Estimation of Vibrational Frequencies and Vibrational Densities of States in Isotopically Substituted Nonlinear Triatomic Molecules

Abstract

For use in unimolecular reactions, a simple method is introduced for obtaining the unknown vibration frequencies of the many asymmetric isotopomers of a molecule from those of the symmetric ones. The method is illustrated for a triatomic molecule XYZ, ozone. It is based on the neglect of a single G matrix element in the GF expression for XYZ, yielding for it a block-factored expression of the XYX type for the frequencies of all the isotopomers XYZ. It agrees with available data to the accuracy needed, a few cm -1 . The first-order perturbation vanishes. (The zeroth-order case is not a symmetric molecule since it contains all three masses.) A simple second-order perturbation result for the GF matrix using data for one asymmetric isotopomer then provides agreement to about 1 cm -1 . The virtues of the method are its simplicity, transparency, and novelty, though normally one would use much more general methods such as ASYM 20 or 40. The method itself is not restricted to triatomic molecules.

Anomalous oxygen isotope enrichment in CO2 produced from O+CO: Estimates based on experimental results and model predictions

“…There is considerable difference ͑40‰-50‰͒ between the enrichments observed in 18 O/ 16 O and 17 O/ 16 O ratios of CO 2 produced in 70 cc reaction vessel ͑sets 1 and 2͒ and in 5 l reaction chamber ͑sets 3 and 4͒. The exact reason for this difference is not clear but part of it could be due to the effect of surface.…”

“…Marcus and co-workers [13][14][15][16][17][18][19] proposed and developed a phenomenological theory, which has been fairly successful to explain many features of the unusual isotope effect associated with ozone formation processes. Marcus and co-workers [13][14][15][16][17][18][19] proposed and developed a phenomenological theory, which has been fairly successful to explain many features of the unusual isotope effect associated with ozone formation processes.…”

“…16 O abundance ratios close to that of the O 2 was made ͑by converting nearly 100% of O 2 by Tesla discharge͒. In sets 1-3 ozone was dissociated by visible light to produce O atoms whereas in set 4, O atom was produced by dissociating pure O 2 with UV light ͑as in BT͒.…”

“…Mauersberger 1 observed that the ozone in stratosphere is enriched in 18 O by as much as 400‰ relative to air oxygen. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] In recent years, measurement of specific rate coefficients [24][25][26][27] of several possible ozone forming channels has brought out the complexities of the isotopic enrichment process. [4][5][6][7][8] Early attempts to explain these anomalous isotope effects lead to the conclusion that symmetry controls the relevant fractionation process.…”

“…Later, evidence of mass independent enhancement of two heavy isotopologues of ozone ͑ 49 O 3 and 50 O 3 ͒ was reported for stratosphere 2,3 as well as in ozone produced in the laboratory. A phenomenological theory [13][14][15][16][17][18][19] has been proposed recently based on a modification of the standard Rice-Ramsperger-Kassel-Marcus ͑RRKM͒ model of unimolecular dissociation, which calculates isotopic fractionation in ozone produced by O + O 2 recombination reaction under restrictions of symmetry. During the last 25 years, several theoretical models have been proposed to explain this anomalous enrichment.…”