The rotation‐vibration spectrum of diatomic molecules with the tietz‐hua rotating oscillator

The Tietz‐Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov‐Uvarov method, we have obtained the exact analytical s‐wave solutions of the radial Schrödinger equation for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Zur Benennung von Verbindungen im Si‐Al‐O‐N‐System

Die Übersetzung basiert auf der „Terminology for Compounds in the Si‐Al‐O‐N System“ der Commission on High Temperature Materials and Solid State Chemistry der Inorganic Chemistry Division der International Union of Pure and Applied Chemistry, veröffentlicht in Pure Appl. Chem. 1999 , 71, 1765–1769. Das Original wurde von R. Metselaar, Technische Universiteit Eindhoven (Niederlande) und D. S. Yan, Academia Sinica, Shanghai (China) für die Veröffentlichung vorbereitet.     

Aggregation‐Induced‐Emission‐Active Macrocycle Exhibiting Analogous Triply and Singly Twisted Möbius Topologies

Molecules with Möbius topology have drawn increasing attention from scientists in a variety of fields, such as organic chemistry, inorganic chemistry, and material science. However, synthetic difficulties and the lack of functionality impede their fundamental understanding and practical applications. Here, we report the facile synthesis of an aggregation‐induced‐emission (AIE)‐active macrocycle (TPE‐ET) and investigate its analogous triply and singly twisted Möbius topologies. Because of the twisted and flexible nature of the tetraphenylethene units, the macrocycle adjusts its conformations so as to accommodate different guest molecules in its crystals. Moreover, theoretical studies including topological and electronic calculations reveal the energetically favorable interconversion process between triply and singly twisted topologies.     

Exact solution of multidimensional hyper‐radial Schrödinger equation for many‐electron quantum systems

In quantum theory, solving Schrödinger equation analytically for larger atomic and molecular systems with cluster of electrons and nuclei persists to be a tortuous challenge. Here, we consider, Schrödinger equation in arbitrary N‐dimensional space corresponding to inverse‐power law potential function originating from a multitude of interactions participating in a many‐electron quantum system for exact solution within the framework of Frobenius method via the formulation of an ansatz to the hyper‐radial wave function. Analytical expressions for energy spectra, and hyper‐radial wave functions in terms of known coefficients of inverse‐power potential function, and wave function parameters have been obtained. A generalized two‐term recurrence relation for power series expansion coefficients has been established. © 2016 Wiley Periodicals, Inc.     

An alternative to the “Star Path” enhancement of the ADMA linear scaling method for protein modeling

With the aim of improving the performance of macromolecular quantum chemistry conformation analysis and reaction path following methods, the Adjustable Density Matrix Assembler (ADMA) method has already been combined with some faster although less accurate density matrix extrapolation methods, such as the Löwdin‐Inverse‐Löwdin (LIL) extrapolation along a potential energy surface, and a strategically arranged back‐and‐forth switching between these methods has been proven to be advantageous. Here, an alternative approach is proposed and investigated, based on several actual test calculations, where the “inexpensive” LIL density matrix extrapolation steps are replaced by only somewhat more expensive, but still ADMA‐based calculations, where in the “rough‐search stage,” only interactions of shorter distances within the macromolecule are considered. It is shown that this approach is viable, as an alternative to the “Star Path” method including both ADMA and LIL steps. © 2017 Wiley Periodicals, Inc.     

Application of Löwdin's canonical orthogonalization method to the Slater‐type orbital configuration‐interaction basis set

We apply Löwdin's canonical orthogonalization method to investigate the linearly dependent problem arising from the variational calculation of atomic systems using Slater‐type orbital configuration‐interaction (STO‐CI) basis functions. With a specific arithmetic precision used in numerical computations, the nonorthogonal STO‐CI basis is easily linearly dependent when the number of basis functions is sufficiently large. We show that Löwdin's canonical orthogonalization method can successfully overcome such problem and simultaneously reduce the dimension of basis set. This is illustrated first through an S‐wave model He atom, and then the real two‐electron atoms in both the ground and excited states. In all of these calculations, the variational bound state energies of the two‐electron systems are obtained in reasonably high accuracy using over‐redundant STO‐CI bases, however, without using extended high‐precision technique. © 2015 Wiley Periodicals, Inc.     

