Resolving Atomic-Scale Defects in Conjugated Polymers On-Surfaces

Atomic scale defects significantly affect the mechanical, electronic, and optical properties of π-conjugated polymers. Here, isolated atomic-scale defects are deliberately introduced into a prototypical anthracene-ethynylene π-conjugated polymer, and its local density of states is carefully examined on the atomic scale to show how individual defects modify the inherent electronic and magnetic properties of this one-dimensional systems. Scanning tunneling and atomic force microscopy experiments, supplemented with density functional theory calculations, reveal the existence of a sharp electronic resonance at the Fermi energy around certain defects, which is associated with the formation of a local magnetic moment accompanied by substantial mitigation of the mobility of charge carriers. While defects in traditionally synthesized polymers lead to arbitrary conformations, the presented results clearly reflect the preferential formation of low dimensional defects at specific polymer sites, which may introduce the possibility of engineering macroscopic defects in surface-synthesized conjugated polymers.     

Advances in vibrational configuration interaction theory - part 2: Fast screening of the correlation space

For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.     

Microwave-enhanced synthesis of new (-)-steganacin and (-)-steganone aza analogues

[reaction: see text]. A novel, microwave-enhanced, highly efficient protocol for the synthesis of hitherto unknown (-)-steganacin and (-)-steganone 7-aza analogues containing a 1,2,3-triazole ring has been presented. Microwave irradiation was found to be highly beneficial in promoting the Suzuki reaction and the 1,3-dipolar cycloaddition reaction to generate the highly strained medium-sized ring system of the title molecules.     

o-Boundedness of free topological groups

Assuming the absence of Q-points (which is consistent with ZFC) we prove that the free topological group F(X) over a Tychonov space X is o-bounded if and only if every continuous metrizable image T of X satisfies the selection principle fin_?(O,Ω) (the latter means that for every sequence 〈un〉_n∈ω of open covers of T there exists a sequence 〈vn〉_n∈ω such that vn∈[un]^<ω and for every F∈[X]^<ω there exists n∈ω with F⊂?vn). This characterization gives a consistent answer to a problem posed by C. Hernándes, D. Robbie, and M. Tkachenko in 2000.     

Embedding the bicyclic semigroup into countably compact topological semigroups

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that a topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other hand, we construct a (consistent) example of a pseudocompact (countably compact) Tychonoff semigroup containing a copy of C(p,q).     

Universally-Convergent Squared-Operator Iteration Methods for Solitary Waves in General Nonlinear Wave Equations

Three new iteration methods, namely the squared-operator method, the modified squared-operator method, and the power-conserving squared-operator method, for solitary waves in general scalar and vector nonlinear wave equations are proposed. These methods are based on iterating new differential equations whose linearization operators are squares of those for the original equations, together with acceleration techniques. The first two methods keep the propagation constants fixed, while the third method keeps the powers (or other arbitrary functionals) of the solution fixed. It is proved that all these methods are guaranteed to converge to any solitary wave (either ground state or not) as long as the initial condition is sufficiently close to the corresponding exact solution, and the time step in the iteration schemes is below a certain threshold value. Furthermore, these schemes are fast-converging, highly accurate, and easy to implement. If the solitary wave exists only at isolated propagation constant values, the corresponding squared-operator methods are developed as well. These methods are applied to various solitary wave problems of physical interest, such as higher-gap vortex solitons in the two-dimensional nonlinear Schrödinger equations with periodic potentials, and isolated solitons in Ginzburg–Landau equations, and some new types of solitary wave solutions are obtained. It is also demonstrated that the modified squared-operator method delivers the best performance among the methods proposed in this article.