Showing papers on "Dihedral angle published in 2020"

A polyhedron comparison theorem for 3-manifolds with positive scalar curvature

Abstract: The study of comparison theorems in geometry has a rich history. In this paper, we establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collections of polyhedra with interior non-negative scalar curvature and mean convex faces, we prove the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding Euclidean model, unless it is isometric to a flat polyhedron.

Synthesis, Crystal Structure, DFT Calculations and Hirshfeld Surface Analysis of 3-Chloro-3-methyl-r(2),c(6)-bis(p-methoxyphenyl)piperidin-4-one

Abstract: The title compound, C20H22ClNO3, [common name: 3-chloro-3-methyl-r(2),c(6)-bis(p-methoxyphenyl)piperidin-4-one] crystallizes in the P21/c space group with unit cell parameters a = 13.4020(11) A, b = 7.7888(5) A and c = 18.1721(14) A, β = 108.250(9)°, Z = 4. The central piperidin-4-one ring (N1/C1–C5), adopts a slightly distorted chair conformation and an equatorial orientation of all its substituents except for chlorine which is axially located. The dihedral angle between the mean planes of the two phenyl rings is 47.9(4)° and between the piperidin-4- one ring and pendant phenyl rings is 68.8(2)° (C6–C11) and 73.1(6)° (C13–C18), respectively. Crystal packing is stabilized by weak C–H⋯O intermolecular interactions forming chains along the b-axis. Additional weak Cg–π interactions between nearby phenyl rings are also observed. A comparison of these bond lengths and angles within the crystal with Density Functional Theory (DFT) geometry optimized calculations at the B3LYP/6-31+G (d) level has been determined. Hirshfeld surface analysis for determining the molecular shape and visually analyzing the intermolecular interactions in the crystal structure employing 3D molecular surface contours and 2D fingerprint plots gave enrichment ratios for H⋯H, O⋯H, Cl⋯H and C⋯H contacts compared to C–C, Cl⋯Cl and C⋯Cl contacts indicating a higher propensity for O–H interactions to form in this crystal. Electronic transitions have also been predicted by DFT Molecular Orbital calculations and compared to experimental absorption spectra. Molecular orbital diagrams provide visual representations of the top level molecular orbital surfaces in the compound.

Insights into the effects of substitution position on the photophysics of mono-o-carborane-substituted pyrenes

Abstract: Three closo-o-carborane-functionalised pyrene compounds (1CB, 2CB, and 4CB) were synthesised and fully characterised. The molecular structures of all compounds exhibited perpendicularity between the C–C bond of the o-carborane and the pyrene groups. The three compounds displayed major absorption bands assignable to π–π* transitions within the pyrene group, as well as weak intramolecular charge-transfer (ICT) transitions between the o-carborane units and the pyrene moieties. While 1CB and 4CB displayed strong ICT-based emissions involving the o-carborane moiety (λem = 500–700 nm) in THF at 298 K, 2CB showed less intense LE-based emissions centred at λem = 407 nm. Although the PL spectra of all compounds demonstrated enhanced ICT-based emission via inhibition of C–C bond variance within the o-carborane in rigid states (THF at 77 K and films), the quantum efficiency of 2CB in films (Φem = 5%) did not significantly increase compared to that in THF at 298 K, while the values for 1CB and 4CB in films were dramatically enhanced to 75% and 62%, respectively. The radiative decay constants of each ICT-based emission showed that non-radiative decay processes were significantly larger for 2CB than in 1CB and 4CB. The relative energies of the various S0 conformations as the dihedral angle between the o-carborane cage and pyrene unit was changed indicated that the o-carborane cages in 2CB could rotate more easily than those in 1CB and 4CB. Furthermore, the involvement of the o-carborane moiety in the LUMO level of 2CB was significantly affected by this dihedral angle. These results suggest that the free rotation of the o-carborane cage of 2CB interrupted its ICT transitions, with experimental and theoretical findings confirming that large structural variations around the o-carborane cage for 2CB also induced ICT-based non-radiative decay processes associated with the o-carborane, further blocking the ICT transition itself.

