Activation and Conversion of Molecular Nitrogen to the Precursor of Ammonia on Silicon Substituted Cyclo[18]Carbon: a DFT Design

Recent synthesis of sp-hybridized cyclo[18]carbon allotrope has attracted immense curiosity. Since then, a generous amount of theoretical studies concerning aromaticity, adsorption, and spectra of the molecule have been performed. However, very few stuides have been carried out concerning its reactivities and catalytic behaviour. In this article, a DFT-based inquisition has been reported regarding the reactivity of Si substituted cyclo[18]carbon molecule towards molecular N₂. Results show that the Si substituted derivative is effective in producing adducts with molecular nitrogen. Charge calculations and IRC trapping methods indicate that only the Si center of C₁₇Si and its (HOMO-1) level participate in N₂ addition. The N-adduct so formed, is then found to spontaneously react with molecular H₂. The addition of two H₂ molecules to the activated nitrogen molecule to give respective amine derivatives have also been studied. The successful generation of the precursor of NH₃ by C₁₇Si lays a clear emphasis on its potentiality.     

A Theoretical Perspective to Decipher the Origin of High Hydrogen Storage Capacity in Mn(II) Metal-Organic Framework

Herein, we report a detailed periodic DFT investigation of Mn(II)-based [(Mn₄Cl)₃(BTT)₈]³⁻ (BTT³⁻=1,3,5-benzenetristetrazolate) metal-organic framework (MOF) to explore various hydrogen binding pockets, nature of MOF…H₂ interactions, magnetic coupling and, H₂ uptake capacity. Earlier experiments found an uptake capacity of 6.9 wt % of H_2, with the heat of adsorption estimated to be ∼10 kJ/mol, which is one among the highest for any MOFs reported. Our calculations unveil different binding sites with computed binding energy varying from −6 to −15 kJ/mol. The binding of H₂ at the Mn²⁺ site is found to be the strongest (site I), with H₂ found to bind Mn²⁺ ion in a η² fashion with a distance of 2.27 Å and binding energy of −15.4 kJ/mol. The bonding analysis performed using NBO and AIM reveal a strong donation of σ (H₂) to the d_z² orbital of the Mn²⁺ ion responsible for such large binding energy. The other binding pockets, such as −Cl (site II) and BTT ligands (site III and IV) were found to be weaker, with the binding energy decreasing in the order I>II>III>IV. The average binding energy computed for these four sites put together is 9.6 kJ/mol, which is in excellent agreement with the experimental value of ∼10 kJ/mol. We have expanded our calculations to compute binding energy for multiple sites simultaneously, and in this model, the binding energy per site was found to decrease as we increased the number of H₂ molecules suggesting electronic and steric factors controlling the overall uptake capacity. The calculated adsorption isotherm using the GCMC method reproduces the experimental observations. Further, the magnetic coupling computed for the unbound MOF reveals moderate ferromagnetic and strong antiferromagnetic coupling within the tetrameric {Mn₄} unit leading to a three-up-one-down spin configuration as the ground state. These were then coupled ferromagnetically to other tetrameric units in the MOF network. The magnetic coupling was found to alter only marginally upon gas binding, suggesting that both exchange interaction and the spin-states are unlikely to play a role in the H₂ uptake. This is contrary to the O₂ uptake studied lately, where strong dependence on exchange-coupling/spin state was witnessed, suggesting exchange-coupling/magnetic field dependent binding as a viable route for gas separation.     

A General Strategy Toward pH-Resistant Phenolic Fluorophores for High-Fidelity Sensing and Bioimaging Applications

Aryl alcohol-type or phenolic fluorophores offer diverse opportunities for developing bioimaging agents and fluorescence probes. Due to the inherently acidic hydroxyl functionality, phenolic fluorophores provide pH-dependent emission signals. Therefore, except for developing pH probes, the pH-dependent nature of phenolic fluorophores should be considered in bioimaging applications but has been neglected. Here we show that a simple structural remedy converts conventional phenolic fluorophores into pH-resistant derivatives, which also offer “medium-resistant” emission properties. The structural modification involves a single-step introduction of a hydrogen-bonding acceptor such as morpholine nearby the phenolic hydroxyl group, which also leads to emission bathochromic shift, increased Stokes shift, enhanced photo-stability and stronger emission for several dyes. The strategy greatly expands the current fluorophores’ repertoire for reliable bioimaging applications, as demonstrated here with ratiometric imaging of cells and tissues.     

