Infrared Spectroscopy of Spherical Top (Td) Molecules A Physical Chemistry Experiment Thomas C. DeVore and Thomas N. Gallaher James Madison University, Harrisonburg, VA 22807 Group theory (symmetry) is one of the more powerful tools of quantum chemistry. I t can provide accurate qualitative answers to many problems without the use of complex numerical calculations. As a result, symmetry and group theory are now commonly discussed in introductory physical chemistry textbooks. (1-4) One practical application of group theory often discussed in these texts is the analysis of the infrared spectrum of a polyatomic molecule. As noted recently there is a need for more challenging exin THIS JOURNAL periments which expose the student to interpretation of spectra of polyatomic molecules (5). Since infrared spectroscopy of polyatomic molecules is also now receiving more coverage in many physical chemistry texts, a lahoratory experiment has been developed which uses group theory to help interpret the infrared spectrum of a polyatomic molecule with Td symmetry (spherical tops). Topics covered by this experiment include: 1) Use of group theory to determine infrared active modes of vibration. 2) Combination and overtone bands of polyatomic molecules. 3) Analysis of the rotational-vihrational spectrum of a polyatomic molecule. 4) Force constants of polyatomic molecules. Theory-Vibrational Analysis There are 3N - 6 normal modes of vihration in a polyatomic molecule. Consequently, the simplest spherical top (5-atom molecules like CH4, C C 4 , or TiC14) would have nine normal modes of vibration. However, in molecules like these which have high symmetry, several of the modes of vibration have the same frequency (i.e., they are degenerate). Thus the number of unique vihrational frequencies is less than the number of normal modes of vihration. Symmetry can be used to determine the number of unique vihrational frequencies and which of these frequencies should be found in the infrared (i.e., are infrared active). The method for determining the symmetry types of the normal modes of vibration can be found in several texts ( 1 4 , 6) and will not be discussed here. Complete analysis shows that the nine normal modes of vibration for 5-atom spherical top molecules produce only four unique frequencies. These vibrations, the standard spectroscopic notation, the symmetry type and degeneracy, and the infrared (IR) and Raman (R) activity of each are summarized in Figure 1. The intensity of an infrared band is proportional to the transitional dipole moment
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Journal of Chemical Education
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