Learning reaction coordinates via cross-entropy minimization: Application to alanine dipeptide

Abstract: We propose a cross-entropy minimization method for finding the reaction coordinate from a large number of collective variables in complex molecular systems. This method is an extension of the likelihood maximization approach describing the committor function with a sigmoid. By design, the reaction coordinate as a function of various collective variables is optimized such that the distribution of the committor pB* values generated from molecular dynamics simulations can be described in a sigmoidal manner. We also introduce the L2-norm regularization used in the machine learning field to prevent overfitting when the number of considered collective variables is large. The current method is applied to study the isomerization of alanine dipeptide in vacuum, where 45 dihedral angles are used as candidate variables. The regularization parameter is determined by cross-validation using training and test datasets. It is demonstrated that the optimal reaction coordinate involves important dihedral angles, which are consistent with the previously reported results. Furthermore, the points with pB*∼0.5 clearly indicate a separatrix distinguishing reactant and product states on the potential of mean force using the extracted dihedral angles.

Pseudo-Improper-Dihedral Model for Intrinsically Disordered Proteins.

Abstract: We present a new coarse-grained Cα-based protein model with a nonradial multibody pseudo-improper-dihedral potential that is transferable, time-independent, and suitable for molecular dynamics. It ...

Effect of alkyl-group flexibility on the melting point of imidazolium-based ionic liquids.

Abstract: The low melting point of room temperature ionic liquids is usually explained in terms of the presence of bulky, low-symmetry, and flexible ions, with the first two factors related to the lattice energy while an entropic effect is attributed to the latter. By means of molecular dynamics simulations, the melting points of 1-ethyl-3-methyl-imidazolium hexafluorophosphate and 1-decyl-3-methyl-imidazolium hexafluorophosphate were determined, and the effect of the molecular flexibility over the melting point was explicitly computed by restraining the rotation of dihedral angles in both the solid and the liquid phases. The rotational flexibility over the bond between the ring and the alkyl chain affects the relative ordering of the anions around the cations and results in substantial effects over both the enthalpy and the entropy of melting. For the other dihedral angles of the alkyl group, the contributions are predominantly entropic and an alternating behavior was found. The flexibility of some dihedral angles has negligible effects on the melting point, while others can lead to differences in the melting point as large as 20 K. This alternating behavior is rationalized by the different probabilities of conformation defects in the crystal.

MOLECULAR STRUCTURE MODELS OF Al2Ti3 AND Al2V3 CLUSTERS ACCORDING TO DFT QUANTUM-CHEMICAL CALCULATIONS

Abstract: Basic parameters of molecular structures of Al2Ti3 and Al2V3 metal clusters (bond lengths, bond angles, and torsion (dihedral) angles), have been calculated using DFT method at the OPBE/QZVP level. It has been shown that the Al2Ti3 cluster may exist in 14 modifications and Al2V3 in 11 ones, differing noticeably in their total energy. Besides, the molecular structures of these metal clusters differ significantly in terms of geometric parameters as well as in external form. Moreover, the most energetically stable modifications of Al2Ti3 and Al2V3 clusters differ each other considerably in geometric form also.

Compressing Double [7]Helicene by Successive Charging with Electrons

Abstract: Chemical reduction of a benzo-fused double [7]helicene (1) with two alkali metals, K and Rb, provided access to three different reduced states of 1. The doubly-reduced helicene 12- has been characterized by single-crystal X-ray diffraction as a solvent-separated ion triplet with two potassium counterions. The triply- and tetra-reduced helicenes, 13- and 14- , have been crystallized together in an equimolar ratio and both form the contact-ion complexes with two Rb+ ions each, leaving three remaining Rb+ ions wrapped by crown ether and THF molecules. As structural consequence of the stepwise reduction of 1, the central axis of helicene becomes more compressed upon electron addition (1.42 A in 14- vs. 2.09 A in 1). This is accompanied by an extra core twist, as the peripheral dihedral angle increases from 16.5° in 1 to 20.7° in 14- . Theoretical calculations provided the pattern of negative charge build-up and distribution over the contorted helicene framework upon each electron addition, and the results are consistent with the X-ray crystallographic and NMR spectroscopic data.

