Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Double degeneration on second-order breather solutions of Maxwell–Bloch equation

The breather solutions of the Maxwell–Bloch equations in a two-level resonant system associated with the self-induced transparency phenomenon are constructed by the Darboux transformation. After constructing the formulas of the second-order breather solutions, the double degeneration and hybrid solutions are studied by the analytical form as well as figures. Our results might be helpful in such application or prevention of the rogue waves from breather solution interactions and degeneration in the nonlinear optical systems associated with the Maxwell–Bloch equations.     

X-ray diffraction study of mesogenic 4-methoxyphenyl-4′-n-nonyloxybenzoate

4-methoxyphenyl-4′-n-nonyloxybenzoate have been investigated by single crystal X-ray structural analysis. Crystal packing of the compounds does not represent a precursor of the mesophse although the typical for liquid crystal compounds separation of crystal packing on aromatic and aliphatic areas is observed here. Possible reason for monotropic properties are discussed.     

Domain-based local pair natural orbital methods within the correlation consistent composite approach

Ab initio composite approaches have been utilized to model and predict main group thermochemistry within 1 kcal mol⁻¹, on average, from well-established reliable experiments, primarily for molecules with less than 30 atoms. For molecules of increasing size and complexity, such as biomolecular complexes, composite methodologies have been limited in their application. Therefore, the domain-based local pair natural orbital (DLPNO) methods have been implemented within the correlation consistent composite approach (ccCA) framework, namely DLPNO-ccCA, to reduce the computational cost (disk space, CPU (central processing unit) time, memory) and predict energetic properties such as enthalpies of formation, noncovalent interactions, and conformation energies for organic biomolecular complexes including one of the largest molecules examined via composite strategies, within 1 kcal mol⁻¹, after calibration with 119 molecules and a set of linear alkanes. © 2019 Wiley Periodicals, Inc.     

Reversible Shape‐Morphing and Fluorescence‐Switching in Supramolecular Nanomaterials Consisting of Amphiphilic Cyanostilbene and Cucurbit[7]uril

We demonstrate a reversible shape‐morphing with concurrent fluorescence switching in the nanomaterials which are complexed with cucurbit[7]uril (CB[7]) in water. The cyanostilbene derivative alone forms ribbon‐like two‐dimensional (2D) nanocrystals with bright yellow excimeric emission in water (λ_em=540 nm, Φ_F=42 %). Upon CB[7] addition, however, the ribbon‐like 2D nanocrystals immediately transform to spherical nanoparticles with significant fluorescence quenching and blue‐shifting (λ_em=490 nm, Φ_F=1 %) through the supramolecular complexation of the cyanostilbene and CB[7]. Based on this reversible fluorescence switching and shape morphing, we could demonstrate a novel strategy of turn‐on fluorescence sensing of spermine and also monitoring of lysine decarboxylase activity.     

Ring-Stacking Water Clusters: Morphology and Stabilities

The structures and interaction energies of water clusters with ring stacking motifs are studied by using ab initio calculations. The structures of the water clusters are constructed by stacking either single rings or multi-rings of tetramer, pentamer, and hexamer. We found that, in the single-ring-stacking motif, the most stable isomers exhibit an alternative clockwise-anticlockwise stacking pattern. We also show that four-layer single-ring-stacking isomers are not energetically favorable in comparison with those of two-layer multi-ring-stacking isomers. The relative stability of the isomers is also analyzed in terms of H-bond strength and elastic distortions of the water molecules.     

Validating additive correction schemes against gradient-based extrapolations

The use of additive correction schemes to obtain structures and vibrational frequencies of increasingly larger molecules is becoming more common. Such approaches, based on the cubic extrapolation formula applied directly to the quantity of interest, have been successfully validated only at the highest levels of computational accuracy: for coupled cluster methods with comparably large basis sets. Here, a systematic validation of geometries and vibrational frequencies is carried out, including more affordable and relevant levels of theory, such as the Møller-Plesset perturbation theory applied with smaller basis sets. Comparisons of such additive schemes against the more rigorous gradient-based extrapolation are presented. The cbs () routine of the open-source quantum-chemistry package Psi4 has been extended for this purpose. The results confirm that geometries and frequencies of covalently bound species obtained with additive correction schemes are in an excellent agreement with the results of gradient-based extrapolations. However, when applied to systems involving noncovalent interactions, the errors due to such schemes are significantly larger. In general, we propose the application of gradient-based extrapolations, as they incur no extra cost compared to additive schemes.     

Interactions between vortex and magnetic rings at high kinetic and magnetic Reynolds numbers

Interactions between magnetic and vortex rings are studied over a wide interval of interaction parameter values ranging from negligible magnetic effects on vorticity structure, to very strong effects. The employed interaction parameter measures the strength of the Lorentz force in units of the inertial force. At small interaction parameters, the vortex ring shapes part of the magnetic ring into a dissipative, curved, magnetic sheet structure. At high interaction parameters, the Lorentz force acts as an agent of proliferation of vortex rings, since it generates two vortex rings adjacent to the original magnetic structure, one of which is pulled (together with the advected magnetic field) into the wake of the original vortex ring, while the other escapes, ready to interact with another magnetic ring. Once within the initial vortex ring wake, both magnetic and vorticity structures are stretched into spirals, whilst the Lorentz force continuously generates new, intense vorticity at high magnetic field sites.     

Modeling halogen bonding with planewave density functional theory: Accuracy and challenges

Inspired by the recent interest of halogen bonding (XB) in the solid state, we detail a comprehensive benchmark study of planewave DFT geometry and interaction energy of lone-pair (LP) type and aromatic (AR) type halogen bonded complexes, using PAW and USPP pseudopotentials. For LP-type XB dimers, PBE-PAW generally agrees with PBE/aug-cc-pVQZ(−pp) geometries but significantly overbinds compared to CCSD(T)/aug-cc-pVQZ(-pp). Grimme's D3 dispersion corrections to PBE-PAW gives better agreement to the MP2/cc-pVTZ(-pp) results for AR-type dimers. For interaction energies, PBE-PAW may overbind or underbind for weaker XBs but clearly overbinds for stronger XBs. D3 dispersion corrections exacerbate the overbinding problem for LP-type complexes but significantly improves agreement for AR-type complexes compared to CCSD(T)/CBS. Finally, for periodic XB crystals, planewave PBE methods slightly underestimate the XB lengths by 0.03 to 0.05 Å. © 2019 Wiley Periodicals, Inc.