group of Dijon in France is illustrated with reference to the methane molecule (CH4
), a spherical top, in the gas phase. The theoretical study of this molecule is not easy. In our opinion, the Dijon approach appears to be the most complete, though it relies on a difficult mathematical formalism. Group theory methods are applied within the framework of the tensor formalism developed in Dijon. More than one chapter would be needed in the case of spherical tops, in order to tackle the various theoretical models elaborated for the calculation of the energy levels and the transitions between these levels. An outline of the model is given to study methane spectroscopy in the gas phase. Based on this theoretical model, applied to the lowest level in the vibration–rotation expansion, the effect of an environment on the spectroscopic characteristics of methane CH4
can be studied when it is embedded in various media, based on the symmetry considerations as presented in the first two chapters. Its application is illustrated on the dipole moment for the IR spectroscopy transitions of methane in the gas phase.
Pierre Richard DAHOO
Professor at University of Versailles St-Quentin
Senior Lecturer at University of Franche-Comté