Algebras of generalized dihedral type

Abstract: We provide a complete classification of all algebras of generalized dihedral type, which are natural generalizations of algebras which occurred in the study of blocks of group algebras with dihedral defect groups. This gives a description by quivers and relations coming from surface triangulations.

Synthesis, crystal structure, DFT calculations and Hirshfeld surface analysis of 3-butyl-2,6-bis-(4-fluoro-phen-yl)piperidin-4-one.

Abstract: The title compound, C21H23F2NO, consists of two fluoro-phenyl groups and one butyl group equatorially oriented on a piperidine ring, which adopts a chair conformation. The dihedral angle between the mean planes of the phenyl rings is 72.1 (1)°. In the crystal, N-H⋯O and weak C-H⋯F inter-actions, which form R 2 2[14] motifs, link the mol-ecules into infinite C(6) chains propagating along [001]. A weak C-H⋯π inter-action is also observed. A Hirshfeld surface analysis of the crystal structure indicates that the most significant contributions to the crystal packing are from H⋯H (53.3%), H⋯C/C⋯H (19.1%), H⋯F/F⋯H (15.7%) and H⋯O/O⋯H (7.7%) contacts. Density functional theory geometry-optimized calculations were compared to the experimentally determined structure in the solid state and used to determine the HOMO-LUMO energy gap and compare it to the UV-vis experimental spectrum.

Anyonic defect braiding and spontaneous chiral symmetry breaking in dihedral liquid crystals

Abstract: Dihedral ('$k$-atic') liquid crystals (DLCs) are assemblies of microscopic constituent particles that exhibit $k$-fold discrete rotational and reflection symmetries. Generalizing the half-integer defects in nematic liquid crystals, two-dimensional $k$-atic DLCs can host point defects of fractional topological charge $\pm m/k$. Starting from a generic microscopic model, we derive a unified hydrodynamic description of DLCs with aligning or anti-aligning short-range interactions in terms of Ginzburg-Landau and Landau-Brazovskii-Swift-Hohenberg theories for a universal complex order-parameter field. Building on this framework, we demonstrate in both particle and continuum simulations how adiabatic braiding protocols, implemented through suitable boundary conditions, can emulate anyonic exchange behavior in a classical system. Analytic solutions and simulations of the mean-field theory further predict a novel spontaneous chiral symmetry breaking transition in anti-aligning DLCs, in quantitative agreement with the patterns observed in particle simulations.

Development and initial applications of an e-ReaxFF description of Ag nanoclusters.

Abstract: Metal nanocrystals are of considerable scientific interest because of their uses in electronics, catalysis, and spectroscopy, but the mechanisms by which nanocrystals nucleate and grow to achieve selective shapes are poorly understood. Ab initio calculations and experiments have consistently shown that the lowest energy isomers for small silver nanoparticles exhibit two-dimensional (2D) configurations and that a transition into three-dimensional (3D) configurations occurs with the addition of only a few atoms. We parameterized an e-ReaxFF potential for Ag nanoclusters (N ≤ 20 atoms) that accurately reproduces the 2D–3D transition observed between the Ag5 and Ag7 clusters. This potential includes a four-body dihedral term that imposes an energetic penalty to 3D structures that is significant for small clusters but is overpowered by the bond energy from out-of-plane Ag–Ag bonds in larger 3D clusters. The potential was fit to data taken from density-functional theory and coupled-cluster calculations and compared to an embedded atom method potential to gauge its quality. We also demonstrate the potential of e-ReaxFF to model redox reactions in silver halides and plasmon motion using molecular dynamics simulations. This is the first case in which e-ReaxFF is used to describe metals. Furthermore, the inclusion of a bond-order dependent dihedral angle in this force field is a unique solution to modeling the 2D–3D transition seen in small metal nanoclusters.

