Junkai Xie* and Jonathan Tennyson

Department of Physics & Astronomy, University College London, London, WC1E 6BT, UK

* Department of Chemistry, Sichuan Normal University, Chengdu 610066, PR CHINA
 

Methane is the third most important greenhouse gas and is present in many planetary atmospheres. The way methane absorbs and emits light remains poorly understood, particularly when it is hot. A better theoretical understanding of the methane rovibrational spectrum would undoubtedly lead not only to more information being obtained from the astronomical spectra, but also to better modeling of methane in many other situations. Some variational vibration-rotation calculation have already been performed for methane. However these studies are tractable because they make approximations based on the molecule being semi-rigid. It is unlikely that these approaches will be reliable for the highly excited states necessary to treat the hot methane problem. Here we report on progress in developing a full variational treatment of the methane rotation-vibration problem. The procedure we have adopted is general to AX4 type molecule and makes no assumption about any decoupling in their potential energy surface. This lack of decoupling leads to perform full nine-dimensional quadrature over the potential. However this cost is moderated by taking advantage of the symmetry inherent in these AX4 systems, itself a subject of considerable study.
So far we have developed a procedure for treating the stretching and bending motion of methane. For the non-rotating methane, the vibrational motions can be divided into stretches (four coordinates) and bends (five independent coordinates). Here, our strategy is to solve separate, reduced Hamiltonian for the stretches and the bends, and to use the results of these to solve the full coupled problem.
For the stretch problem, we evaluate the kinetic energy matrix elements for each of five possible total symmetry types and eight different basis types. A similar approach is used to deal with the bending methane vibration (five dimensional problem) in symmetry coordinate variables. These coordinates lead a very complicated symmetrized wavesfunctions. To overcome this problem, we transform the coordinates. In the new coordinate system, we use Jacobi polynomial for the four degrees of the angular motion, and the sine and cosine function for the other angle. For the bends, we also evaluate the bends kinetic energy matrix each of five possible total symmetry types  and 12 different basis types. Results of the separate stretching and bending calculation will form a basis of the fully coupling nine dimensional methane vibration problems.