Proper quantization rule approach to three‐dimensional quantum dots

In this article, we develop a formalism to obtain the energy levels of the electron in a central force potential confined in a spherical quantum dot with radius r_C by the proper quantization rule and the Wentzel‐Kramers‐Brillouin approximation. It is shown that the numerical results are in good agreement with exact solutions. To illustrate this method, we consider the linear harmonic oscillator and Coulomb potential confined within an impenetrable sphere of radius r_C in three dimensions. © 2013 Wiley Periodicals, Inc.     

Low pressure vapor–liquid equilibrium in ethanol + congener mixtures using the Wong–Sandler mixing rule

Phase equilibrium in binary ethanol mixtures found in alcoholic beverage production has been analyzed using a cubic equation of state (EoS) and suitable mixing and combining rules. The main objective of the study is the accurate modeling of the congener concentration in the vapor phase (substances different from ethanol), considered to be an important enological parameter in the alcohol industry. The Peng–Robinson (PR) equation of state has been used and the Wong–Sandler (WS) mixing rules, that include a model for the excess Gibbs free energy, have been incorporated into the equation of state constants. In the Wong–Sandler mixing rules the van Laar (VL) model for the excess Gibbs energy has been used. This combination of equations of state, mixing rules and combining rules are commonly applied to high pressure phase equilibrium and have not yet been treated in a systematic way to complex low pressure ethanol mixtures as done in this work. Nine binary ethanol + congener mixtures have been considered for analysis. Comparison with available literature data is done and the accuracy of the calculations is discussed, concluding that the model used is accurate enough for engineering applications.     

Restricted and unrestricted Hartree–Fock approaches applied to spherical quantum dots in a magnetic field

The Roothaan and Pople–Nesbet approaches for real atoms are adapted to quantum dots in the presence of a magnetic field. Single‐particle Gaussian basis sets are constructed, for each dot radius, under the condition of maximum overlap with the exact functions. The chemical potential, charging energy, and total spin expected values are calculated, and we have verified the validity of the quantum dot energy shell structure as well as Hund's rule for electronic occupation at zero magnetic field. At finite field, we have observed the violation of Hund's rule and studied the influence of magnetic field on the closed and open energy shell configurations. We have also compared the present results with those obtained within the LS‐coupling scheme for low electronic occupation numbers. We focus only on ground‐state properties and consider quantum dots populated up to 40 electrons, constructed by GaAs or InSb nanocrystals. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Palladium–cadmium sulfide nanopowder at oil–water interface as an effective catalyst for Suzuki–Miyaura reactions

A simple and effective strategy is described for the synthesis of Pd–CdS nanopowder by the reduction of an organopalladium(II) complex, [PdCl₂(cod)] (cod = cis ,cis ‐1,5‐cyclooctadiene), in the presence of CdS quantum dots (QDs) at a toluene–water interface. We investigated the impact of addition of CdS QDs on catalytic activity of Pd nanoparticles (NPs). The Pd–CdS nanopowder functions as an efficient catalyst for Suzuki–Miyaura reactions for the formation of carbon–carbon bonds. There is a high electron density on Pd NPs and due to their high electron affinity they behave as an electron scavenger from CdS increasing the rate of oxidative addition, which is the rate‐determining step of the catalytic cycle, and, just as we expect, the C─C coupling reaction with the Pd–CdS nanopowder is faster and occurs in less time than that with Pd nanocatalysts. Compared to classical reactions, this method consistently has the advantages of short reaction times, high yields in a green solvent, reusability of the catalyst without considerable loss of catalytic activity and low cost, and is a facile method for the preparation of the catalyst.     

The infrared-driven cis–trans isomerization of nitrous acid HONO III: A mixed quantum–classical simulation

A mixed quantum–classical simulation of the IR-driven cis–trans isomerization of HONO in a Kr matrix at 30 K is presented, treating the hydrogen atom as quantum particle and the Kr matrix as well as intermolecular degrees of freedom of the ONO-body as classical. A new method is presented to time-propagate the coupled set of equations in a DVR basis in internal spherical coordinates, rather than in laboratory frame fixed cartesian coordinates. In spherical coordinates, a much more precise computation of the weak vibrational couplings is possible using a still manageable basis size. Good qualitative agreement between simulation and experiment is obtained, underestimating relaxation and isomerization rates by a modest factor ≈5. Upon matrix fluctuations, frequent curve crossings occur between the initially excited OH-stretch vibration and a closely lying combination mode of torsional and bending coordinate that lead to a transfer of population. The subsequent pathway of energy flow is deduced and discussed within a tier model, where trans-states, that belong to the second tier, are populated through a first tier of states that is composed of combinations of bending and torsional excitations. No specific energy pathway is revealed that would funnel the hydrogen atom directly towards the trans-side, hence the experimentally observed high cis → trans quantum yield of close to one probably has to be explained in a statistical scenario on a timescale much longer than that of the present simulation.     

