Fiee rotation

In Rhodamine 6G, also sold as Rhodamine F5G [989-38-8] (15), the caiboxy estei gioup prevents fiee rotation of the lower phenyl group. Its position is roughly perpendicular to the plane of the other three rings. Retention of color strength is good because there is less electronic interaction between the lower ring and the rest of the molecule. 

Figure 9.8 (a) There is fiee rotation about the C—C single bond. All three Lewis structures represent the same molecule, (b) There is no rotation... 

Here is the free energy assoeiated with direetor axis rotation withont ehange of layer spacing, is dne to layer distortions, and F is the cross term describing the conpling of these layer distortions and the fiee-rotation process. 

There are several possible origins for the small intercalate-specific contribution. The first is suggested by the complex Fermi surface of K3 60 (16). In addition to bandwidth variations, which depend directly on the lattice parameter, the volume of the Fermi surface may be subdy different for different intercalates, or may vary with lattice parameter or pressure, or both effects could occur. Another possibility is a pressure-induced phase transition involving molecular orientations. In pure C, fiee molecular rotations freeze out at = 249 K at 1 bar, locking into specific orientations with respect to the crystal axes (17), and... 

Cyclohexane has a non-planar structure that makes it almost fiee from ring strain. The most important conformations that it can have include chair conformation and boat conformation. The chair conformation is more stable than the boat conformation. The boat conformation can sometimes be more stable than it usually is, by a slight rotation in the C-C bonds and is called the twist boat conformation. Nevertheless, the chair conformation is the most stable cyclohexane form. 

An important point to note is that 5 in the field-fiee Hamiltonian (11.7) is the rotational moment operator, and canhave different values in (11.8) and (11.9). From these general expressions we can calculate the matrix elements involving the five primitive functions as shown below. In order to evaluate these matrix elements it is necessary to specify a value of L Freund and Miller pointed out that L = 2 for a d electron. This is the pure... 

Pig. 30 (a) HOMO and LUMO of free Al4Li4. (b) Resulteint MOs formed by the interaction of the HOMO-LUMO of fiee MjXm and px and py AOs of the BH cap. (c) Resulteint MOs formed by the interaction of the HOMO-LUMO of free Al4Li4 and px and py AOs of the C cap LUMO of (a), HOMO-1 of (b), and HOMO-2 of (c) are rotated by 90° for clarity. Reprinted with permission from [163]. Copyright ACS Journal Archives... 

Free radicals in the cage execute translational and rotational motions. The latter can be important for fiee radicals to react, because such a reaction requires a pair of... 

Rotation-fiee atomic polar tensors were calculated using Eq. (4.142). Finally, D(v) matrices were obtained with the aid of the respective C 1 matrices [Eq. (4.146)]. As an example, the structures of C and C 1 arrays for the water molecule are shown below. 

The flexibihty of the polymer chain is dependent on the fiee space ly available for rotation. If v is the specific volume of the polymer and is the volume when it is solidly packed, then ly is nothing but the difference between the two (v — v ). If the firee space ty is reduced by the presence of large substituents, as in polyethylene terephthalates, the Tg value goes up, as observed earlier. 

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