Bright,Highly Water‐Soluble Triazacyclononane Europium Complexes To Detect Ligand Binding with Time‐Resolved FRET Microscopy

Luminescent europium complexes are used in a broad range of applications as a result of their particular emissive properties. The synthesis and application of bright, highly water‐soluble, and negatively charged sulfonic‐ or carboxylic acid derivatives of para‐substituted aryl–alkynyl triazacyclononane complexes are described. Introduction of the charged solubilizing moieties suppresses cellular uptake or adsorption to living cells making them applicable for labeling and performing assays on membrane receptors. These europium complexes are applied to monitor fluorescent ligand binding on cell‐surface proteins with time‐resolved Förster resonance energy transfer (TR‐FRET) assays in plate‐based format and using TR‐FRET microscopy.     

Bound state solutions of D‐dimensional schrödinger equation with exponential‐type potentials

In this article, using an exactly‐solvable multiparameter exponential‐type potential we propose a unified treatment of the analytical bound—state solutions of the Schrödinger equation for exponential‐type potentials in D‐dimensions. Our proposal accepts different approximations to the centrifugal term; however, its usefulness is exemplified in the frame of the Green and Aldrich approach. This fact enables us to compare our results with specific potentials found in the literature and that are obtained here as particular cases of our proposal. That is, instead of solving a specific exponential‐type potential, by resorting each time to a specialized method, the energy spectra and wavefunctions are derived straightforward from the proposed approach. Furthermore, our proposal can be used as an alternative way in the search of solutions to new exponential‐type potentials besides that one can study different approximations to the term . © 2014 Wiley Periodicals, Inc.     

The Rayleigh‐Schrödinger perturbation series of quasi‐degenerate systems

We describe the first representation of the general term of the Rayleigh‐Schrödinger series for quasidegenerate systems. Each term of the series is represented by a tree and there is a straightforward relation between the tree and the analytical expression of the corresponding term. The combinatorial and graphical techniques used in the proof of the series expansion allow us to derive various resummation formulas of the series. A relation with several combinatorial objects used for special cases (degenerate or non‐degenerate systems) is established. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

X‐Ray Diffraction and Mössbauer Spectroscopy Studies of Pressure‐Induced Phase Transitions in a Mixed‐Valence Trinuclear Iron Complex

The mixed‐valence complex Fe₃O(cyanoacetate)₆(H₂O)₃ ( 1 ) has been studied by single‐crystal X‐ray diffraction analysis at pressures up to 5.3(1) GPa and by (synchrotron) Mössbauer spectroscopy at pressures up to 8(1) GPa. Crystal structure refinements were possible up to 4.0(1) GPa. In this pressure range, 1 undergoes two pressure‐induced phase transitions. The first phase transition at around 3 GPa is isosymmetric and involves a 60° rotation of 50 % of the cyanoacetate ligands. The second phase transition at around 4 GPa reduces the symmetry from rhombohedral to triclinic. Mössbauer spectra show that the complex becomes partially valence‐trapped after the second phase transition. This sluggish pressure‐induced valence‐trapping is in contrast to the very abrupt valence‐trapping observed when compound 1 is cooled from 130 to 120 K at ambient pressure.     

