Universal Algorithm for Simulating and Evaluating Cyclic Voltammetry at Macroporous Electrodes by Considering Random Arrays of Microelectrodes

An algorithm for the simulation and evaluation of cyclic voltammetry (CV) at macroporous electrodes such as felts, foams, and layered structures is presented. By considering 1D, 2D, and 3D arrays of electrode sheets, cylindrical microelectrodes, hollow‐cylindrical microelectrodes, and hollowspherical microelectrodes the internal diffusion domains of the macroporous structures are approximated. A universal algorithm providing the timedependent surface concentrations of the electrochemically active species, required for simulating cyclic voltammetry responses of the individual planar, cylindrical, and spherical microelectrodes, is presented as well. An essential ingredient of the algorithm, which is based on Laplace integral transformation techniques, is the use of a modified Talbot contour for the inverse Laplace transformation. It is demonstrated that first‐order homogeneous chemical kinetics preceding and/or following the electrochemical reaction and electrochemically active species with non‐equal diffusion coefficients can be included in all diffusion models as well. The proposed theory is supported by experimental data acquired for a reference reaction, the oxidation of [Fe(CN)6]4− at platinum electrodes as well as for a technically relevant reaction, the oxidation of VO2+ at carbon felt electrodes. Based on our calculation strategy, we provide a powerful open source tool for simulating and evaluating CV data implemented into a Python graphical user interface (GUI)

Reactivity of Sodium Pentaphospholide Na[cyclo-P5] towards C≡E (E=C, N, P) Triple Bonds

A diglyme solution of Na[cyclo-P5] (1) reacts with alkynes and isolobal nitriles and phosphaalkynes to afford the otherwise elusive (aza)phospholide anions 2 a–c, 4 a,b, and 6. The reaction of Na[cyclo-P5] with alkynes and nitriles was studied by means of DFT methods, which suggested a concerted mechanism for the formation of 2 a and 4 b. The anions 2 a–c, 4 a,b, and 6 coordinate in an η5-fashion towards FeII to give the sandwich (aza)phosphametallocenes 3 a–c, 5 a,b and 7 in moderate to good yields. The new compounds were characterized by means of multinuclear NMR spectroscopy, single-crystal X-ray diffraction and cyclic voltammetry

Searching for Monomeric Nickel Tetrafluoride: Unravelling Infrared Matrix Isolation Spectra of Higher Nickel Fluorides

Binary transition metal fluorides are textbook examples combining complex electronic features with most fundamental molecular structures. High‐valent nickel fluorides are among the strongest known fluorinating and oxidizing agents, but there is a lack of experimental structural and spectroscopic investigations on molecular NiF3 or NiF4. Apart from their demanding synthesis, also their quantum‐chemical description is difficult due to their open shell nature and low‐lying excited electronic states. Distorted tetrahedral NiF4 (D2d) and trigonal planar NiF3 (D3h) molecules were produced by thermal evaporation and laser ablation of nickel atoms in a fluorine/noble gas mixture and spectroscopically identified by a joint matrix‐isolation and quantum‐chemical study. Their vibrational band positions provide detailed insights into their molecular structures

Reactivity of Sodium Pentaphospholide Na[cyclo ‐P 5] towards C≡E (E=C, N, P) Triple Bonds

A diglyme solution of Na[cyclo‐P5] (1) reacts with alkynes and isolobal nitriles and phosphaalkynes to afford the otherwise elusive (aza)phospholide anions 2 a–c, 4 a,b, and 6. The reaction of Na[cyclo‐P5] with alkynes and nitriles was studied by means of DFT methods, which suggested a concerted mechanism for the formation of 2 a and 4 b. The anions 2 a–c, 4 a,b, and 6 coordinate in an η5‐fashion towards FeII to give the sandwich (aza)phosphametallocenes 3 a–c, 5 a,b and 7 in moderate to good yields. The new compounds were characterized by means of multinuclear NMR spectroscopy, single‐crystal X‐ray diffraction and cyclic voltammetry

Resistance to antiangiogenic therapy is directed by vascular phenotype, vessel stabilization, and maturation in malignant melanoma

