The general setting for the zero‐flux condition: The lagrangian and zero‐flux conditions that give the heisenberg equation of motion

Generalizing our recent work on relativistic generalizations of the quantum theory of atoms in molecules, we present the general setting under which the principle of stationary action for a region leads to open quantum subsystems. The approach presented here is general and works for any Hamiltonian, and when a reasonable Lagrangian is selected, it often leads to the integral of the Laplacian of the electron density on the region vanishing as a necessary condition for the zero‐flux surface. Alternatively, with this method, one can design a Lagrangian that leads to a surface of interest (though this Lagrangian may not be, and indeed probably will not be, “reasonable”). For any reasonable Lagrangian for the electronic wave function and any two‐component method (related by integration by parts to the Hamiltonian) considered, the Bader definition of an atom is recaptured. © 2018 Wiley Periodicals, Inc.     

Revisiting the foundations of the quantum theory of atoms in molecules: The subsystem variational procedure and the finite nuclear models

The role of finite nuclear models (FNMs) is scrutinized within the context of the quantum theory of atoms in molecules (QTAIMs). It is demonstrated that the newly proposed analytic‐algebraic definition of the topological atoms is consistently extendable to the cases where a FNM is employed to construct the molecular hamiltonian. The whole variational procedure is reconsidered, and the insensitivity of final results relative to the employed FNMs is explicitly demonstrated. The analysis once again clearly demonstrates that the analytic‐algebraic condition is an independent axiom that must be added to the subsystem variational procedure to construct the QTAIMs. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Accurate integration over atomic regions bounded by zero‐flux surfaces

The approach for the integration over a region covered by zero‐flux surface is described. This approach based on the surface triangulation technique is efficiently realized in a newly developed program TWOE . The elaborated method is tested on several atomic properties including the source function. TWOE results are compared with those produced by using well‐known existing programs. Absolute errors in computed atomic properties are shown to range usually from 10^?6 to 10^?5 au. The demonstrative examples prove that present realization has perfect convergence of atomic properties with increasing size of angular grid and allows to obtain highly accurate data even in the most difficult cases. It is believed that the developed program can be bridgehead that allows to implement atomic partitioning of any desired molecular property with high accuracy. © 2012 Wiley Periodicals, Inc.     

Revisiting the foundations of the quantum theory of atoms in molecules: Toward a rigorous definition of topological atoms

An explicit classification of consistent variational constraints within the context of the “quantum theory of proper open subsystems” as well as the “quantum theory of atoms in molecules” (QTAIM) it presented. It is demonstrated that the general variational procedure is not sensitive enough to discriminate between different mathematically consistent variational conditions. The uniqueness of the regional kinetic energy is employed to derive the net zero‐flux condition and the regions satisfying this condition are named as quantum divided basins. A modified form of the local zero‐flux is proposed in order to define topological atoms within the context of the orthodox QTAIM. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Chitosan‐modified graphene oxide as a modifier for improving the structure and performance of forward osmosis membranes

Chitosan (CS) with good hydrophilicity and charged property was used to modify graphene oxide (GO), the obtained GO‐CS was used as a novel modifier to fabricate thin film composite forward osmosis (FO) membranes. The results revealed that the amino groups on CS reacted with carboxyl groups on GO, and the lamellar structure of the GO nanosheets was peeled off by CS, resulting in the reducing of their thicknesses. The GO‐CS improved the hydrophilicity of polyethersulfone (PES) substrate, and their contact angles decreased to 64° with the addition of GO‐CS in the substrate. GO‐CS also increased the porosity of the substrate and surface roughness of FO membrane, thereby optimizing the water flux and reverse salt flux of FO membrane. The average water flux of the FO membrane reached the optimal flux of 21.34 L/(m² h) when GO‐CS addition was 0.5 wt%, and further addition of GO‐CS to the substrate would decrease the water flux of FO membrane, and the reverse salt flux also decreased to the lowest value of 2.26 g/(m² h). However, the salt rejection of the membrane increased from 91.4% to 95.1% when GO‐CS addition increased from 0.5 to 1.0 wt% under FO mode using 1 mol/L sodium chloride (NaCl) solution as draw solution (DS). In addition, high osmotic pressure favored water permeation, and at the same concentration of DS, magnesium chloride (MgCl₂) exhibited better properties than NaCl. These results all suggested that GO‐CS was a good modifier to fabricate FO membrane, and MgCl₂ was a good DS candidate.     