Supported dual‐acidic 1,3‐disulfoimidazolium chlorozincate@HZSM‐5 as a promising heterogeneous catalyst for synthesis of indole derivatives

HZSM‐5‐supported Brönsted and Lewis acidic ionic solid 1,3‐disulfoimidazolium chlorozincate materials ([dsim]₂[ZnCl₄]@HZSM‐5) were synthesized with various ratios (3, 6, 9, 17 and 50% w/w). The heterogeneous materials were characterized via a variety of spectroscopic techniques. Dual acidity of these materials was determined using specified techniques. These acidic solids were examined as stable heterogeneous catalysts for the Fischer indole reaction of equimolar amounts of phenylhydrazine hydrochloride and various aliphatic or aromatic ketones at 80–90°C in neat condition to produce substituted indole derivatives. The efficient 17% ionic salt‐loaded HZSM‐5 composite was easily reused for ten consecutive cycles with a slight loss of its activity. The recycled catalyst was further analysed using powder X‐ray diffraction and inductively coupled plasma optical emission spectrometric techniques.     

[32]π Fused Core‐Modified Heptaphyrin with Möbius Aromaticity

A new fused core‐modified 32π heptaphyrin with Möbius aromatic character is reported. The ¹H NMR data indicated a weak Möbius aromaticity at 298 K; however, at 213–183 K, the molecule predominates [4n]π Möbius conformation with strong diatropic ring current, which was further confirmed by X‐ray analysis. The protonation experiment led to preservation of the Möbius aromaticity at 298 K. Nevertheless, the experimental results were further supported by theoretical studies. Overall, this study represents the first example of Möbius aromatic fused core‐modified expanded porphyrin.     

Transparent,Ultrahigh‐Gas‐Barrier Films with a Brick–Mortar–Sand Structure

Transparent and flexible gas‐barrier materials have shown broad applications in electronics, food, and pharmaceutical preservation. Herein, we report ultrahigh‐gas‐barrier films with a brick–mortar–sand structure fabricated by layer‐by‐layer (LBL) assembly of XAl‐layered double hydroxide (LDH, X=Mg, Ni, Zn, Co) nanoplatelets and polyacrylic acid (PAA) followed by CO₂ infilling, denoted as (XAl‐LDH/PAA)_n‐CO₂. The near‐perfectly parallel orientation of the LDH “brick” creates a long diffusion length to hinder the transmission of gas molecules in the PAA “mortar”. Most significantly, both the experimental studies and theoretical simulations reveal that the chemically adsorbed CO₂ acts like “sand” to fill the free volume at the organic–inorganic interface, which further depresses the diffusion of permeating gas. The strategy presented here provides a new insight into the perception of barrier mechanism, and the (XAl‐LDH/PAA)_n‐CO₂ film is among the best gas barrier films ever reported.     

Probing the relationship between spin contamination and first hyperpolarizability: Open‐shell Möbius anion

Möbius strip has attracted extensive interest due to its one‐side structure, special physical and chemical properties. A new extended porphyrin with Möbius structure has been synthesized (St?pień et al., Angew. Chem. Int. Ed. 2007, 46, 7869). In this work, an electron is injected into Möbius to form Möbius anion. For Möbius, four methods (B3LYP, BHandHLYP, CAM‐B3LYP, and LC‐BLYP) obtain the similar first hyperpolarizability (β₀). However, for Möbius anion, four methods obtain very different β₀ values (ranging from 9.85 × 10³ to 8.33 × 10⁵ au). Moreover, the β₀ values of Möbius anion are larger than those of Möbius. Why? The considerable variation (ranging from 0.8162 to 1.7630) of spin contamination (S²) of open‐shell Möbius anion captures our attention. To probe the relationship between S² and β₀, the β₀ values of Möbius anion were calculated using 23 methods. Interestingly, the Hartree‐Fock (HF) composition increases from 0 to 50, the S² value ranges from 0.7522 to 1.3372, and the β₀ value increases from 4.3 × 10³ to 7.36 × 10⁴ au. Further, methods are “dissected” to investigate the effect of HF composition on the S². © 2014 Wiley Periodicals, Inc.     

