A mass-dependent fractionation model for the photolysis of stratospheric nitrous oxide G. A. Blake a, M. C. Liang b, C. G. Morgan a, Y. L. Yung a This poster is organized by M. C. Liang a Division of Geological & Planetary Sciences, Caltech , Pasadena, CA USA b Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box , Taipei, 106, Taiwan Reference 1 Matthew S. Johnson, Gert Due Billing, & Alytis Gruodis 2001, J. Phys. Chem. A. 105(38), Thom Rahn & Martin Wahlen 1997, Science, 278, Reinhard Schinke 1993, Spectroscopy and Fragmentation of Small Polyatomic Molecules, Cambridge University Press 4 Yuk L. Yung & Charles E. Miller 1997, Science, 278, 1778 Background Naturally occurring greenhouse gases include water vapor, carbon dioxide (CO 2 ), methane (CH 4 ), nitrous oxide (N 2 O), and ozone(O 3 ) along with industrially produced sulfur hexafluoride (SF 6 ). The continuing increase of nitrous oxide concentration (~0.25%/yr) in the atmosphere is a serious problem because it is an efficient greenhouse gas as well as the principal source of odd nitrogen that regulates the ozone layer. While N 2 O emissions are much lower than CO 2 emissions, N 2 O is approximately 310 times more powerful than CO 2 at trapping heat in the atmosphere (IPCC 1996). Since an accurate mass balance budget is not completely constructed, our ability to control this imbalance is limited. The increase is believed to result from fertilizer, waste management activities, emissions from combustion engines, biomass burning, and industrial processes. It is naturally produced by the microbial processes of nitrification and denitrification in soils and in the oceans and is destroyed in the stratosphere via photolysis (~90%) and reaction with excited atomic oxygen O 1 D (~10%). N 2 O + h ( E > 42,000 cm -1 ) N 2 + O( 1 D) (~90%) N 2 O + O( 1 D) 2NO (~ 6%) N 2 O + O( 1 D) N 2 + O 2 (~ 4%) Initial work on the total 15 N and 18 O of atmospheric nitrous oxide demonstrated that the stratosphere must return N 2 O enriched in the heavier isotopes to the troposphere in order counter the isotopically light nitrous oxide produced biologically. Environmental Protection Agency 1999 sources of N2O Model Since only the absorption cross section (dissociation, N 2 O NO + O) of the parent isotopologue of nitrous oxide has been determined in the laboratory within the wide wavelength range of interest, there is not enough information to study the enrichment of heavier isotopes due to photolysis. To set up an experiment to measure the dissociation cross section is expensive; therefore it is worthwhile to develop a good model to predict the cross section of isotopologues. Such a model, based the reflection principle, is described below. Reflection principle 3 We use the dissociation of diatomic molecule as a simple example. The classical Hamiltonian can be expressed in center-of-mass coordinates as H(R, P) = P 2 / 2 m + V(R), where R is the internuclear distance, P is the linear momentum, and m is the reduced mass. Then the dissociation cross section can be written as σ(E) ~ e -2  R (Rt-Re) 2 /h |dV/dR| -1 R=Rt(E), where Rt is the classical turning point defined by H(Rt, P) = E. ZPE model 4 To the first order, the absorption cross section of an isotopologue can be approximated as the shift of zero point energy (the shift of ground state energy). The cross section will shift to higher energy because of the heavier isotope substitution. The isotope cross section can be expressed as σ’(E+  ZPE) = σ(E) Contraction of wavefunction along with ZPE model In addition to the ZPE difference, we include the contraction of wavefunction, i.e. the contraction of ground state wavefunction with isotopic substitution. This contraction leads to significant changes in the region far from the resonance point (~185  m). 456: 14 N 15 N 16 O, 546: 15 N 14 N 16 O, 447: 14 N 14 N 17 O, 448: 14 N 14 N 18 O. N15(avg) refers to the average of the 456 and 546 enrichment factors. The white bars (with 2 σ errors) are the average of the observed enrichment factors in the atmosphere. The red bars are the enrichments factors from ZPE model. The blue bars are the enrichment factors from the model run using the modified cross sections of Johnson et al. 1, and the green bars are the enrichment factors from the model run using the formalism presented in the text. Results Nitrous oxide is believed to suffer an irreversible sink and the enrichment factor remains constant regardless of its concentration. This process is known as Rayleigh distillation 2, Ray = Ray 0 x f  - 1, where Ray and Ray 0 are the residual and initial isotope ratio and  is the ratio of reaction or photolysis rates and f here is the concentration of nitrous oxide. This relationship can be expressed as  =  0 +  x ln(f), where enrichment factor  = 1000(  - 1) in per mil (1/1000). In terms of absorption cross section, we can express  as the ratio of absorption cross sections,  = σ / σ 0. To take ZPE shift and contraction of wavefunction into account, the enrichment factor  can be approximated by where ZPE and ZPE’ are the zero point energy of the parent and isotopically substituted molecule, and  ZPE is the difference between ZPE and ZPE’. Applying this model to the atmosphere, the predicted enrichments of heavy isotopes is perfectly consistent with the experimental measurements within errors (see figure at right).