Kinetic energy flows in activated dynamics of biomolecules.

Abstract: Protein conformational changes are activated processes essential for protein functions. Activation in a protein differs from activation in a small molecule in that it involves directed and systematic energy flows through preferred channels encoded in the protein structure. Understanding the nature of these energy flow channels and how energy flows through them during activation is critical for understanding protein conformational changes. We recently [W. Li and A. Ma, J. Chem. Phys. 144, 114103 (2016)] developed a rigorous statistical mechanical framework for understanding potential energy flows. Here, we complete this theoretical framework with a rigorous theory for kinetic energy flows: potential and kinetic energies interconvert when impressed forces oppose inertial forces, whereas kinetic energy transfers directly from one coordinate to another when inertial forces oppose each other. This theory is applied to analyzing a prototypic system for biomolecular conformational dynamics: the isomerization of an alanine dipeptide. Among the two essential energy flow channels for this process, dihedral ϕ confronts the activation barrier, whereas dihedral θ1 receives energy from potential energy flows. Intriguingly, θ1 helps ϕ to cross the activation barrier by transferring to ϕ via direct kinetic energy flow all the energy it received-an increase in θ1 caused by potential energy flow converts into an increase in ϕ. As a compensation, θ1 receives kinetic energy from bond angle α via a direct mechanism and bond angle β via an indirect mechanism.

Intramolecular-rotation driven triplet-to-singlet upconversion and fluctuation induced fluorescence activation in linearly connected donor-acceptor molecules.

Abstract: Thermally activated triplet-to-singlet upconversion is attractive from both fundamental science and exciton engineering, but controlling the process from molecular configuration is still unrevealed. In particular, the flexibility of the freedom of molecular geometry is of major importance to understand the kinetics of the phonon-induced upconversion. Here, we focus on two linearly connected donor-acceptor molecules, 9,9-dimethyl-9,10-dihydroacridine-2,4,6-triphenyl-1,3,5-triazine (DMAC-TRZ) and hexamethylazatriangulene-2,4,6-triphenyl-1,3,5-triazine (HMAT-TRZ), as the model system. While DMAC-TRZ possesses a rotational degree of freedom in the dihedral angle between the donor and acceptor moieties, i.e., C-N bond in tertiary amine, the rotation is structurally restricted in HMAT-TRZ. The rotationally flexible DMAC-TRZ showed significant triplet-to-singlet upconversion caused by thermal activation. On the other hand, the rotation-restricted HMAT-TRZ showed negligible thermal upconversion efficiency. We elaborate on the origin of the photophysical properties from the viewpoint of the geometries in the excited states using time-resolved infrared spectroscopy and quantum chemical calculations. We uncovered that the structural restriction of the intramolecular flexibility significantly affects the optimized geometry and phonon modes coupled to the spin conversion. As a result of the rotation restriction, the spin flipping in HMAT-TRZ was coupled to bending motion instead of the rotation. In contrast, the free rotation fluctuation in the DMAC-TRZ mixes local-excitation and charge-transfer characters, leading to successful activation of the delayed fluorescence as well as the reverse intersystem crossing. Our discovery sheds light on the mechanism of the triplet-to-singlet upconversion, providing a microscopic strategy to control the optoelectronic properties from a molecular viewpoint.

