Rotational distortion

Amat, G., and Nielsen, H. H. (1958a), Rotational Distortion in Linear Molecules Arising from l-Type Resonance, J. Mol. Spectrosc. 2, 163. 

The q = 1 components of the first term on the right-hand side of this equation represents a correction to the so-called rotational distortion term, whose matrix elements were given in equations (8.363) and (8.364). In the light of this term we should replace —2B by (—2B + y) in the off-diagonal elements (8.364), add nothing to the energy of the 2n3/2 component, and subtract y from the energy of the 2ni/2 component. 

This is, in essence, the result needed to construct figure 8.47. There is more to be done, however, because it is necessary to use (8.430) to derive matrix elements for the parity-conserved functions, and then to take note of the rotational distortion which mixes the fine-structure states. This mixing can be represented by an effective 12 value, which is designated 12 eff in table 8.28, where the results of the Stark experiments are listed. 

Using the basis representation rj, A J, A) we see that the first, second and fourth terms in (10.99) are diagonal, whereas the third and fifth terms have matrix elements off-diagonal in A, and therefore mix other electronic states with the 1 Ag state. If we include the first rotational distortion term it is easy to show that, from (10.99), the rotational energies are given by... 

The four terms in X7, however, require closer attention. The second term, which in molecule-fixed cartesian coordinates may be expressed as L2X + L2y, affects all levels equally and is therefore usually omitted. The third term, which does not involve the orbital angular momentum, is known as the rotational distortion term. Its matrix elements are readily obtained ... 

FIGURE 6. Pyramidalization and rotational distortion around the C—N bond of enamines. (Reproduced with permission from Reference 234)... 

The nomenclature has not been consistent in attempts to describe deviations from the idealized configurations. We will generally refer to a deviation in 0 simply as partial rotation. The term twist has been used for this, but has often been used to describe rotational distortion about the C=C axis. Partial rotation about the remaining axis has been called skewing. The stereochemically nonrigid process of alkene rotation primarily involves changes in 9, but would also... 

Fig. 9.12. Sequence of phases associated with Au(OOl). At high temperatures, distorted hexagonal phases are superseded by disordered phase with 1x1 symmetry. RDH refers to rotated-distorted hexagonal phase, DH refers to distorted hexagonal phase and DIS refers to disordered phase. Note that the schematic of the rotated hexagon associated with RDH exaggerates the rotation. In addition, the orientation relationship between the hexagonal structures and the subsurface atoms is not represented.

X < Unperturbed —> Distorted Distorted Periodic oscillation Periodic oscillation Periodic rotation-1 Periodic rotation-1 Periodic rotation-2 Periodic rotation-2 Quasi-periodic rotation Quasi-periodic rotation —> Distorted or periodic rotation Pitchfork Supercritical Hopf Gluing Saddle-node Supercritical Hopf Homoclinic °... 

The symmetry consequences of octahedral tilting, rotation, distortion and cation ordering in KjNiF phases is dealt with by ... 

As already mentioned, for the fixed direction of the nematic director n the shear modulus is absent because the shear distortion is not coupled to stress due to the material slippage upon a translation. The compressibility modulus B is the same as for the isotropic liquid. New feature in the elastic properties originates from the spatial dependence of the orientational part of the order parameter tensor, i.e. director n(r). It is assumed that the modulus S of the order parameter Qij r) is unchanged. In Fig. 8.4 we can see the difference between the translation and rotation distortion of a nematic. 

Fig. 5 The in-plane diffraction pattern for the Au(001) surface, (a) The unreconstructed phase (b) the distorted hexagonal phase (c) the rotated, distorted hexagonal phase. In each case, the filled symbols represent the scattering from...

TABLE 9.1 Ground state molecular rotational and vibrational constants for selected diatomic molecules. Values for the vibrational constants are based on varying numbers of anharmonic terms. In this table Dq is the v = 0 rotational distortion constant. Missing values indicate the constant was not measured in the corresponding experiment... 

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