Air‐Free Synthesis of a Ferrous Metal‐Organic Framework Featuring HKUST‐1 Structure and its Mössbauer Spectrum

Single crystals of the Fe^II metal‐organic framework (MOF) with 1,3,5‐benzenetricarboxylate (BTC) as a linker were solvothermally obtained under air‐free conditions. X‐ray diffraction analysis of the crystals demonstrated a structure for Fe^II‐MOF analogous to that of [Cu₃(BTC)₂] (HKUST‐1). Unlike HKUST‐1, however, the Fe^II‐MOF did not retain permanent porosity after exchange of guest molecules. The Mössbauer spectrum of the Fe^II‐MOF was recorded at 80 K in zero field yielding an apparent quadrupole splitting of ΔE_Q = 2.43 mm · s^–1, and an isomer shift of δ = 1.20 mm · s^–1, consistent with high‐spin central iron(II) atoms. Air exposure of the Fe^II‐MOF was found to result in oxidation of the metal atoms to afford Fe^III. These results demonstrate that Fe^II‐based MOFs can be prepared in similar fashion to the [Cu₃(BTC)₂], but that they lack permanent porosity when degassed.     

Flexible Viologen‐Based Porous Framework Showing X‐ray Induced Photochromism with Single‐Crystal‐to‐Single‐Crystal Transformation

A viologen‐based Borromean entangled porous framework was found to be sensitive to both Cu_Kα and Mo_Kα X‐ray sources, showing rapid photochromic response and recovery within one minute. The X‐ray‐induced photochromic process is accompanied by a reversible single‐crystal‐to‐single‐crystal (SC‐SC) structural transformation, an unprecedented phenomenon for X‐ray sensitive materials. The complex can be further processed into portable thin films for detecting the dose of the X‐ray exposure. Moreover, the photochromism can occur over a broad temperature range of 100–333 K, both in the form of single crystals and thin films, making it a potential candidate for practical indoor and outdoor applications.     

A New pH Indicator Based on 2,5‐Diaryl‐1‐salicylideneamino‐1,3,4‐triazole Derivative

2‐Phenyl‐5‐p‐tolyl‐1‐salicylideneamino‐1,3,4‐triazole (PTST) was studied among 2,5‐diaryl‐1‐salicylidene amino‐1,3,4‐triazole derivatives as a novel potential pH indicator. In terms of absorption intensity coming from the acid‐base reactions, PTST showed strong yellow‐green colour with high extinction coefficient in the pH range 7.0–9.5. In addition, the corresponding colour development at the transition point can be attributed to the resonance structures of PTST, which were caused by the hydrogen ion dissociation from the acidic form of the compound in the presence of alkali. The full geometric optimization and achievement of the electronic structure of the molecule were performed by an AM1 semiempirical method. The triazole compound was compared with phenolphthalein (PT), which is widely used as an acid‐base indicator in titrimetry, for accuracy test.     

Applications of automatic differentiation to the time‐dependent Schrödinger equation

A new approach based upon the Taylor series method is proposed for propagating solutions of the time‐dependent Schrödinger equation. Replacing the spatial derivative of the wave function with finite difference formulas, we derive a recursive formula for the evaluation of Taylor coefficients. The automatic differentiation technique is used to recursively calculate the required Taylor coefficients. We also develop an implicit scheme for the recursive evaluation of these coefficients. We then advance the solution in time using a Taylor series expansion. Excellent computational results are obtained when this method is applied to a one‐dimensional reflectionless potential and a two‐dimensional barrier transmission problem. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Scattering state of the multiparameter potential with an improved approximation for the centrifugal term in D‐dimensions

Recently, multi‐parameter potential has been introduced and had been discussed as special cases of other potential model, that is why we are interested to the study of such a potential. In order to study this potential, the D‐dimensional Schrödinger has been presented in detail and the scattering state with any arbitrary J‐state due to this potential has been investigated approximately. After this step, we have discussed analytically the scattering and bound state for some special cases in D‐dimensional situations which play important roles in physics. © 2015 Wiley Periodicals, Inc.