Cj point group

All have pyramidal molecules (Cj point group for OSX2), and OSFCl is chiral though stereochemically labile. Dimensions are in Table 15.14 the short O-S distance is notable. The unstable compound OSI2 was mentioned on p. 692. 

FIGURE 11. The molecular model (Cj, point group) and torsional form of (003)2802 . The projection formula represents a view along one of the S—C bonds. 

Table 5. Correlation of the fundamental vibrations v, and Vj of the point group with and Cj point groups [103, 115],...

To decompose this representation, Eq. 3.1 must be applied for each of the four irreducible representations in the Cj, point group ... 

No fullerene organometallics have been made yet with the Cj point group. 

These two vectors may be used in the description of the stretching vibrations of the molecule. The molecular symmetry is Cj. Figure 4-7 helps to visualize the effects of the symmetry operations of this group on the selected basis. There are four symmetry operations in the Cj point group, E, Cj, i, and a. E leaves the basis unchanged, so the corresponding matrix representation is a unit matrix ... 

Table 4-5. Complete Character Table for the Cj, Point Group...

As environmental symmetry decreases, the orbitals will become split to an increasing extent. In the Cj point group, for example, all atomic orbitals become split into nondegenerate levels. This is not surprising since the C2, character table contains only one-dimensional irreducible representations. This result shows at once that there are no degenerate energy levels in this point group. This has been stressed in Chapter 4 in the discussion of irreducible representations. 

Reductive elimination through the s-trans pathway retains C2 symmetry and has to overcome the activation barrier of 29.4 kcal/mol. On the other hand, initial complex (lA Init) and transition state (1A TS) for s-cis pathway belong to Cj point group and the activation energy is 4.9 kcal/mol higher than for the former (Table 2). In the latter process, the product buta- 1,3-diene will be released in the s-gauche (C2) form. Reductive elimination reactions are exothermic by... 

Generation of a set of 1 x 1 matrix representations of the symmetry operations in the Cj point group using the (a) orbital, (b) orbital, and (c) Pj, orbital as a basis set. The shaded lobe of the orbitals indicates a positive sign for the wave function, whereas the hollow lobe indicates a negative sign for the wave function. The three p orbitals transform with the same representations as the corresponding coordinate axes. 

While we examine these applications of group theory to some molecular problems, a cynical observer could point out that group theory is less helpful to the many molecules in the Cj point group, which has only one representation A. If all the states have the same symmetry, what can be simplified or classified by the group theory Group theory does tell us that, for molecules... 

The relative energy of IPR satisfying Isomers of Css at various levels of theory. Isomers 1,5,7,11,12, and 13 have Q symmetry. Isomers 2,3,4,6,14, and 17 possess C2 point group. Isomers 9 and 10 have C2V point group. Isomers 8,15, and 16 have Cj point group. Isomers 18 and 19 possess C3 and P3 point groups respectively (The data was taken from ref. Sun and Kertesz (2002))... 

Under the operations of the Cj, point group, the 24 vibrational modes can be decomposed into the representations ... 

The most frequently encountered type of conical intersection is partly induced by symmetry in the following sense. Let us consider a molecular system that possesses at lea.st one nontrivial symmetry element, e.g., a plane of reflection (Cj. point group), and thus at least two irreducible representations (A and A" in the case of the C,- point group). Consider two electronic states transforming according to different irreducible representations. In this case, the Hamiltonian of equation (18) takes the form... 

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