Integrability of the discretization of the controlled Euler Top

The Euler equations with two controls are discretized by using the bilinear transformation method. The discrete equations are explicit and exhibit a sufficient number of conserved quantities for integrability. The explicit solution to the discrete controlled Euler top are deduced in terms of elliptic functions.     

Invariant Measures and the Soliton Resolution Conjecture

The soliton resolution conjecture for the focusing nonlinear Schrödinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that disperses like a linear solution, plus a localized component that behaves like a soliton or multisoliton solution. Considered to be one of the fundamental open problems in the area of nonlinear dispersive equations, this conjecture has eluded a proof or even a precise formulation to date. This paper proves a “statistical version” of this conjecture at mass‐subcritical nonlinearity, in the following sense: The uniform probability distribution on the set of all functions with a given mass and energy, if such a thing existed, would be a natural invariant measure for the NLS flow and would reflect the long‐term behavior for “generic initial data” with that mass and energy. Unfortunately, such a probability measure does not exist. We circumvent this problem by constructing a sequence of discrete measures that, in principle, approximate this fictitious probability distribution as the grid size goes to 0. We then show that a continuum limit of this sequence of probability measures does exist in a certain sense, and in agreement with the soliton resolution conjecture, the limit measure concentrates on the unique ground state soliton. Combining this with results from ergodic theory, we present a tentative formulation and proof of the soliton resolution conjecture in the discrete setting. The above results, following in the footsteps of a program of studying the long‐term behavior of nonlinear dispersive equations through their natural invariant measures initiated by Lebowitz, Rose, and Speer and carried forward by Bourgain, McKean, Tzvetkov, Oh, and others, are proved using a combination of techniques from large deviations, PDEs, harmonic analysis, and bare‐hands probability theory. It is valid in any dimension. © 2014 Wiley Periodicals, Inc.     

Lag synchronization and scaling of chaotic attractor in coupled system

We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response. The stability of the lag synchronization is ensured by using the Hurwitz matrix stability. We are able to scale up or down the size of a driver attractor at a response system in presence of a lag. This allows compensating the attenuation of the amplitude of a signal during transmission through a delay line. The delay coupling is illustrated with numerical examples of 3D systems, the Hindmarsh-Rose neuron model, the Ro?ssler system, a Sprott system, and a 4D system. We implemented the coupling in electronic circuit to realize any desired lag synchronization in chaotic oscillators and scaling of attractors.     

On certain correspondences among various coupled-cluster theories for closed-shell systems

In this paper certain correspondences have been shown among various formulations of coupled-cluster theories for many electron closed-shell systems. Specifically it is shown that (i) the energy functional using unitary ansatz of the form exp (T−T ⁺) is exactly sameorder by order inT with the size-consistent energy functional 〈ψ|H|ψ〉/〈ψ|ψ〉 recently obtained by us in coupled-cluster framework; (ii) in the framework of unitary ansatz of the form exp (T−T ⁺), both non-variational and variational approaches lead to identical equations upto any given order inT andT ⁺ inT∼T ₂ approximation; (iii) variational procedure using our size-consistent energy functional or using the functional obtained in the framework of unitary ansatz (as envisaged by Kutzelnigg) leads to energy in both cases, inT∼T ₂ approximation, for a total of quadratic powers inT andT ⁺, same as Cizek’s linearised coupled pair many electron theory energy; (iv) in case of practical calculation of the energy through the variational procedures using our size-consistent energy functional and the functional in unitary ansatz framework, there is a loss of upper bound.