Symmetry rules for predicting the course of chemical reactions

Rules are given for a reaction of any molecularity which show whether it is allowed or forbidden by orbital symmetry properties. The rules are based on a rigorous treatment, but correspond to simple concepts in practice. A rough MO sequence for the reactants is all that is needed.

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Zusammenfassung Für Reaktionen beliebiger Molekularität werden Regeln dafür angegeben, ob die Reaktion aus Symmetriegründen erlaubt oder verboten ist. Diese Regeln werden streng hergeleitet, sind jedoch in der Praxis einfach anwendbar. Benötigt wird lediglich die Reihenfolge der MO der Reaktionen.

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Résumé On donne des règles de sélection pour une réaction de molécularité arbitraire selon les propriétés de symétrie orbitale. Les règles sont basées sur un traitement rigoureux mais correspondent en practique à des concepts simples. On a seulement besoin de connaître l'ordre des orbitales moléculaires des réactants.

     

AB initio calculations of the electronic properties of N4− in KN3

The energies of the ground state and low-lying excited states of the N₄^? defect in KN₃ have been calculated using ab initio techniques. A rectangular equilibrium geometry with dimensions X = 2.76 and Z = 2.47 a.u. and ground state symmetry of Γ₄⁺ was determined by calculating N₄^? as a free radical. For this ground state the unpaired electron is in a π orbital which is consistent with the experimental hyperfine tensor only if one edge of the N₄^? radical is parallel to the c axis in KN₃. These results were used to calculate the X²Γ₄⁺ state of N₄^? in the crystal field of KN₃, yielding an energy of ?217.899 Hartrees. The isotropic hyperfine constant was calculated to be a = 2.1 G and the components of the anisotropic hyperfine tensor as B_xx = ?3.4 G, B_yy = 7.0 G and B_zz = ?3.6 G, in good agreement with experimental and INDO results. Several excited states were calculated for the N₄^? defect in KN₃. When an estimate was made of the correlation energy, the transition energy of the X²Γ₄⁺→A²Γ₃^? transition agreed well with the peak energy of the 780 nm absorption band which has been attributed to N₄^?.     

Uniqueness of the inversive plane of order 7

A search has shown that any inversive plane of order 7 must be isomorphic with the Miquelian plane. The method used was explicitly set out in a companion paper, which was concerned with a plane of order 5.     

Adsorption of molecular nitrogen by the W(110) plane

Characteristics of the adsorption of nitrogen on the (110) plane of tungsten were determined by thermal desorption and work function measurements. The low temperature γ-N₂ state desorbs with first order kinetics and an activation energy of 6 kcal mole^?1. The absence of isotope mixing between ¹⁴N₂ and ¹⁵N₂ demonstrates γ-N₂ is adsorbed molecularly. Monolayer coverage shows a decrease of 0.19 eV in work function. A Topping model plot indicates the layer is immobile at 123 K.     

Linear relativistic hamiltonians

A 2(2J + 1)-component relativistic Hamiltonian H that describes free particles of mass m and spin J is said to be linear if it has the form $\text{H = h}\text{x}\text{?}\text{·}\text{p}\text{+ gm}$, where $\text{x}\text{\_.}\text{= i[H,}\text{x}\text{]}{}_{\mathrm{?}}$, h is a numerical factor, and g commutes with x and p. All such Hamiltonians are found, provided that the metric is either the unit matrix or ?₃ and provided that the theory is invariant under the discrete symmetries. If the operator Γ in the generator $\text{K}\text{=}\text{1}\text{2}\text{[}\text{x}\text{, H]}{}_{\mathrm{+}}\text{+ Γ}$ of Lorentz boosts is required to be local, there are only two possibilities; either Γ = 0, which generalizes the Dirac spin-$\text{1}\text{2}$ theory, or $\text{Γ = ??}{}_3\text{(}\text{1}\text{2m}\text{)}\text{S × p}$, which generalizes the Sakata-Taketani spin-0 and spin-1 theories. The relationship to linear manifestly covariant equations and its significance is discussed.     

