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The goal of the present work is to predict the infrared (IR) spectrum of methane (CH4), which is of great interest to many areas in the Space Science Enterprise. These areas include the study of the atmospheres of Jupiter-like planets and the study of brown dwarfs.
The IR spectrum of methane has been studied extensively in the laboratory, but the complexity of the spectrum has severely hampered its study. Only the stronger bands arising from low-lying vibrational levels have been analyzed, and these data are insufficient for Space Science applications.
In principle, most of the problems of experimental studies can be circumvented by theoretical results, but theory must overcome many new problems. The main difficulty lies in obtaining results that are of useful accuracy. Many theoretical studies of the energy levels of CH4 have been performed, all using a quartic expansion of the potential energy surface (PES). In all cases, the quartic PES parameters were determined either by ab initio electronic structure calculations or by least-square fitting to experimental energy levels.
The present study examined the question as to whether or not a quartic PES is sufficient to predict uncharacterized energy levels. Ab initio electronic structure calculations of an octic PES for CH4 were made and compared with the results of the PES truncated to a quartic expansion. These calculations advance the state of the art in theoretical spectroscopy in two respects. First, they were the first calculations to compute an octic PES for a molecule containing five atoms. Electronic structure calculations were made at nearly 8000 geometries using a high-level theoretical technique. Second, the vibrational calculations were the first to use an accurate kinetic energy operator. Thus for the first time it was possible to make predictions of the energy levels of CH4 with confidence.
The study produced several major conclusions. The quartic representation of the PES only qualitatively represents the octic PES in the low energy regime. As the energy goes up, the quartic expansion can be grossly in error. In addition, the errors in previous theoretical studies based on second-order perturbation treatments of the vibrational energy levels were found to be commensurate with the errors in the quartic PES. Thus it is consistent to use a quartic PES with second-order perturbation theory to estimate low-lying energy levels. However, using the quartic PES with a more accurate determination of the vibrational energy levels is not consistent. In particular, optimizing the quartic PES to match observed energy levels should not yield reliable predictions of uncharacterized energy levels. Finally, the ab initio octic PES produced energy levels that agreed well with all characterized experimental energy levels.
Although the present accuracy is not yet sufficient to satisfy the Space Science Enterprise needs, significant progress is quite possible in the near future.
A detailed account of the present work can be found in D. W. Schwenke and H. Partridge, Spectrochimica Acta, vol. 57, page 887-895 (2001).
Point of Contact: D. Schwenke
(650) 604-6634
schwenke@pegasus.arc.nasa.gov
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