Rhorix: An interface between quantum chemical topology and the 3D graphics program blender

Chemical research is assisted by the creation of visual representations that map concepts (such as atoms and bonds) to 3D objects. These concepts are rooted in chemical theory that predates routine solution of the Schrödinger equation for systems of interesting size. The method of Quantum Chemical Topology (QCT) provides an alternative, parameter‐free means to understand chemical phenomena directly from quantum mechanical principles. Representation of the topological elements of QCT has lagged behind the best tools available. Here, we describe a general abstraction (and corresponding file format) that permits the definition of mappings between topological objects and their 3D representations. Possible mappings are discussed and a canonical example is suggested, which has been implemented as a Python “Add‐On” named Rhorix for the state‐of‐the‐art 3D modeling program Blender. This allows chemists to use modern drawing tools and artists to access QCT data in a familiar context. A number of examples are discussed. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

A combined experimental and DFT investigation of the adsorption of humic acid by-products on polypyrrole

This study sheds light on the removal of humic acid by-products (trimellitic and pyromellitic acids; TMA and PMA, respectively) from aqueous solution using conducting polypyrrole (PPy) as an effective adsorbent. The effects of experimental factors including contact time, solution pH, initial concentration, adsorbent dose, and temperature were systematically investigated. The pseudo-second-order kinetic model provides the best correlation with adsorption experimental data. The equilibrium adsorption was well described by the Langmuir model with maximum mono-layer adsorption capacities of 47.62 and 71.43?mg?g^?1 for TMA and PMA, respectively. The analysis of thermodynamic parameters indicated that the adsorption process was spontaneous and endothermic in nature. In addition, we investigated the adsorption mechanism using the density functional theory (DFT) calculations. The TMA and PMA were physisorbed on the PPy surface through the formation of hydrogen bonds between carboxylic groups of adsorbate molecules and the amino group of the adsorbent. The calculated theoretical data were in good agreement with experiments.     

A continuum description for cholesteric and nematic twist-bend phases based on symmetry considerations

ABSTRACT

The recently discovered twist-bend nematic phase, N_tb, is a non-uniform equilibrium nematic phase that presents a spontaneous bend with a precession of the nematic director, n, on a conical helix with a tilt angle θ and helical pitch P. The stability of the N_tb phase has been recently demonstrated from the elastic point of view by extending the Frank elastic energy density of the nematic phase to include the symmetry element of the helical axis, t. In the present article, we investigate the influence of an external bulk field (magnetic or electric) on the N_tb phase. Using symmetry arguments we derive the expression for the flexoelectric polarisation in twist-bend nematic phases. We show that, besides the standard contribution related to the spatial variation of the nematic director, two new contributions connected with the existence of the helical axis appear. In the ground state, where the nematic deformation is a pure heliconical deformation, the new contribution vanishes identically, and the total flexoelectric polarisation is perpendicular to the nematic director. Furthermore, as an example, we study the role of an external magnetic field applied parallel to the helical axis for a material with positive magnetic susceptibility anisotropy. We show that the field modifies the range of values of the coupling parameter between the director and the helical axis, thus shifting the interval of values for which this coupling results in the N_tb phase.     

Comparative molecular field analysis of chromatographic hydrophobicity indices for some coumarin analogs

The chromatographic hydrophobicity index (CHI) is an HPLC‐based parameter that provides reliable guidance in optimization of pharmacological efficiency and adsorption, distribution, metabolism and exertion (ADME) profile of drug candidates. In the present work, classical and three‐dimensional quantitative structure–property relationship (QSPR) models were developed for prediction of CHI values of some 4‐hydroxycoumarin analogs on immobilized artificial membrane column. Comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) as 3D–QSPR methods were performed to gain insight into the key structural factors affecting on the chromatographic hydrophobicity of interested chemicals. The calculated parameters of Q ², R ² and standard error were 0.545, 0.996 and 0.773 for CoMFA model and 0.815, 0.986 and 1.44 for CoMSIA model, respectively. The contour maps for steric fields of the CoMFA model illustrate that the hydrophobicity of chemicals will be higher when the positions of R6, R7 and R8 in the 4‐hydroxycuomarin ring are substituted by alkyl groups. Moreover, by the analysis of the plots of electrostatic fields, it was concluded that the CHI value greatly increases if one hydrogen on coumarin ring is substituted by the F, Cl, Br, OH or OCH₃ group.     

The string of variable density: Perturbative and non-perturbative results

We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which hold regardless of the inhomogeneity of the string. Working on specific examples we obtain very accurate approximations which are compared both with the results of WKB method and with the numerical results obtained with a collocation approach. Finally, we show that the asymptotic behaviour of the energies of the string obtained with perturbation theory, worked to second order in the inhomogeneities, agrees with that obtained with the WKB method and implies a different functional dependence on the density that in two and higher dimensions.     

Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

The work continues and develops authors’ previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a “canonical” form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers).     

Equation of state of zero-temperature quark matter

We outline the key elements of a recent calculation aimed at determining the equation of state of deconfined (but unpaired) quark matter at zero temperature and high density, using finite quark masses. The computation is performed in perturbation theory up to three loops, and necessitates the development and application of some novel computational tools. In this talk, we introduce the basic features of these new techniques and review the main sources of motivation for considering finite mass effects in perturbation theory.     

Quasi-periodic stability of normally resonant tori

We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorov-like variation of the internal frequencies and simultaneously versality of the Floquet matrix unfolding. We focus on the reversible setting, but our results carry over to the Hamiltonian and dissipative contexts.