Angiogenesis is not only dependent on endothelial cell invasion and proliferation, it also requires pericyte coverage of vascular sprouts for stabilization of vascular walls. Clinical efficacy of angiogenesis inhibitors targeting the vascular endothelial growth factor (VEGF) signaling pathway is still limited to date. We hypothesized that the level of vessel maturation is critically involved in the response to antiangiogenic therapies. To test this hypothesis, we evaluated the vascular network in spontaneously developing melanomas of MT/ret transgenic mice after using PTK787/ZK222584 for anti-VEGF therapy but also analyzed human melanoma metastases taken at clinical relapse in patients undergoing adjuvant treatment using bevacizumab. Both experimental settings showed that tumor vessels, which are resistant to anti-VEGF therapy, are characterized by enhanced vessel diameter and normalization of the vascular bed by coverage of mature pericytes and immunoreactivity for desmin, NG-2, platelet-derived growth factor receptor β, and the late-stage maturity marker α smooth muscle actin. Our findings emphasize that the level of mural cell differentiation and stabilization of the vascular wall significantly contribute to the response toward antiangiogenic therapy in melanoma. This study may be useful in paving the way toward a more rational development of second generation antiangiogenic combination therapies and in providing, for the first time, a murine model to study this

Numerical self-consistent field method for polyatomic molecules

Andrae D. Numerical self-consistent field method for polyatomic molecules. MOLECULAR PHYSICS. 2001;99(4):327-334.A method for non-relativistic self-consistent field (SCF) electronic structure calculations for polyatomic molecules is described, which retains the linear combination of atomic orbitals ansatz for molecular orbitals (MO-LCAO), but replaces the usual algebraic expansion of atom-centred radial parts in terms of basis functions (usually some kind of Gauss-type functions) by a numerical representation on a set of radial grid points around each centre. The radial parts are optimized, according to the variation principle, until self-consistency is achieved. Even though Fourier integral transform techniques are used the method works completely in ordinary space. Intermediate quantities defined in momentum space are evaluated in closed form

Finite nuclear charge density distributions in electronic structure calculations for atoms and molecules

Andrae D. Finite nuclear charge density distributions in electronic structure calculations for atoms and molecules. PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS. 2000;336(6):413-525.The present review provides comprehensive information on finite nuclear charge density distribution models, not only for the purpose of quantum chemical electronic structure calculations for atoms and molecules, but also for other fields of atomic and molecular physics, A general discussion of the electrostatic behaviour of nuclear charge density distributions, spherical ones and non-spherical ones, is given. A large and reasonably complete set of spherical finite nucleus models, covering all models widely used in atomic and nuclear physics, is discussed in detail. Analytic expressions are given for charge density distributions, for important radial expectation values, and for their corresponding electrostatic potentials; these include new material not found in the literature. Thus, the necessary prerequisites for the use of finite nucleus models which are more realistic than the simple, frequently considered models (e.g., the 'homogeneous', 'Gaussian', and Fermi models) are fulfilled. The use of finite nucleus models in standard quantum chemical electronic structure programs is briefly reviewed. In order to detect differences between physical properties obtained with various finite nucleus models. six standardized models were selected to study and compare energy shifts (non-relativistic and relativistic) in hydrogen-like atoms. It is shown that within this set a clear differentiation of models can be made, not only from the point of View of total energy shifts but also from the point of view of energy differences and in fact even for rather low nuclear charge numbers. This could be important for future experimental as well as theoretical work on hydrogen-like atoms. (C) 2000 Elsevier Science B.V. All rights reserved

Molecular knots, links, and fabrics: prediction of existence and suggestion of a synthetic route

Andrae D. Molecular knots, links, and fabrics: prediction of existence and suggestion of a synthetic route. NEW JOURNAL OF CHEMISTRY. 2006;30(6):873-882.The possible existence and formation of molecular knots, molecular links, and molecular fabrics, built from quite arbitrary monomers, is discussed. General theoretical considerations lead to the conclusion that such molecular species are likely to represent local minima on potential energy hypersurfaces and, therefore, should be stable and able to exist, if once formed. A surface template technique is suggested as a possible experimental avenue to actually form molecular knots and links. This technique may open the door to the directed and controlled synthesis of knots, thus transcending present-day methods based on self-assembly of constituting monomers or oligomers

Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom

Andrae D. Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom. JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS. 1997;30(20):4435-4451.An algorithm for the recursive evaluation of expectation values (r(k)) for a given state of the relativistic one-electron atom with a point-like nucleus of charge number Z is proposed. In contrast to previous approaches, the present algorithm is based on only a single recurrence relation, which is a recurrence relation for a special type of generalized hypergeometric F-3(2) series. Two sequences of values of such 3 F-2 series are generated. Finally, the members of these two sequences are assembled to yield the expectation values. The algorithm can be considered as a relativistic analogue of the Kramers-Pasternack recursion for expectation values (r(k)) for states of the non-relativistic hydrogen-like atom. As an application closed-form expressions for (r(k)), -6 less than or equal to k less than or equal to 5, were derived. In addition, numerical values for (r(k)) are given for some representative states of one-electron atoms with Z = 1, 80 and 137