Spectrophotometric Methods for the Determination of Acediasulfone in Mixture with Cinchocaine

Abstract

Derivative spectrophotometry techniques (ratio‐spectra first derivative and zero‐crossing first derivative) were described for simultaneous determination of acediasulfone and cinchocaine. Acediasulfone was also determined via the formation of a colored product as a result of its reaction with p‐dimethylaminobenzaldehyde. In the ratio‐spectra first derivative method, the measurements were taken at 310 and 233.9 nm for acediasulfone and cinchocaine, respectively. By the zero‐crossing first derivative method, lines of regression were taken at 318 and 233 nm for acediasulfone and cinchocaine, respectively. In the colorimetric method, absorbance measurements were obtained at 452 nm. Acediasulfone showed linearity over concentration ranges 2–14 µg/ml, 2–16 µg/ml, and 12–60 µg/ml for ratio‐spectra first derivative, zero‐crossing first derivative, and colorimetric methods, whereas cinchocaine showed linearity over concentration ranges 1–10 µg/ml and 2.28–16 µg/ml for ratio‐spectra first derivative and zero‐crossing first derivative techniques. The proposed methods proved to be specific and accurate for the analysis of the cited drugs in laboratory‐prepared mixtures and dosage form. The obtained results agree statistically with those obtained by reference methods.     

Frequently Asked Questions on “Some Fundamental Problems with Zero Flux Partitioning of Electron Densities”

A number of fundamental problems with the topological analysis of molecular electron densities using the atoms in molecules (AIM) theory developed by Bader and coworkers have been highlighted recently. In the present article we provide complements and further details on this topics in the form of a frequently asked questions text.     

Definition of magneto-structural correlations for the MnII ion

The electronic properties of the high spin mononuclear MnII complexes [Mn(tpa)(NCS)2] (1) (tpa=tris-2-picolylamine), [Mn(tBu3-terpy)2](PF6)2 (2) (tBu3-terpy=4,4',4'-tri-tert-butyl-2,2':6',2'-terpyridine) and [Mn(terpy)2](I)2 (3) (terpy=2,2':6',2'-terpyridine) with an N6 coordination sphere have been determined by multifrequency EPR spectroscopy. The X-ray structures of 1.CH3CN and 2.C4H10 O.0.5 C2H5OH.0.5 CH3OH reveal that the MnII ion lies at the center of a distorted octahedron. The D-values of 1-3 all fall in the narrow range of 0.041 to 0.105 cm(-1). The comparison of the results reported here and those found in the literature is consistent with the following observation: the D value is sensitive to the coordination number (6 or 5) of the MnII ion as long as the coordination sphere involves only nitrogen and/or oxygen based ligands. This magneto-structural correlation has been analyzed in this work though DFT model calculations. The zero-field splitting (zfs) parameters of 1-3 have been calculated and are in reasonable agreement with the experimental values. Hypothetical simplified models [Mn(NH3)x(OH2)y]2+ (x+y=5 or 6 and [Mn(NH3)5X]+ (X=OH, Cl)) have been constructed to investigate the origin of the zfs. This investigation reveals i) that D is sensitive to the coordination number (5 or 6) of the MnII ion, ii) for the five coordinate systems the major contribution to D is the spin-orbit coupling part, iii) for the six coordinate systems the major contribution to D is the spin-spin interaction and iv) the deprotonation of a water ligand leads to an increase of D, consistent with the relative ligand fields of OH(-) versus H2O.     

