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The bi(anthracene‐9,10‐dimethylene) photoisomer has remarkably long C–C single bonds. To examine the lengthening of the C–C bond, we propose a novel procedure for quantitatively analyzing orbital interactions in a molecule at the level of the ab initio molecular orbital method. In this procedure, we can cut off the specific through‐space/bond interactions in a molecule by artificially increasing the absolute magnitude of the exponents in a Gaussian function. Then, the spatial orbital interactions were perfectly cut off, and, each term that makes up the total energy, that is, the nuclear–electron attractions, the electron–electron repulsions, and the nuclear–nuclear repulsions cancel each other. Several model molecules of the photoisomer were analyzed by this procedure. It was found that the orbital interaction between the p orbital on the benzene ring and the σ* orbital on the C–C bond in question, σ→σ* electron transfer through π orbital, weakens the C–C bond efficiently when these orbitals were located in the “periplanar” conformation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001 相似文献
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Michael Renardy 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1994,45(3):497-501
We study a singular Sturm-Liouville eigenvalue problem which arises in studying the stability of rotating shallow-water shear flows on an equatorial -plane. Earlier studies have shown that the problem has only stable eigenvalues if a certain parameter exceeds 3/4. On the other hand, numerical studies have found unstable eigenvalues if is sufficiently small. In this note, we give an analytical proof that the bound of 3/4 is indeed sharp, i.e. there are instabilities for any < 3/4. 相似文献
4.
Michael Renardy 《Proceedings of the American Mathematical Society》1996,124(8):2451-2453
Let be the infinitesimal generator of a -semigroup of operators in a Hilbert space. We consider the class of operators , where is bounded. It is proved that the spectrum of determines the growth of the associated semigroup for ``most" operators (in the sense of Baire category).
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Michael Renardy 《Communications in Mathematical Physics》1980,76(3):277-287
We discuss bounded solutions of the equation $$r^2 \left( {\frac{{\partial ^2 u}}{{\partial r^2 }} + \frac{{\partial ^2 u}}{{\partial t^2 }}} \right) = u^3 - u$$ in the halfspacer>0. All solutions depending only ont/r are characterized topologically. Then we prove the existence of infinite dimensional manifolds oft-periodic as well as nonperiodic solutions which are small in a suitable norm. 相似文献
6.
Perfluoroalkylation of alkynes with RfI(Ph)OSO2CF3 is described. This offers the first example of electrophilic perfluoroalkylation of alkynes. 相似文献
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It is shown that NiN(2) and noble gas atoms, Ar, Ne, and He, combine with the binding energy of 11.52, 4.06, and 7.37 kcal/mol, respectively, by the multireference perturbational (CASPT2) method. By the density functional theory calculations using MPWPW91 functionals, the Ni-N-N bending frequency in NiN(2) and Ar-NiN(2) is estimated as 310.7 and 358.7 cm(-1), respectively, the latter of which is in good agreement with the corresponding experimental frequency, 357.0 cm(-1), determined for NiN(2) isolated in solid argon. 相似文献
8.
Michael Renardy 《Journal of Mathematical Fluid Mechanics》2012,14(2):355-361
The well-posedness of the equations of fluid mechanics in the hydrostatic limit is well known to be a difficult problem. Partial results, both positive and negative, will be reviewed below. In this paper, it is shown that, for ideal magnetohydrodynamics, a magnetic field parallel to the flow direction can ensure well-posedness. The only condition required is that the flow is subalfvenic. The result has some relevance to viscoelastic flows of the upper convected Maxwell fluid, which, in the infinite Weissenberg number limit, is related to ideal MHD. 相似文献
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