Identification of molecular point groups

Exercise 2.4-1 Identify the symmetry point groups to which the following molecules belong. [Hint. For the two staggered configurations, imagine the view presented on looking 

Prove the following results by using projection diagrams. 

Two planes 7, a2 intersect along n and make an angle p/2 with one another. Show that 72 7 =R( j n). Do 71 and a2 commute  

7 Evaluate the following DPs showing the symmetry operators in each group. [Hint For (a)-(e), evaluate products using projection diagrams. This technique is not useful for products that involve operators associated with the C3 axes of a cube or tetrahedron, so in these cases study the transformations induced in a cube.] Explain why the DPs in (d)-(f) are semidirect products. 

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Consider the halogen-substituted cyclooctatetraenes with general formula CsHs- X, n = 0,1,2,..., 8. Write down which H atoms are to be replaced to obtain the isomers which have the following symmetries (i) Ci (ii) Csj (iii) Cij (iv) Civj (v) S4 (vi)Di. reference W.-K. Li, Identification of molecular point groups. J. Chem. Educ. 70,485-7 (1993). 

The theorems described in section 3.2 provide for the ready calculation of the r , and Fs reducible characters, generated by the transformation properties of s, p and d-atomic orbitals distributed over the vertices of the structure orbits of the various point groups, which decompose into the direct sums of irreducible components listed in Tables 3.1 to 3.4. Application of the theorems requires the identification of sufficient numbers of central harmonics to act as basis functions for the irreducible components of the regular orbits of these molecular point groups. 

At the outset, one must understand certain principles of GC to assess if it is a proper analytical tool for the purpose. If so, how to achieve the best separation and identification of component mixtures in the sample with reasonable precision, accuracy, and speed And what kind of detector and column should be selected for the purpose It is, therefore, important to examine the type of compounds that are to be analyzed and certain physical and chemical properties of these compounds. Information regarding the structure and the functional groups, elemental composition, the polarity in the molecule, its molecular weight, boiling point, and thermal stability are very helpful for achieving the best analysis. After we know these properties, it is very simple to perform the GC analysis of component mixtures. To achieve this, just use an appropriate column and a proper detector. Properties of columns and detectors are highlighted below in the following sections. 

The presence of the —OH group in a molecule is often indicated by the formation of an ester upon treatment with an acid chloride or anhydride (Sec. 18.16). Some esters are sweet-smelling others are solids with sharp melting points, and can be derivatives in identifications. (If the molecular formulas of starting material and product are determined, it is possible to calculate how many —OH groups are present.)... 

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