Potential‐Energy Surfaces,the Born–Oppenheimer Approximations,and the Franck–Condon Principle: Back to the Roots

The concept of a potential‐energy surface (PES) is central to our understanding of spectroscopy, photochemistry, and chemical kinetics. However, the terminology used in connection with the basic approximations is variously, and somewhat confusingly, represented with such phrases as “adiabatic”, “Born–Oppenheimer”, or “Born–Oppenheimer adiabatic” approximation. Concerning the closely relevant and important Franck–Condon principle (FCP), the IUPAC definition differentiates between a classical and quantum mechanical formulation. Consequently, in many publications we find terms such as “Franck–Condon (excited) state”, or a vertical transition to the “Franck–Condon point” with the “Franck–Condon geometry” that relaxes to the excited‐state equilibrium geometry. The Born–Oppenheimer approximation and the “classical” model of the Franck–Condon principle are typical examples of misused terms and lax interpretations of the original theories. In this essay, we revisit the original publications of pioneers of the PES concept and the FCP to help stimulate a lively discussion and clearer thinking around these important concepts.     

Formulation of unrestricted and restricted Hartree–Fock–Bogoliubov equations

The Hartree–Fock–Bogoliubov (HFB) method, dealing with Bogoliubov orbitals, which consist of particle and hole part, can provide states with pair correlations associated with Cooper pairs. The dimension of HFB Fock matrices can be reduced by restrictions of spin states of Bogoliubov orbitals similarly to ordinary Hartree–Fock (HF) equations such as restricted HF (RHF), unrestricted HF (UHF), and generalized HF (GHF). However, there are few studies of moderate restricted HFB equations such as UHF‐based HFB equations. In this article, formulation and calculations of restricted HFB equations are described. The solutions of general and restricted HFB equations are compared. Pair correlations taking account of restricted and general HFB equations are discussed. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Spectroscopical UV–Vis implications of an intramolecular η2–Mg coordination in bacteriochlorophyll–a from the Fenna–Matthews–Olson complex

Chlorophylls and their related compounds prominently feature a Mg²⁺ ion in the center of a porphyrine, with an intermolecular fifth coordination usually observed to place the ion out of the macrocyclic plane. Herein, we assess the role of a potential intramolecular η²–(C = C)Mg interaction and compare it to the intermolecular coordination from the Hystidine groupt to Mg²⁺ for Bacterichlorophyll–a (Bchl–a), the main photosynthetic pigment in the Fenna–Matthews–Olson complex present in green and purple bacteria. The influence of this fifth coordination on the UV‐Vis spectroscopy (CAM‐B3LYP/cc‐pVDZ), and the concomitant change in geometry around Mg in Bchl–a from planar to pyramidal is assessed by the quantum theory of atoms in molecules based non–covalent interactions scheme and through energetic analysis via natural bond orbital population methods at the M06‐2X/cc‐pVDZ and compared to the reference multi–hapto compound, magnesocene, Cp₂Mg.     

Effect of nitrogen on mechanical,oxidation and structural behaviour of Ti–Si–B–C–N nanocomposite hard coatings deposited by DC sputtering

Ti–Si–B–C–N film was deposited by DC magnetron sputtering at different argon and nitrogen ratios such as N₂/Ar = 1 : 5, 2 : 4, 3 : 3, 4 : 1 and 5 : 0. The formation of TiN and TiB phases was observed because of incorporation of nitrogen. The hardness, modulus, microstructure, structure and bond formation with different nitrogen contents during the deposition were studied by nanoindentation, scanning electron microscope, X‐ray diffraction and X‐ray photoelectron spectroscopy, respectively. The oxidation kinetics of Ti–Si–B–C–N was investigated. The nitrogen incorporation during deposition influences different properties of the coating. Hardness and modulus decreased, and microstructure showed very fine grain presence, and film changes to fully amorphous because of incorporation of nitrogen in the film. Copyright © 2016 John Wiley & Sons, Ltd.     

Using the UPLC–ESI–Q‐TOF–MSE method and intestinal bacteria for metabolite identification in the nonpolysaccharide fraction from Bletilla striata

Bletilla striata (Thunb.) Reichb. f. (Orchidaceae), also known as Bai‐ji, is a traditional Chinese herb that is widely used in Asia to treat hematemesis, hemoptysis, traumatic bleeding and other similar disorders. Most studies have focused on the pharmacological activities of polysaccharide extracts from B. striata. Our previous studies found that the nonpolysaccharide fraction from B. striata extract also has a hemostatic effect; however, the active constituents responsible for this pharmacological action are unclear. Thus, the metabolic profiles of the nonpolysaccharide fraction were investigated in Sprague–Dawley rats and intestinal bacteria models using ultra‐performance liquid chromatography coupled with quadrupole time‐of‐flight tandem mass spectrometry. Mass data were acquired by the MS^E method. Eight components including five prototypes and three metabolites were identified in rat biofluids after oral administration of the nonpolysaccharide fraction. The parent compounds underwent various metabolic processes, including hydrolysis, deglucosylation, glycosylation and sulfate conjugation. The results not only reveal the possible metabolic pathway, but also indicate the potential pharmacological components. Further mechanistic studies using nonpolysaccharide compounds of the B. striata extract are required to obtain potential candidate compounds.     

