A New Look at Carbonyl Electronic Transitions Giles Henderson Eastern Illinois University, Charleston, IL 61920 Formaldehyde has served as a useful model compound in the descri~tionof electronic s ~ e c t r of a the carhonvl chromophore (1-5). In the traditional analysis, group theory is employed to deduce the symmetry type of the various transition moment integrands to determine whether the corresponding integrals vanish. Students may thereby use symmetry properties of the appropriate molecular orbitals to determine if a given electronic transition is allowed or forbidden. Although this sort of analysis nicely illustrates the utility of group theory, it obscures the understanding of the underlvine . ...Drocess: What is eoine on durine the transition? How does the ground state electronic orbital evolve in time to the excited state molecular orhital? Whv is the transition polarized in the direction predicted by the symmetry analvsis? Moreover, if we naivelv assume that the electronic excited state of thekolecule heiongs to the same symmetry point group as the ground state, the analysis may predict that an experimentally observed transition is symmetry forbidden. In this paper the dynamics of the nuclear and electronic a * and n a * transitions of motion of the so called ir formaldehyde are calculated from approximate solutions of the time-dependent Schrodinger equation. Computer graphics are employed to animate the spatial and temporal properties of the electric charge density as the ground state molecular orhital evolves t o an excited state. These calculations provide a conceptually clear picture of the origin and direction of the transition moment and perhaps a new insight to the symmetry basis of selection rules.
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Table 1. m e G. Character Table
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Table 2. Molecular ParamMers ofFormaldehyde around state (9a) ~ C O
~CH
HCH
b
Symmetry
Using time-dependent perturbation theory and a semiclassical description of the interaction between radiation and matter, we can show (6) that the probability of a j k transition between two molecular states induced by the ahsorption of electromagnetic radiation is proportional to the square of the corresponding transition moment integral:
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where fij and f i k are the wavefunctions for the j and k states and fi is the electric dipole moment operator. This very important integral permits a theoretical calculation of the absorption band intensity or the integrated Beer's law absorption coefficient (7).Alternatively the transition moment integral may also be used to calculate the oscillator strength (8):
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where m, and e are the mass and charge of the electron, k transition frequency, and h is respectively, ujk is the j Planck's constant divided by 2s. Transitions that are quantum mechanicallv allowed are intense and have large - absorDtion coefficients and oscillator strengths approaching unify. In contrast. forhidden transitions have /
