Symmetry point groups diagram

Figure 2.10 shows a classical diagram that allows determination of the symmetry point group and distinguishes between achiral and chiral molecules. 

OCAMS departs from the WH-LHA procedure by carrying out the analysis in the symmetry point group conunon to the reactant and the product, here C2v The subgroup into which the reacting molecule has to be desymmetrized along the reaction path, or - equivalently - the irreducible representation of the non-totally symmetric symmetry coordinate(s) that has(have) to be incorporated into the reaction coordinate, is determined by a Correspondence Diagram, In its most rudimentary form, we take into account only the occupied orbitals on each side that are considered to be directly involved in the isomerization process. 

The positions of cyclobutene and butadiene in the diagram have been reversed in order to emphasize the fact that the reactant and product have equal status in any symmetry analysis. Formally, they belong to the regular representation of the symmetry point group. 

If the reactants and product are set up in C, all of the occupied MOs would correlate across the diagram. Alternatively, a correspondence diagram, in which the reactants are set up in C2V and the product is anasymmetrized to that symmetry point group, would show that formal desymmetrization of the pathway to C, - i.e. to the true molecular symmetry of the product -is called for. The methylene bridge of cyclopentadiene is innocuous so, as it turns out, is the bridging carbonyl group in tropone. It will become evident from subsequent examples, however, that the presence of heteroatoms and/or multiple bonds can make a substantial difference to the conclusions drawn from an orbital symmetry analysis. 

Determine the symmetries of the resultant moleeular orbitals in the D3h point group. Draw a qualitative orbital energy diagram using the HMO energies you have ealeulated. 

Tabic 6-2. Correlation diagram of the C2/, point group of the isolated T6 molecule (left column) with the C2i, factor group for solid T(, (right column) via the site symmetry C group (center). L, M, and N indicate the principal molecular transition dipole moments, while a, b, and c arc the crystalline axes. 

The MOs and electronic states of carbene have been discussed in Chapter 7. The orbital and state correlation diagrams for addition of CH2 to ethylene is shown in Figure 14.9. The Walsh bonding picture for the MOs of cyclopropane requires that the and a MOs of the ethylene also be included in the diagram. The a2 and least-motion pathway preserves a vertical plane of symmetry (as well as the other elements of the C2v point group), and the... 

A flowchart for assigning point symmetry. The symmetry elements, and the rules and procedures for their use in determining the symmetry of molecules, can be formalized in a flow chart such as that shown in Fig. 3.16. It contains all of the point groups discussed above (enclosed in square boxes) as well as a few others not commonly encountered. In addition, the symmetries assigned above by inspection may be derived in a more systematic way by the use of this diagram. 

It will be realized that the values of n and m of A will depend on the metal site symmetry and n will only have even values for states of the same parity. In a frequently overlooked paper Eisenstein [554] tabulated the symmetry classifications of the metal ion and ligand orbitals for most of the point group site symmetries of interest. These classifications are often very useful in constructing a molecular orbital energy diagram. Predictions regarding the number and classification of the excited electronic states can then easily be made with the help of such diagrams. We will, however, resist the temptation to reproduce those tables here, in order to conserve space, as they are easily available. 

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