Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.     

Rare Events in Random Geometric Graphs

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions for a variety of conditional probabilities related to the number of edges in the random geometric graph and develop conditional Monte Carlo algorithms for estimating rare-event probabilities on this basis. We prove rigorously a reduction in variance when compared to the crude Monte Carlo estimators and illustrate the magnitude of the improvements in a simulation study. In higher dimensions, we use conditional Monte Carlo to remove the fluctuations in the estimator coming from the randomness in the Poisson number of nodes. Finally, building on conceptual insights from large-deviations theory, we illustrate that importance sampling using a Gibbsian point process can further substantially reduce the estimation variance.

     

A concise synthesis of β-lactam-sulfonamide hybrids

Using ring closing metathesis (RCM) as the key operation, a rapid access to β-lactams fused to a sultam moiety of variable ring size was developed from low cost, commercially available starting materials. An efficient RCM of 4-vinyl-azetidin-2-ones to give 1-aza-bicyclo[4.2.0]oct-4-en-8-ones is also reported.     

Syntheses and X-Ray Crystal Structures of 2-Aminoindenes and Aminocymantrenes

Substituted 2-aminoindenes have been synthesized in almost quantitative yields by reactions of amines such as methylpiperazine, trimethylethylenediamine, 1,4-diaza-cycloheptane and N,N′-dimethylethylenediamine with 2-indanone. The 2-aminoindenes can be deprotonated and reacted with BrMn(CO)₃(Py)₂ to produce the respective aminoindenyl-cymantrenes in yields between 55–70%. The X-ray crystal structures of 2-(methylpiperazine)indenyl-cymantrene 5 (P1 , a = 12.667(3) Å, b = 16.630(3) Å, c = 17.382(3) Å, α = 72.70(3)°, β = 74.59(3)°, γ = 88.66(3)°, V = 3364.1(12) Å ³, Z = 8, R1(2σ(I)) = 4.02%, wR2(2σ(I)) = 10.30%) and the HClO₄ adduct of 2-(trimethylethylenediamine)-indenyl-cymantrene 6 (Cc, a = 23.722(5) Å, b = 6.9080 Å, c = 13.264 Å, β = 111.77(3)°, V = 2018.6(7) Å 3, Z = 4, R1(2σ(I)) = 2.94%, wR2(2σ(I)) = 7.90%) were determined. In both complexes the indenyl-carbon bonded to nitrogen displays significantly longer bonds to manganese [223.5(3)–225.8(3) pm] than the other four carbon atoms [213.3(3)–219.1(3) pm]. The short indenyl-nitrogen bonds of 136.2(4) and 137.8(4) pm are indicative of a substantial multiple bond character. The complexation of Zn²⁺ by the nitrogen atoms of 6 results in significant shifts of the CO stretching frequencies.     

Farbe und Konstitution bei anorganischen Feststoffen, 11. Mitt.: Die Lichtabsorption des oktaedrisch koordinierten Co2+-Ions in der Mischkristallreihe Mg1−x Co x O und anderen oxidischen Wirtsgittern

Zusammenfassung Für das oktaedrisch koordinierte Co²⁺-Ion werden ein Termschema und Energiegleichungen für zwei charakteristischeDq/B-Werte angegeben und mit deren Hilfe aus den Spektren der Co²⁺-haltigen Ilmenite MgTiO₃ und CdTiO₃ ¹ die Zuordnung des intensitätsstärksten Quartett-Dublett-Überganges ( _a ⁴ T_{1g b} ² T_1g) auf eindeutige Weise ermöglicht.Weiter wird das spektrale Verhalten der Mg_1–x CO _x O-Mischkristalle (0,05x1,0) in Abhängigkeit von der Co²⁺-Konzentration untersucht. Die Änderungen der Bandenintensitäten und desRacah-ParametersB werden wie in der analogen MgO-NiO-Mischkristallreihe² auf Spin-Spin-Wechselwirkungen der über Sauerstoff benachbarten Co²⁺-Ionen zurückgeführt.

---

The energy levels of the octahedrally coordinated Co²⁺-ion and energy equations for two characteristicB-values are given, which allow to identify the quartet-doublet-transition ( _a ⁴ T_{1g b} ² T_1g) of the highest intensity from the spectrum of the Co²⁺ containing ilmenites MgTiO₃ and CdTiO₃ ¹.In addition, the variation of the spectra of the Mg_1–x Co _x O-mixed crystals (0.05x1.0) with the Co²⁺ concentration is investigated. The changes in the intensities of the absorption bands and of theRacah-parameterB are (as for the corresponding MgO-NiO-mixed crystals² interpreted as being caused by spin-spin-interactions between Co²⁺ ions bonded to the same oxygen.