Synthesis of nanoscale zero‐valent iron modified graphene oxide nanosheets and its application for removing tetracycline antibiotic: Response surface methodology

Nowadays, pharmaceutical antibiotics are known as a serious class of pollutants. Therefore, it is important to develop effective methods for removing these pollutants from aqueous media. Different methods were applied for this purpose, and among these methods, chemical reduction by a cheap and eco‐friendly nanocatalyst is the most efficient and simplest method. In this research, based on graphene oxide supported by zero‐valent iron in mono‐, bi‐, and tri‐metallic systems, various nanocomposites were synthesized and used to degrade tetracycline as a model antibiotic from aqueous media. An investigation was carried out on the synergic effect among graphene oxide and the nano zero‐valent iron‐based tri‐metallic system as well as removal efficiencies. It was found that higher degradation efficiency is yielded by graphene oxide supported by Fe/Cu/Ag tri‐metallic system. The maximum synergic effect occurs at an acidic medium. The Brunauer–Emmett–Teller, Fourier transform spectroscopy, scanning electron microscopy‐energy dispersive X‐ray analysis, transmission electron microscopy, and X‐ray diffraction analysis were used to characterize the synthesized nanocomposites, which has successfully proved the loading of nanoscale Fe/Cu/Ag tri‐metallic on a graphene oxide support. The central composite design was used to model and optimize all involved variables affecting antibiotic removal efficiency. The consequences illustrated the optimum condition regarding the removal of 50 ppm of tetracycline, for the nanocomposites dose of 3.0 mg ml^?1, the contact time of 30 min, and pH of 2, was achieved using the simplex non‐linear optimization method. Moreover, antibiotic adsorption kinetic models were also investigated. Finally, the tetracycline removal from aqueous media at different concentrations, 25, 50, and 75 ppm, was successful by applying the proposed nanocomposite, and the results showed tetracycline removal efficiencies of above 70%.     

A computational study of the LiH dimer

A theoretical study of the properties of the linear LiH dimer was undertaken. In this dimer, an unusual type of hydrogen bonding (termed "inverse" hydrogen bonding by some authors), which involves the hydrogen bonded molecule acting as an electron donor (rather than as a proton donor), is exhibited. The optimized geometry, dipole moment, interaction energy, atomic charges, harmonic vibrational frequencies, and frequency shifts for the dimer are computed at the SCF, MP2, and QCISD levels of theory using mainly a 6-31++G(d,p) basis set. We also examined the relative stability of the mono-deuterated isotopomers of linear (LiH)(2), i.e., Li-H...Li-D and Li-D...Li-H. Analysis of the normal vibrational modes, changes in the partial atomic charges, and changes in the vibrational frequencies of LiH on complexation were used to gain insight into the bonding and properties of the linear LiH dimer and its isotopomers.     

Offset‐compensated and zero‐quantum suppressed ROESY provides accurate 1H–1H distances in small to medium‐sized molecules

A robust version of the off‐resonance ROESY pulse scheme is suggested for the measurement of proton–proton distances or slow chemical exchange in small to medium‐sized molecules. The method implements adiabatic ramps to establish a pair of opposite frequency off‐resonance spin lock fields – with optionally randomized duration – and adiabatic inversion pulses with simultaneous gradients for efficient zero‐quantum suppression. The amended pulse sequence yields pure absorption cross‐peaks and works safely for small to medium‐sized molecules. The applicability of the method has been demonstrated using small, rigid molecules (strychnine and codeine) and was also applied for a cyclic peptide and a small protein. We found that the pure phase cross‐peaks of the new ROESY version are beneficial for distance measurements. The one‐dimensional (selective) version of the new method is also powerful for measuring selected pair‐wise interactions and distance determination. Copyright © 2016 John Wiley & Sons, Ltd.     

