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Determine the point groups for a triangular prism .
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- Show that any two of the irreducible representations of the following point groups are orthogonal to each other. a C2 b C2v c D2h d Oh e TdWhat are the number of classes and the order of the following point groups? a C2v b D2h c D6h d S4 e Cs.Show that any irreducible representation of these point groups is normalized. a C2 b D2d c Oh d C4h e C6v
- Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S.Identify all the symmetry elements present in the tetrahedron, the cube, and the octahedron.Determine which single symmetry operation of the following point groups is equivalent to the given combination of multiple symmetry operations. a In C2v, C2v=? b In C2h, iC2=? c In D6h, C6h=? d In D2d, C2C2=? e In Oh, iS4=?
- Identify the symmetry elements present in the following objects. a The Eiffel Tower. You may have to look up a picture of it if you dont remember its shape b Any book ignore the printing. c An octagonal wood block. d A jack from the set of jacks pictured here: Note that some of the points end differently.Identify the symmetry elements present in the following objects. a A ream of blank paper, no holes. b A ream of blank three-holed paper. c A round pencil, unsharpened, with cylindrical eraser. d A round pencil, sharpened, with cylindrical eraser.Show that the irreducible representations of the D2d point group satisfy the closure requirement. You will have to use the great orthogonality theorem to reduce one combination.
- Determine the point group of the following molecules. a cis1,2 Dichloroethylene b trans1,2 Dichloroethylene c Toluene, C6H5CH3 d 1,3-Cyclohexadiene.In your own words, explain why an object that has more symmetry elements is said to have higher symmetry than an object with fewer symmetry elements.Determine the point groups of the following molecules. a Fe(CO)5, which has a trigonal bipyramidal structure, b CO32, which has three resonance structures that contribute to its overall shape, c The perfectly staggered conformation of ethane, d The perfectly eclipsed conformer of ethane.