Degree of electron–nuclear entanglement in molecular states

The degree of electron–nuclear entanglement in molecular states is analyzed. This entanglement has, generally, two sources: delocalization of the electronic and nuclear wave functions and vibronic coupling. For a diatomic molecular ground‐state with a single potential energy minimum, it is demonstrated that the entanglement is a function of the product of the vibrational energy and the Born–Huang potential energy correction evaluated at the minimum. In the case of a double‐well potential energy surface, the deviation from maximal entanglement is determined by the overlap of the electronic and nuclear wave functions evaluated at and around the two minima. The adiabatic states of the E⊗ϵ Jahn–Teller model are shown to be maximally entangled and a relation between the degree of entanglement and Ham's reduction factor for this model is derived. Numerical calculations in the E⊗ϵ model demonstrate a nontrivial relation between entanglement and vibronic coupling. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 526–533, 2000     

Baeyer–Villiger oxidation of cyclohexanone by molecular oxygen with Fe–Sn–O mixed oxides as catalysts

Fe–Sn–O mixed oxides were synthesized and used as catalysts for Baeyer–Villiger oxidation of cyclohexanone, which showed both high catalytic activity and selectivity. X‐ray powder diffraction and scanning electron microscopy suggested that the Fe–Sn–O catalysts had a tetragonal structure with a grain size of 29.3 nm. An ε‐caprolactone yield as high as 98.8% was obtained in a small‐scale experiment (5 mmol of cyclohexanone). In a scale‐up test (20 mmol of cyclohexanone), the cyclohexanone conversion and ε‐caprolactone yield were 96.7 and 96.5%, respectively. In addition, the catalysts can be reused five times without any major decline in catalytic activity. Copyright © 2015 John Wiley & Sons, Ltd.     

Preparation and characterization of MPEG–PCL diblock copolymers with thermo‐responsive sol–gel–sol phase transition

MPEG–PCL diblock copolymers consisting of methoxy polyethylene glycol (MPEG, 750 g/mol) and poly(?‐caprolactone) (PCL) were synthesized by ring‐opening polymerization. Aqueous solutions of the synthesized diblock copolymers were prepared by dissolving the MPEG–PCL diblock copolymers at concentrations in the range of 0–20 wt %. When the PCL molecular weight was 3000 or greater, the polymer was only partially soluble in water. As the temperature was increased from room temperature, the diblock copolymer solutions showed two phase transitions: a sol‐to‐gel transition and a gel‐to‐sol transition. The sol‐to‐gel phase transition temperature decreased substantially with increasing PCL length. The sol–gel–sol transition with the increase in temperature was confirmed by monitoring the viscosity as a function of temperature. The temperature ranges of the phase transitions measured by the tilting method were in full agreement with those determined from the viscosity measurements. The maximum viscosity of the copolymer solution increased with increasing hydrophobicity of the diblock copolymer and with increasing copolymer concentration. X‐ray diffraction (XRD) and differential scanning calorimetry (DSC) analyses revealed that the diblock copolymers exhibited crystalline domains that favored the formation of an aggregated gel because of the tight aggregation and strong packing interactions between PCL blocks. Scanning electron micrographs of the diblock copolymer solutions in the sol state showed interconnected polyhedral pore structures, whereas those of the gel state revealed a fibrillar‐like morphology. Atomic force microscope (AFM) studies of the sol and gel surfaces showed that the sol surface was covered with fine globular particles, whereas the gel surface was covered with particles in micron‐scale irregular islets. These findings are consistent with uniform mixing of the diblock copolymer and water in the sol state, and aggregation of PCL blocks in the gel state. In conclusion, we confirm that the MPEG–PCL diblock copolymer solution exhibited a sol–gel–sol transition as a function of temperature. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5413–5423, 2006     

On the hydrogen atom beyond the Born–Oppenheimer approximation

Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this article, we comment on the plausibility of simulating atomic systems beyond the Born–Oppenheimer approximation by means of the signed particle formulation of quantum mechanics. First, to show the new perspective offered by this new formalism, we provide an example studying quantum tunnelling through a simple Gaussian barrier in terms of the signed particle formulation. Then, we perform a direct simulation of the hydrogen atom as a full quantum two‐body system, showing that the formalism can be a very promising tool for first‐principle‐only quantum chemistry.