---

---

Mit 3 Abbildungen     

Synthesis of [(MeCyt)2H]I-structure and stability of a dimeric threefold hydrogen-bonded 1-methylcytosinium 1-methylcytosine cation

Reaction of trimethylsilyl-protected cytosine with methyl iodide afforded N1-methylated product. Subsequent treatment with ethanol resulted in cleavage of the protection group forming [(MeCyt)2H]I (4). Identity of was confirmed by microanalysis, mass spectrometry, 1H and 13C NMR spectroscopy and by single-crystal X-ray diffraction analysis. Crystals of consist of dimeric [(MeCyt)2H]+ cations and I- anions. These ions are arranged in the crystal such that there is a strong base stacking (mean stacking distance 3,467 angstroms) and, furthermore, pi interactions between I- and cytosine rings (mean distance 3,737 angstroms). The dimeric [(MeCyt)2H]+ cations are centrosymmetric having three strong hydrogen bonds, namely two terminal N4-H...O' ones (N4...O' 2.815(4) angstroms) and a central N3-H...N3' (N3...N3' 2.813(4) angstroms) one. Quantum chemical calculations on the DFT level of theory show that the gas phase structure of the dimeric cation exhibits two different terminal N-HO hydrogen bonds, a stronger (N4...O' 2.722 angstroms) and a weaker one (N4'...O 2.960 angstroms). The central N3-HN3[prime or minute] hydrogen bond (N3...N3' 2.852 angstroms) was characterized to have an unsymmetrically located proton and a typical double minimum potential with a very low activation barrier. The interaction energy between [(MeCyt)H]+ and MeCyt yielding [(MeCyt)2H]+ was calculated to be -42.4 kcal mol(-1)(ZPE and BSSE corrected). Comparison with the interaction energy (calculated on the same level of the theory) between cytosine and guanine yielding the triply hydrogen-bonded Watson-Crick dimer (-24.2 kcal mol(-1)) revealed a much higher stability of the hydrogen bonds in [(MeCyt)2H]+.     

A novel MCR of isocyanates, aldehydes, and dienophiles

[reaction: see text] A novel one-pot procedure for the three-component coupling reaction of isocyanates, aldehydes, and dienophiles (IAD reaction) has been developed. Condensation of isocyanates and aldehydes and subsequent Diels-Alder reactions with electron-deficient dienophiles furnishes endo-selective amino-substituted cyclohexenes in good yield.     

On the determination of the worst sampling error in a communication system for pulse amplitude modulated signals. Part II: The finite dimensional model

This paper is dedicated to the problem of optimizing the transmission properties of a Pulse Amplitude Modulation (PAM) system. The system is disturbed by a random timing jitter in the sampling device which periodically evaluates the continuous output signal at discrete times. Mathematically the timing jitter is a random variable with unknown probability distribution. So, our optimization problem turns out to be actually a minimax problem, for which mathematical game theory with its powerful concepts becomes the suitable frame for our analysis.In the first part [4] we have established a general existence theorem for the minimax problem, and we have worked out some properties of solutions in the case that the feasible impulse responses form a space of infinite dimension.This part summarizes results which we obtain, if we allow only for impulse responses lying in a certainn-dimensional subspace of the original space (see [2, 3]). By general results from semi-infinite optimization (see [1]) we know that, writing the minimax problem as a semi-infinite optimization problem, we can reduce the number of restrictions from infinity to a numbersn+1. On the basis of our special model we present a theory of uniformly singular quadratic forms, which has been developed (see [3]) in order to get additional statements abouts.In this way we supplement the work of Krabs [6], who was the first to present such a finite dimensional model, arguing that it is impossible for an engineer to construct a system in a way that an arbitrary impulse response is realized, unless this impulse response has a simple structure (for instance a low pass filter).The first two paragraphs have been taken almost literally from part I in order to render the lecture more comfortable. The interesting parts, however, are the following ones, where the results specific for the finite dimensional case are worked out.     

Electrostatic representations of molecular groups

The treatment of electrostatic interactions between molecular groups is based on quantum mechanical electron density distributions. A general method is suggested using tesseral harmonic multipole expansions and representing each set of point multipoles by a cluster of discrete charges small with respect to atomic dimensions. The procedure is carried out for the amino group with an electron density derived from the wave function of ammonia. We evaluate the optical rotation of two aminopyrrolidones as a test case. Expansions are compared for several approximate wave functions for ammonia.     

Various carbon dust particles

Nano-sized carbon dusts are suspected of having negative effects on human health. An exact characterization of such particles is necessary to understand possible toxic effects, i.e. in the lung. Observed by transmission electron microscopy (TEM), the carbon dusts are a composite of very small primary particles and larger agglomerates of these. A differentiation of the primary particles and agglomerates according to source is not possible by TEM, however, thermogravimetry investigations in synthetic air atmosphere are helpful. Standardized carbon black and graphite show a single-step oxidation behaviour, whereas ethene soot and diesel soot, for example, show more complex-reaction mechanisms. The results of ethene soot exemplarily demonstrate the oxidation mechanism. In addition to the oxidation reaction to carbon dioxide, a sintering process takes place. To confirm the oxidation mechanism, thermal behaviour of ethene soot has been simulated by kinetic modulation using a three-step reaction mechanism of n-th order. The reaction order indicates a complex mechanism for the first-reaction step. For the second and third-reaction step, a phase boundary mechanism could be suggested.