Transformation of organic molecules on the low-valent [M(Ph(2)PCH(2)CH(2)PPh(2))(2)] moiety derived from trans-[M(N(2))(2)(Ph(2)PCH(2)CH(2)PPh(2))(2)] or related complexes (M = Mo, W)

A zero-valent [M(Ph(2)PCH(2)CH(2)PPh(2))(2)] moiety (M = Mo, W) generated in situ by dissociation of the N(2) ligands in trans-[M(N(2))(2)(Ph(2)PCH(2)CH(2)PPh(2))(2)] can activate pi-accepting organic molecules including isocyanides and nitriles, which undergo the electrophilic attack caused by a strong pi-donation from a zero-valent metal center. Cleavage of a variety of C-X bonds (X = H, C, N, O, P, halogen) also occurs at their electron-rich sites through oxidative addition to form reactive intermediates, which subsequently degradate to yield smaller molecules either bound to or dissociated from the metal center. The mechanism is substantiated unambiguously by isolation of numerous intermediate stages.     

Nonextractive Trace Level Simultaneous Determination of Mercury(II) and Zinc(II) in Environmental Samples with 2‐(5‐Bromo‐2‐pyridylazo)‐5‐diethylaminophenol and Cetylpyridinium Chloride

Abstract

A simple, rapid, selective, and sensitive method for the derivative spectrophotometric determination of Hg(II) and its simultaneous determination in the presence of Zn(II) using 2‐(5‐bromo‐2‐pyridylazo)‐5‐diethylaminophenol in the presence of cetylpyridinium chloride, a cationic surfactant, has been developed. The molar absorption coefficient and analytical sensitivity of the 1∶1 Hg(II) complex at 558 nm (λ_max) are 5.78×10⁴ L mol^?1 cm^?1 and 0.67 ng mL^?1, respectively. The detection limit of Hg(II) is 1.40×10^?2 ng mL^?1, and Beer's law is valid in the concentration range 0.05–2.40 µg mL^?1. Overlapping spectral profiles of Hg(II) and Zn(II) complexes in zero‐order mode interfere in their simultaneous determination. However, 0.10–2.00 µg mL^?1 of Hg(II) and 0.065–0.650 µg mL^?1 of Zn(II), when present together, can be simultaneously determined at zero cross point of the derivative spectrum, without any prior separation. The relative standard deviation for six replicate measurements of solutions containing 0.134 µg mL^?1 of Hg(II) and 0.620 µg mL^?1 of Zn(II) is 1.72 and 1.47%, respectively. The proposed method has successfully been evaluated for trace level simultaneous determination of Hg(II) and Zn(II) in environmental samples.     

Hydrogen‐Bonded Films for Zero‐Order Release of Leuprolide

Leuprolide has been widely used in androgen deprivation therapy for the treatment of advanced prostate cancer, but its use is still limited due to its short half‐life. Herein, hydrogen‐bonded layer‐by‐layer films are fabricated from PEGylated leuprolide (PEG‐LEU) and tannic acid (TA). Because of its dynamic nature, the film disintegrates gradually in water and releases PEG‐LEU and TA. The in vitro release profile indicated perfect zero‐order kinetics, which is explained by the unique release mechanism. When implanted subcutaneously in male rats, the films maintain a constant serum drug level. For a 60‐bilayer film, the serum drug level is maintained constant for ≈24 days. No initial burst release is observed, suggesting that the in vivo release also follows zero‐order kinetics. Initially, an increase in the level of serum testosterone is induced by the released drug, followed by testosterone suppression to a constant level below the castrate level, which could be maintained as long as a constant serum drug level is maintained. Since the new drug carriers avoid an initial burst release of the drug and maintain a constant serum drug level and hence a constant serum testosterone level below the castrate level, these carriers are highly promising for androgen deprivation therapy.     

