Rotation of molecules

Huntress WT 1970 The study of anisotropic rotation of molecules in liquids by NMR quadrupolar relaxation Adv. Magn. Reson. 4 1-37... 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

The rotation of the ammonium ion in salts at ordinary temperatures provides justification for the customary treatment of the ion as spherically symmetrical in the theoretical discussion of the structure of ionic crystals. Further, the rotation of molecules such as NHj and H20 about symmetry axes accounts for the fact that these molecules occupy positions in crystals with symmetry elements not compatible with those of the non-rotating molecule. Thus in Ni(NH3)6CU the NHj molecules lie on four-fold axes, and in alum the H2O molecules on three-fold axes. The rotation of the molecules,... 

Rotational suspension separation encapsulation process, 16 450 Rotational viscometers, 21 731-737 computers in, 21 732 operation of, 21 736 Rotations, of molecules cause of color, 7 326t, 328 Rotavirus vaccine, 25 496 Rotaxanes, 17 61, 24 31, 33, 51 as molecular computers, 24 60 Rotenone (Chem-Fish Synergized,... 

Even if one restricts one s attention to vibrations and rotations of molecules, there are a variety of Lie algebras one can use. In some applications, the algebras associated with the harmonic oscillator are used. We mention these briefly in Chapter 1. We prefer, however, even in zeroth order to use algebras associated with anharmonic oscillators. Since an understanding of the algebraic methods requires a comparison with more traditional methods, we present in several parts of the book a direct comparison with both the Dunham expansion and the solution of the Schrodinger equation. 

It is assumed that the reader has previously learned, in undergraduate inorganic or physical chemistry classes, how symmetry arises in molecular shapes and structures and what symmetry elements are (e.g., planes, axes of rotation, centers of inversion, etc.). For the reader who feels, after reading this appendix, that additional background is needed, the texts by Cotton and EWK, as well as most physical chemistry texts can be consulted. We review and teach here only that material that is of direct application to symmetry analysis of molecular orbitals and vibrations and rotations of molecules. We use a specific example, the ammonia molecule, to introduce and illustrate the important aspects of point group symmetry. 

These experiments while moving beyond simple structure determination, still depend primarily on structure determination as their primary tool. A number of experiments have moved beyond this to exploit other characteristics of NMR. For example, spin saturation transfer can be used to study internal rotation of molecules (59, 60), and line shape analyses can be used to study intramolecular exchange processes (61), conformational interchange (62) and... 

The Vibration and Rotation of Molecules.—The nature of the vibrational motion and the values of the vibrational energy levels of a molecule are determined by the electronic energy function, such as that shown in Figure VII-1. The simplest discussion of the vibrational motion of a diatomic molecule is based upon the approximation of the energy curve in the neighborhood of its minimum by a parabola that is, it is assumed that the force between the atoms of the molecule is proportional to the displacement of the internuclear distance from its equilibrium value r.. This corresponds to the approximate potential function... 

Rocky Mountain spotted fever 7 Rods (visual receptor cells) 390 Root hairs, dimensions of 30 Roseoflavin 788, 789s Rossmann fold. See Nucleotide-binding domain Rotamases 488 Rotary diffusion constant 463 Rotation of molecules 462,463 Rotational barrier 44 Rotifers 24, 25... 

For intramolecular vibrations, each site was considered independently. However, the reorganizations in the surrounding solvent are necessarily properties of both sites since some of the solvent molecules involved are shared between reactants. The critical motions in the solvent are reorientations of the solvent dipoles. These motions are closely related to rotations of molecules in the gas phase but are necessarily collective in nature because of molecule—molecule interactions in the condensed phase of the solution. They have been treated theoretically as vibrations by analogy with lattice vibrations of phonons which occur in the solid state.32,33... 

Problems involving rotation occur frequently in the quantum theory. This section discusses two models which look rather artificial, but which serve to introduce some important ideas. They have a direct application to the rotations of molecules, but are especially useful in the context of atomic structure, discussed in Chapters 4 and 5. 

H. W. Spiess, Rotation of Molecules and Nuclear Spin-Relaxation in NMR Basic Principles and Progress , Springer, New York, 1978, Vol. 15, p. 55. 

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