Symmetry in Inorganic Chemistry Molecules Term Paper

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The overall molecule responds to symmetry operations in a manner that is captured by the behavior of the particular group to which the molecule belongs, individual atoms, bonds, atomic orbitals and any other component of the overall molecule may respond to symmetry operations in a variety of ways (Avetisov and Goldanskii). Therefore, there is a subclassification system associated with each point group to allow classification of the behavior or various submolecular parts of a molecule. All of the ways in which a particular bond, atom or set of atoms respond to a given set of symmetry operations are represented by a set of "irreducible representations," with their own cryptic labeling system and a list of characters, which can be found in character tables, the principle tool of group theory. The characters of a given irreducible representation in some more simple point groups behaves in the same way as the parts of the molecule that are said to belong to this irreducible representation.Buy full Download Microsoft Word File paper
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Term Paper on Symmetry in Inorganic Chemistry Molecules Assignment

Any object associated with a molecule can be labeled with one or more of these irreducible representation labels for purposes of classification (Avetisov and Goldanskii). For example, the water molecule, confined to the yz plane as is the modern convention, and oriented so that the z-axis bisects the molecule. The combination of the two hydrogen atoms of water, as an "object," can be considered with respect to the symmetry operations of the C2v point group. Rotation by 180 degrees about the principle axis leaves the hydrogen atoms in an indistinguishable position, as does reflection through either of its mirror planes. Therefore, the combination of two hydrogen atoms of water is said to behave as the "A1 representation" of the C2v point group. Other objects that transform in the same way are the in-phase combination of the 1s orbitals on each atom, the pair of O-H bonds, the symmetric stretching of the two O-H bonds, and each of the 1s, 2s, and 2pz orbitals on the oxygen. The characters for this irreducible representation in C2v are all +1, reflecting no change with respect to each element. In contrast, the py orbital on oxygen, and the antisymmetric stretching motion of the two O-H bonds are said to "transform as B2." The implications of this label are best understood through the characters for the B2 representation. These are +1, which reflect through the plane containing the molecule and E, or do nothing to the molecule, corresponding to operations that leave these objects unchanged after the operation. In contrast, the character to reflect through the plane perpendicular to the molecular plane and C2 or rotate by 180 degrees about the principle axis is -1, reflecting a change in sign of the wave function on such reflection or rotation, or a reversal in the direction of the stretching motion of each bond in the antisymmetric stretch.

Identifying the irreducible representation associated with a given bond, atom or sets thereof, is of great value for three reasons. First, it is a convenient way of labeling orbitals for reference. Second, one may determine which sets of atomic orbitals can combine with each other to form molecular orbitals. Third, one may determine the number and nature of vibrational motions for a given molecule to give the most common applications.

References

Avetisov, V., and V. Goldanskii. "Mirror Symmetry Breaking at the Molecular Level." Proc Natl Acad Sci USA 93.21 (1996): 11435-42.

Kitaev, Y.E., et al. "Why Biomolecules Prefer Only a Few Crystal Structures." Phys Rev E. Stat Nonlin Soft Matter Phys 67.1 Pt 1 (2003): 011907.… [END OF PREVIEW] . . . READ MORE

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