Efficient One‐Pot Synthesis of 2‐Amino‐4,6‐diarylbenzene‐1,3‐dicarbonitrile under Solvent‐Free Conditions

A facile parallel synthesis of 2‐amino‐4,6‐diarylbenzene‐1,3‐dicarbonitrile derivatives via a one‐pot reaction of aromatic aldehydes, aromatic ketone, and malononitrile under solvent‐free conditions has been developed. This new protocol has the advantages of shorter time, higher yields, lower cost, and environmental friendliness.     

Polyaddition of bifunctional spiro orthoesters with bifunctional acid chlorides accompanying double ring‐opening isomerization

Polyaddition of bifunctional spiro orthoesters (SOEs) with bifunctional acid chlorides was examined to develop zero‐shrinkage polymerization. The polyaddition afforded the corresponding polyether‐esters by repeating the addition reaction accompanying the double ring‐opening isomerization of the SOE moiety in a manner similar to the reaction of monofunctional SOEs with acid chlorides. The polyaddition accompanied a slight shrinkage or expansion in volume. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 68–73, 2000     

Large Zero‐Field Splittings of the Ground Spin State Arising from Antisymmetric Exchange Effects in Heterometallic Triangles

[Ru₂Mn(O)(O₂CtBu)₆(py)₃] has an S=⁵/₂ ground state with a very large zero‐field splitting (ZFS) of D=2.9 cm^?1, as characterized by EPR spectroscopy at 4–330 GHz. This is far too large to be due to the Mn^II ion (D <0.2 cm^?1), as shown from the {Fe₂Mn} analogue, but can be modeled by antisymmetric exchange effects.     

A quantum theory atoms in molecules investigation of Lewis base protonation

This investigation uses atomic properties derived from the quantum theory of atoms in molecules formalism to rationalize the infrared intensity of the stretching vibration that arises as a Lewis base (B) is protonated (B‐H mode). Moreover, the interacting quantum atom (IQA) partition is employed to evaluate the energetics of protonation. All calculations are performed at the CCSD/cc‐pVQZ level except by the IQA analysis, which is carried out by means of the B3LYP/cc‐pVQZ//CCSD/cc‐pVQZ treatment. First, an efficiency scale is established for Lewis bases in terms of the electronic charge transfer potential. Next, this study shows that the intensity of the B‐H stretching depends mostly on the electronic charge amount transferred to the proton. Thus, intensity data provide empirical assessment of Lewis base charge transfer efficiency. Finally, the group separation observed during correlation of proton affinities and electronic charge transfer potential is explained by the interaction energy between fragments of the protonated system.     

Magnetic Anisotropy of Mononuclear NiII Complexes: On the Importance of Structural Diversity and the Structural Distortions

Mononuclear Ni^II complexes are particularly attractive in the area of single‐molecule magnets as the axial zero‐field splitting (D) for the Ni^II complexes is in the range of ?200 to +200 cm^?1. Despite this advantage, very little is known on the origin of anisotropy across various coordination ligands, coordination numbers, and particularly what factors influence the D parameter in these complexes. To answer some of these questions, herein we have undertaken a detailed study of a series of mononuclear Ni^II complexes with ab initio calculations. Our results demonstrate that three prominent spin‐conserved low‐lying d–d transitions contribute significantly to the D value. Variation in the sign and the magnitude of D values are found to correlate to the specific structural distortions. Apart from the metal–ligand bond lengths, two different parameters, namely, Δα and Δβ, which are correlated to the cis angles present in the coordination environment, are found to significantly influence the axial D values. Developed magneto–structural D correlations suggest that the D values can be enhanced significantly by fine tuning the structural distortion in the coordination environment. Calculations performed on a series of Ni^II models with coordination numbers two to six unfold an interesting observation—the D parameter increases significantly upon a reduction in coordination number compared with a reference octahedral coordination. Besides, if high symmetry is maintained, even larger coordination numbers yield large D values.