Theoretical models of fractionation

Photolytic fractionation was put on firm theoretical footing beginning with the zero-point energy (ZPE) model of Yung and Miller (1997). During photolysis, N2O undergoes a transition from the electronic ground state to the continuum level B(1A). The larger mass of the isotopically substituted species lowers their ground-state energies, which shifts their absorption spectra to shorter wavelengths (Fig. 14.7). Since most photolysis occurs at wavelengths on the red side of the absorption peak, cross sections for 446 will be larger than for the heavy species and 446 will be photolysed preferentially, leaving the remaining pool enriched in the heavy species. As discussed earlier, the fractionation constant is the ratio of the heavy to light cross sections. The ratio, or fractionation constant, decreases with increasing wavelengths up to the absorp tion peak, where the model predicts that a crossover in the absorption spectra occurs, and the heavy cross sections become larger than the light ones, and the heavy species become depleted.

The model predicts the correct relational order between the heavy N2O fractionation constants, but its quantitative estimates of the constants are about a factor of 2 smaller than laboratory-based results (Rahn et al., 1998; Umemoto, 1999; Rockmann et al., 2000; Turatti et al., 2000; Zhang et al., 2000; Rockmann et al., 2001a). Improvements to the ZPE model using more sophisticated quantum mechanical calculations (Johnson et al., 2001; Blake et al., 2003; Liang et al., 2004) produce quantitative results in good agreement with experiments (Kaiser et al., 2003); though the best matches to the experimental fractionation constants are found using the high-resolution absorption spectra of Selwyn and Johnston (1981) (Kaiser et al., 2003).

Plot Fit Logistic Curve

Fig. 14.7. Schematic diagram illustrating the shift in the absorption spectrum for the heavy isotopologues. In the ZPE model (Yung and Miller, 1997), the additional mass of the heavy isotopologues decreases the ZPE level and blue-shifts the absorption spectrum, causing enrichment of the isotopologues at wavelengths longer than the peak absorption.

Fig. 14.7. Schematic diagram illustrating the shift in the absorption spectrum for the heavy isotopologues. In the ZPE model (Yung and Miller, 1997), the additional mass of the heavy isotopologues decreases the ZPE level and blue-shifts the absorption spectrum, causing enrichment of the isotopologues at wavelengths longer than the peak absorption.

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