal coordinate formulations. Molecular dynamics can be carried out at significantly higher temperatures due to the elimination of the high frequency bond and angle vibrations. The sampling strategy presented here combines high temperature torsion angle dynamics with repeated trajectories using different initial velocities. The best solutions can be identified by the free R value, or the R value if experimental phase information is appropriately included in the refinement. Applications to crystallographic refinement. Applications to crystallographic refinement show a significantly increased radius of convergence over conventional techniques. For a test system with diffraction data to 2 A resolution, slow-cooling protocols fail to converge if the backbone atom root mean square (rms) coordinate deviation from the crystal structure is greater than 1.25 A, but torsion angle refinement can correct backbone atom rms coordinate deviations up to approximately 1.7 A.

Structure Determination of Trialanine in Water Using Polarization Sensitive Two-Dimensional Vibrational Spectroscopy

Abstract: Using polarization sensitive two-dimensional (2D) vibrational spectroscopy on the amide I mode, the central backbone structure of trialanine in aqueous solution is investigated. We exploit the polarization sensitivity of the 2D pump−probe signal to reveal the cross-peak structure hidden under the strong diagonal peaks. The dihedral angles φ and ψ characterizing the peptide backbone structure are derived directly from the cross-peak intensity and anisotropy, demonstrating the potential of 2D spectroscopy as a tool for peptide structure elucidation.