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Ideas of Quantum Chemistry P98

Ideas of Quantum Chemistry P98 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 936 C. GROUP THEORY IN SPECTROSCOPY Now only those ÿi are allowed in optical transitions from the ground state Ag that are labelled by B3u because only the direct product B3u x B3u may contain the fully symmetric irreducible representation Ag. Thus the transitions Ag B3u as well as B3u Ag are allowed if the light is polarized along x i.e. perpendicular to the ring of the molecule. polarization y Now let us take light polarized along y i.e. within the molecular plane perpendicularly to the N-N line. This time we are interested in the irreducible representations that arise from Ag x B2u because y transforms according to B2u. Very similarly by analyzing a a we find that Ag x B2u B2 . This means that the allowed states are now of the B2u type. polarization z Similarly for polarization along z z belongs to B1u i.e. along the nitrogennitrogen direction we have Ag x Bi Bi . Thus for polarization parallel to the NN axis of the molecule absorption may occur from the ground state to any state of the B1u type and vice versa . Nothing more can be said when relying solely on group theory. We will not get any information about the energies of the transitions or about the corresponding intensities. To get this additional and important information we have work hard to solve the Schrodinger equation rather than count on some easy profits obtained by the primitive multiplication of integers as in group theory . To obtain the intensities we have to calculate the transition moment integrals kl. However group theory transition by excluding from the spectrum many transitions forbidden ones provides a lot moment of important information on the molecule. Table C.7 collects the calculated light frequencies41 v in wavenumbers or cm-1 v cv where v is the usual frequency the oscillator strengths fki in a.u. fki 4P v ki 2 C.28 as well as the polarization of light for excitations from the electronic ground state for pyrazine and the pyrazine monocation. It is seen that the left-hand side of .