Deflection of light by black holes and massless wormholes in massive gravity

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov, JHEP 0904:100, 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass M and an extra parameter S namely ‘scalar charge’. These black hole reduce to the standard Schwarzschild black hole solutions when the scalar charge is zero and the mass is positive. In addition, a parameter \(\lambda \) in the metric characterizes so-called ‘hair’. The geodesic equations are used to examine the behavior of the deflection angle in four relevant cases of the parameter \(\lambda \). Then, by introducing a simple coordinate transformation \(r^\lambda =S+v^2\) into the black hole metric, we were able to find a massless wormhole solution of Einstein–Rosen (ER) (Einstein and Rosen, Phys Rev 43:73, 1935) type with scalar charge S. The programme is then repeated in terms of the Gauss–Bonnet theorem in the weak field limit after a method is established to deal with the angle of deflection using different domains of integration depending on the parameter \(\lambda \). In particular, we have found new analytical results corresponding to four special cases which generalize the well known deflection angles reported in the literature. Finally, we have established the time delay problem in the spacetime of black holes and wormholes, respectively.     

Microstructural characterization of ultrafine-grain interstitial-free steel by X-ray diffraction line profile analysis

This paper highlights the microstructural features of commercially available interstitial free (IF) steel specimens deformed by equal channel angular pressing (ECAP) up to four passes following the route A. The microstructure of the samples was studied by different techniques of X-ray diffraction peak profile analysis as a function of strain (ε). It was found that the crystallite size is reduced substantially already at ε=2.3 and it does not change significantly during further deformation. At the same time, the dislocation density increases gradually up to ε=4.6. The dislocation densities estimated from X-ray diffraction study are found to correlate very well with the experimentally obtained yield strength of the samples.     

Stereoelectronic and dynamical effects dictate nitrogen inversion during valence isomerism in benzene imine

Benzene imine (1) ⇌ 1H-azepine (2) isomerization occurs through sequential valence and endo–exo isomerism. Quantum chemical and quasiclassical trajectory (QCT) simulations reveal the coupled reaction pathway – ring-expansion followed by N-inversion to the most stable isomer, exo-1H-azepine (Exo-2). Direct-dynamics produce a mixture of endo- and exo-1H-azepine stereoisomers and govern the endo-1H-azepine (Endo-2) ⇌ exo-1H-azepine (Exo-2) ratio. Exo-2 is computationally identified as the most stable product while Endo-2 is fleetingly stable with a survival time (S_T) ∼50 fs. N-Methyl substitution exclusively results in an exo-1-methyl-1H-azepine isomer. F-substitution at the N-site increases the barrier for N-inversion and alters the preference by stabilizing Endo-2. Interestingly, the exo-1-fluoro-1H-azepine (minor product) is formed through bifurcation via non-statistical dynamics. A highly concaved Arrhenius plot for 1a → 2a highlights the influence of heavy-atom tunneling on valence isomerism, particularly at low temperatures. Heavy-atom tunneling also results in a normal N–H(D) secondary KIE above 100 K even though the increase in hybridization from sp² to sp³ at nitrogen should cause an inverse KIE classically.

Non-classical processes such as heavy-atom tunneling and post transition-state dynamics govern stereoselectivity for benzene imine ⇌ 1H-azepine.     

Dipolar interactions and hydrogen bonding in supramolecular aggregates: understanding cooperative phenomena for 1st hyperpolarizability

Weak intermolecular forces like dipolar interactions and hydrogen-bonding lead to a variety of different packing arrangements of molecules in crystals and self-assemblies. Such differences in the arrangements change the extent of excitonic splitting and excitation spectra in the multichromophore aggregates. In this tutorial review, the role of such interactions in fine tuning the linear and 1st non-linear optical (NLO) responses in molecular aggregates are discussed. The non-additivity of these optical properties arise specifically due to such cooperative interactions. Calculations performed on dimers, trimers and higher aggregates for model systems provide insights into the interaction mechanisms and strategies to enhance the 1st hyperpolarizabilities of pi-conjugated molecular assemblies. Flexible dipole orientations in the alkane bridged chromophores show odd-even variations in their second-harmonic responses that are explained through their dipolar interactions in different conformations. Parameters for the optical applications of molecules arranged in constrained geometry, like in Calix[n]arene, have been elucidated. We also highlight the recent developments in this field of research together with their future prospects.     

Conformational preference in heteroatomic analogues of ethane, H3X-YH3 (X = B, Al; Y = N, P): implications of charge transfer

Quantum chemical conformational analysis for electron donor-acceptor (EDA) systems, H3B-NH3, H3B-PH3, H3Al-NH3 and H3Al-PH3, has been performed. For H3B-NH3 and H3B-PH3, the rotational barrier is found to be invariant with an increase in the central bond (X-Y) length. For H3Al-NH3 and H3Al-PH3, however, the rotational barrier increases with an increase in the central bond length. Decomposition of the total energy into various components and their contributions to the frontier orbitals (HOMO, HOMO-1, HOMO-2 and HOMO-3) have been analyzed in detail to explain the origin of such anomalous changes in the rotational barrier. Charge transfer and favorable "back bonding" are found to be the crucial factors governing the variations in the rotational barrier for such systems.     

Competing magnetic interactions in a dinuclear Ni(II) complex: antiferromagnetic O-H...O moiety and ferromagnetic N3- ligand

Synthesis, structural characteristics, magnetic studies and DFT calculations in Ni(II) dinuclear complexes containing two bridging N3- and an O-H...O linkage reveal the existence of ferromagnetic interactions between Ni(II) centers via N3- ligands and antiferromagnetic interactions through the H-bonded moiety. The overall magnetic behavior of the system depends on the delicate balance between these two competing interactions.     

Metal‐Free Reduction of CO2 to Methoxyborane under Ambient Conditions through Borondiformate Formation

An abnormal N‐heterocyclic carbene (aNHC) based homogeneous catalyst has been used for the reduction of carbon dioxide to methoxyborane in the presence of a range of hydroboranes under ambient conditions and resulted in the highest turnover number of 6000. A catalytically active reaction intermediate, [aNHC‐H?9BBN(OCOH)₂] was structurally characterized and authenticated by NMR spectroscopy. A detailed mechanistic cycle of this catalytic process via borondiformate formation has been proposed from tandem experimental and computational experiments.