Development of transferable coarse-grained models of amino acids

Abstract: We have developed transferable coarse-grained (CG) models of the twenty standard amino acids, which can be used to perform molecular dynamics (MD) simulations of peptide amphiphiles (PAs) in the presence of explicit solvent. A 2 : 1 to 4 : 1 mapping scheme – in which a CG bead is comprised of two to four heavy atoms, respectively, and associated hydrogens – has been employed. Non-bonded parameters were optimized using the artificial neural network assisted particle swarm optimization (ANN-assisted PSO) method to reproduce experimental properties (density, surface tension, and heat of vaporization) of analogues of the side chains, termini, and backbone functional groups of the amino acids. The density (error <3.04%) and surface tension (error <7.38%) predicted by CG models were in good agreement with those of experimental properties. The peptide backbone is modeled with two charge neutral beads while amino acid side chains are modeled with one to three beads. Each terminus (N-terminus and C-terminus) is modeled as one charge neutral bead. Bonded parameters for the CG models were obtained from bond, angle, and dihedral distributions from AA MD simulations of dipeptides and/or tripeptides, which showed a reasonable agreement. Moreover, densities of these dipeptides and tripeptides calculated from AA MD simulations and CG models were in excellent agreement.

A three-dimensional potential of mean force to improve backbone and sidechain hydrogen bond geometry in Xplor-NIH protein structure determination.

Abstract: We introduce a new hydrogen bonding potential of mean force generated from high-quality crystal structures for use in Xplor-NIH structure calculations. This term applies to hydrogen bonds involving both backbone and sidechain atoms. When used in structure refinement calculations of 10 example protein systems with experimental distance, dihedral and residual dipolar coupling restraints, we demonstrate that the new term has superior performance to the previously developed hydrogen bonding potential of mean force used in Xplor-NIH.

The near-symmetry of protein oligomers: NMR-derived structures

Abstract: The majority of oligomeric proteins form clusters which have rotational or dihedral symmetry. Despite the many advantages of symmetric packing, protein oligomers are only nearly symmetric, and the origin of this phenomenon is still in need to be fully explored. Here we apply near-symmetry analyses by the Continuous Symmetry Measures methodology of protein homomers to their natural state, namely their structures in solution. NMR-derived structural data serves us for that purpose. We find that symmetry deviations of proteins are by far higher in solution, compared to the crystalline state; that much of the symmetry distortion is due to amino acids along the interface between the subunits; that the distortions are mainly due to hydrophilic amino acids; and that distortive oligomerization processes such as the swap-domain mechanism can be identified by the symmetry analysis. Most of the analyses were carried out on distorted C2-symmetry dimers, but C3 and D2 cases were analyzed as well. Our NMR analysis supports the idea that the crystallographic B-factor represents non-classical crystals, in which different conformers pack in the crystal, perhaps from the conformers which the NMR analysis provides.

Measuring mass via coordinate cubes

Abstract: Inspired by a formula of Stern that relates scalar curvature to harmonic functions, we evaluate the mass of an asymptotically flat 3-manifold along faces and edges of a large coordinate cube. In terms of the mean curvature and dihedral angle, the resulting mass formula relates to Gromov’s scalar curvature comparison theory for cubic Riemannian polyhedra. In terms of the geodesic curvature and turning angle of slicing curves, the formula realizes the mass as integration of the angle defect detected by the boundary term in the Gauss–Bonnet theorem.

Hamiltonian Reweighing To Refine Protein Backbone Dihedral Angle Parameters in the GROMOS Force Field.

Abstract: Molecular dynamics simulations of proteins depend critically on the underlying force field, which may be parameterized against experimental data or high-quality quantum calculations. Here, we develop search algorithms based on Monte Carlo and steepest descent calculations to optimize the backbone dihedral angle parameters from a single reference simulation. We apply these tools to improve the agreement between simulations of single, capped amino acids and experimentally determined J values and secondary structure propensities of these molecules. The parameters are further refined based on simulations of a set of seven proteins and finally validated in simulations on a large set of 52 protein structures. Improvements in the dihedral angle distributions are observed, and structural propensities of the proteins are reproduced very well. Overall, the GROMOS 54A8_bb parameter set forms an improvement to previous parameter sets, both for small molecules and for protein simulations.