Principal axis

In linear, spherical and synnnetric tops the components of a along and perpendicular to the principal axis of synnnetry are often denoted by a and respectively. In such cases, the anisotropy is simply Aa = tty -If the applied field is oscillating at a frequency w, then the dipole polarizability is frequency dependent as well a(co). The zero frequency limit of the dynamic polarizability a(oi) is the static polarizability described above. 

The two coeflScients y and describe the material response and the Cartesian coordinate must be chosen as a principal axis of the material. 

The electric field gradient is again a tensor interaction that, in its principal axis system (PAS), is described by the tluee components F Kand V, where indicates that the axes are not necessarily coincident with the laboratory axes defined by the magnetic field. Although the tensor is completely defined by these components it is conventional to recast these into the electric field gradient eq = the largest component,... 

Chemical shift anisotropy (CSA) 2 Reorientation of the CSA principal axis Increases with the square of the magnetic field [13]... 

Intramolecular quadrupolar 2 Reorientation of the electric field gradient principal axis Dominant for />1 (covalently bonded) [14]... 

Given the bond distances and intemuclear angle in Problem 9, what is the moment of inertia of the H2O molecule about its principal axis through the oxygen atom (the y-axis in File 4-5) ... 

The rotation axis of highest order is called the principal axis of rotation it is usually placed in the vertical direction and designated the z-axis of the molecule. Planes of reflection which are perpendicular to the principal axis are called horizontal planes (h). Planes of reflection which contain the principal axis are called vertical planes (v), or dihedral planes (d) if they bisect 2 twofold axes. 

At least I rolaliofl axis of order > 1 ( principal axis)... 

The functions I accordingly correspond to an oblate antiprism and II to a prolate antiprism. There is a simple explanation for the difference in orientation of the principal axes. The theorem that the sum of the squares of the values of the functions for a complete set (a subshell) is constant requires that the shape parameters vary in a satisfactory way with change in orientation of the principal axes. For the prolate set (II) the maximum value in the plane orthogonal to the principal axis of the function lies in the basal plane of rhe antiprism, and thus serves to increase the electron... 

Lagorceix, H., Reynaud, R, 1995, Squeezing highly Birefringent Fiber for an Accurate Nondestructive Determination of Principal-Axis Orientation along the Waveguide application to Fiber Babinet Compensator Implementations Optical Fiber Technology 1, 171... 

Vibrations of the symmetry class Ai are totally symmetrical, that means all symmetry elements are conserved during the vibrational motion of the atoms. Vibrations of type B are anti-symmetrical with respect to the principal axis. The species of symmetry E are symmetrical with respect to the two in-plane molecular C2 axes and, therefore, two-fold degenerate. In consequence, the free molecule should have 11 observable vibrations. From the character table of the point group 04a the activity of the vibrations is as follows modes of Ai, E2, and 3 symmetry are Raman active, modes of B2 and El are infrared active, and Bi modes are inactive in the free molecule therefore, the number of observable vibrations is reduced to 10. 

The circular polarization (CIPO) beamline at the Elettra synchrotron (Trieste, Italy) operates in the VUV-SXR range with radiation from a combination permanent magnet-electromagnetic elliptical wiggler [94, 95]. This does not achieve full circular polarization in the VUV region, but rather an elliptical output with principal axis lying in the horizontal plane (ii > 0, 2 = 0, < 1). 

In the smectic mesophases the molecules are oriented, as in a nematic mesophase, with their principal axis roughly parallel to the director, but they are also defining layers. These layers can be perpendicular to the director, as in the smectic A mesophase (SmA), or tilted, as in the smectic C (SmC). The SmA and SmC mesophases are the less ordered and more common smectic mesophases. Other less common types of smectic mesophases are known, which differ in the degree or kind of molecular ordering within and between the layers [2]. 

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