Energy-adjusted ab-initio pseudopotentials for multinuclear systems

Die Leistungsfähigkeit heute verfügbarer Atom-Pseudopotentiale und der zugehörigen Basissätze in quantenchemischen ab-initio-Standardrechnungen wird zunächst an weiteren Beispielen deutlich gemacht. Zum einen an Hand von Anregungs- und Ionisierungsenergien der Atome der Gruppe 8 (Fe, Ru, Os), welche bei Anwendung von Methoden zur Berücksichtigung der Elektronenkorrelation bis auf wenige Zehntel Elektronenvolt genau berechnet werden können, ohne daß dabei übermäßig hoher Aufwand betrieben werden müßte. Zum anderen wird am Beispiel der Anfangsglieder der homologen Reihe der α,α'-verknüpften Oligothiophene eine breite Palette quantenchemischer Standardmethoden eingesetzt und die erhaltenen Ergebnisse verschiedener physikalischer Größen werden diskutiert. Es zeigt sich dabei, daß Pseudopotentiale, die den Effekt von "Atomrümpfen" auf das "Valenzsystem" in quantenchemischen ab-initio-Rechnungen beschreiben, auf allen Stufen der Theorie zuverlässige Daten liefern. Insbesondere bei größeren Molekülen und bei Superposition der Pseudopotentiale für mehrere "Atomrümpfe" war dies nicht von vornherein zu erwarten. Anschließend wird ein Weg aufgezeigt, auf welchem Gruppen-Pseudopotentiale (Pseudopotentiale für mehrkernige Systeme, wie Molekülfragmente, Liganden, Substituenten oder gar ganze Moleküle) erzeugt werden können. Für die planaren Moleküle Ethen, Cyclopentadienyl und Benzen wird untersucht, ob und wie das Gruppen-Pseudopotential den "Molekülrumpf" des "σ-Gerüstes" ersetzen kann. Es wird gezeigt, daß die Justierung des gesamten Parametersatzes eines solchen Gruppen-Pseudopotentials an geeignete energetische Daten, trotz Problemen, die bei der Justierung (und auch der Anwendung) von Atom-Pseudopotentialen unbekannt sind, ebenso zufriedenstellend möglich ist wie bei den Atom-Pseudopotentialen. Als erste Anwendung eines Gruppen-Pseudopotentials für Benzen wurde der Benzen-Chlorwasserstoff-Komplex, C6H6 · HCl, untersucht. Weiterentwicklungen des hier vorgestellten Ansatzes könnten Gruppen-Pseudopotentiale für Substituenten, wie Methyl-, Phenyl- oder Amino-Gruppen, oder auch für Solvensmoleküle liefern.The effectiveness of the available atomic pseudopotentials (also known as effective core potentials) and their corresponding basis sets is firstly demonstrated through application in quantum chemical ab-initio calculations. Excitation and ionization energies of atoms of group 8 (Fe, Ru, Os) can be calculated without too much effort to within a few tenths of an electron volt, if electron correlation is properly included. Then the first few members of the homologous series of the α,α'-oligothiophenes are studied with a variety of quantum chemical standard methods. Reliable data for various physical properties can be obtained again also in this study, where a superposition of atomic pseudopotentials simulates the effect of the atomic cores of all non-hydrogen atoms on the remaining, explicitly treated valence part. This behaviour could not be expected from the outset. It is then shown how group pseudopotentials (pseudopotentials for multinuclear systems, like molecular fragments, ligands, substituents or even complete molecules) can be generated in a general way. The method is tested for the planar molecules ethene, cyclopentadienyl and benzene, such that the group pseudopotential replaces the system of σ-bonds. It is demonstrated that an energy-adjustment of the parameters in the group pseudopotential can be achieved, despite of problems unknown from the parameter adjustment for atomic pseudopotentials. The benzene-hydrogenchloride complex, C6H6 · HCl, is studied as a first application of a group pseudopotential that was designed to simulate the σ-bonds in benzene. The approach developed here may be used to generate group pseudopotentials for, e.g., methyl, phenyl or amino groups, or for solvent molecules