The paley-wiener theorem for the radon transform

We prove that the support of a complex-valued function f in ?^k is contained in a convex set K if and only if the support of its Radon transform k(s, ω) is, for each ω, contained in s ≦ S_K (ω); here S_K is the support function of the set K. This theorem is used to determine the propagation speeds of hyperbolic differential equations with constant coefficients, to prove the nonexistence of point spectrum for a certain class of partial differential operators, and to give a simple reduction of Lions' convolution theorem to the one-dimensional convolution theorem of Titchmarsh.     

Number fluctuation analysis of random locomotion. Statistics of a Smoluchowski process

We analyze a scheme, originally suggested by Smoluchowski, by which a diffusion coefficientD can be estimated by measuring the number of particles occupying a fixed region of a surface at various times. An expression is derived relating the variance of the estimated valueD to several experimental parameters. This expression is evaluated numerically to determine how statistical uncertainty depends on adjustable variables. Particular attention is given to experiments involving locomotion of migrating leukocytes.     

Assessment of pulmonary air trapping and obstruction in expiration: an experimental MRI study

PURPOSE: The aim of this experimental study was to evaluate the potential of a simple expiration technique by means of magnetic resonance imaging (MRI) in an animal model to detect pulmonary air-trapping areas after artificial bronchial obstruction. MATERIAL AND METHODS: Sixteen pigs were evaluated by means of a modified T1-weighted FLASH with fat saturation in respiratory arrest (TR=4.6 ms, TE=1.8 ms, alpha=10 degrees, S.D.=3-5 mm). A measurement of the signal intensity (SI) in the peripheral lung tissue was made in both inspiration and expiration before and after inhalation of 2 ml of 0.5% acetylcholine to simulate a bronchial obstruction. A final measurement of the lung SI was also made after bronchospasmolytic induction through salbutamol (beta2-mimetic bronchodilator). RESULTS: In expiration, a mean SI increase in peripheral lung tissue of about 183% was seen in comparison to inspiration (mean SI increase of 11-32). After inhalation of 0.5% acetylcholine, the expirational signal increase in peripheral lung tissue was only 114% of the original SI. The expirational signal homogeneity decreased after inhalation of acetylcholine. After inhalation of salbutamol, the lung tissue signal elevation in expiration was 193%. CONCLUSION: We interpret the low expiratory signal elevation after acetylcholine inhalation as a result of an air-trapped bronchial constriction in certain areas. The simple expiratory technique in an animal model showed that it is suitable to demonstrate obstructive air trapping using MRI.     

Viscoelastic shear properties of in vivo breast lesions measured by MR elastography

Elastography is a technique to assess the viscoelastic properties of tissue by measuring an acoustic wave propagating though the object. Here, the technique is applied in the course of standard MR mammography to 15 patients with different pathologies (six breast cancer cases, six fibroadenoma cases and three mastopathy cases). Low-frequency mechanical waves are coupled longitudinally into the tissue in order to obtain sufficient wave amplitude throughout the entire breast. This leads to the presence of a substantial fraction of compressional waves, which contribute to the total displacement field. It is shown theoretically that the correct evaluation of these contributions from the compressional wave is rather difficult due to the almost incompressible nature of tissue. To overcome this problem, it is proposed to apply the curl-operator to the measured displacement field in order to completely remove contributions from the compressional wave. Results from simulations and a breast phantom demonstrate the feasibility of the technique. The in vivo results show a good separation between breast cancer and benign fibroadenoma utilizing the shear modulus. Breast cancer appears on average 2.2 (P<.001) times stiffer. All breast cancer cases showed a good delineation to the surrounding breast tissue with an average elevation of a factor of 3.3 (P< 1.4 x 10(-6)). The results as obtained for the shear viscosity do not indicate to be useful for separating benign from malignant lesions.