A New Java Program for Graphical Illustration of the Franck−Condon Principle:: Application to the I2 Spectroscopy Experiment in the Undergraduate Physical Chemistry Laboratory

• George Lucchese ^[1] ; Robert R. Lucchese ^[1] ; Simon W. North ^[1]
  1. [1] Texas A&M University

     Texas A&M University

     Estados Unidos

     
• Localización: Journal of chemical education, ISSN 0021-9584, Vol. 87, Nº 3 (March), 2010, págs. 345-345
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Requires FCIntensity.jar Themeasurement and subsequent analysis of I2 absorption and emission spectra is a standard experiment in the undergraduate physical chemistry laboratory (1-5). The observation of interesting intensity alternations in the dispersed fluorescence spectrum and the lack of clear alternations in the absorption spectrum are a manifestation of the Franck-Condon principle, which is an important concept in physical chemistry.

    Discussion of the Franck-Condon principle, although often neglected in the undergraduate curriculum, can illustrate the connection between vibrational eigenfunctions and transition probabilities.

    We have developed a portable, flexible, and user-friendly program to illustrate the relationship between Franck-Condon factors and the observed spectral intensities. Students also explore the effects of changing spectroscopic parameters on the predicted spectra. FCIntensity is a Java program that computes the eigenfunctions and eigenvalues of the Morse oscillator Hamiltonian using numerical methods. The program is easily uploaded and implemented on a personal computer and permits facile manipulation of input parameters (Figure 1).

    As part of the analysis of our I2 laboratory, the students are given the ground state Re (2.6664 Å) value and asked to obtain the best-fit B-state Re by comparing the calculated intensity distribution to experiment. Although the calculated intensity patterns do not exactly match experiment (given the Morse approximation that can be discussed), only B-state Re values near 3 Å provide an acceptable fit. The remarkable sensitivity is surprising to most students. The comparison between calculation and experiment also reveals the dependence of the spectrum to other parameters. For example, changes in Te, ve, and De for the B-state result in shifts of the spectral positions of all emission lines, while changes in De and ve for the ground state result in changes in the spacing between emission lines.

    Once the emission spectrum has been analyzed, we ask the students to use the program to simulate the measured absorption spectrum using the same parameters. Calculations using v00 =0, 1, 2 provide visual confirmation of the location of the hotbands and, through inspection of the vibrational wave functions, the origins of the nonoscillatory behavior relative to the emission spectrum.