Calculation of the vibration–rotation line intensities in the Raman spectra of gases

Abstract

The method of irreducible tensorial sets is used for deriving general formulae describing the intensities of vibrationrotation Raman lines of molecules of different symmetries. Using this method, generalization of the parameters characterizing isotropic, anisotropic and antisymmetric scattering. taking into account vibratiowrotation interactions, has been carried out. The effect of vibration-rotation interactions on the Raman scattering cross-section is considered. IISTRODUCTION-A general formalism for the calculation of the Raman inlensities of vibration-rotation lines (scattering crosssections) of gases, including different intramolecular interactions, is described.The intensity of the i + j vibration-rotation molecular transition is known to be determined by the square of the matrix element (i I C I j) of the scattering tensor C for both spontaneous Raman scattering (see, e.g., Refs 1-5), and coherent anti-Stokes Raman scattering (Refs 6 and 7 and references cited therein), or resonance RamanIn the formulae for line intensities, in addition to the matrix elements (il C l j ) , some thermodynamic parameters (e.g. temperature and pressure) and parameters characterizing intramolecular states (e.g. energy, line centres and partition function) are involved. However, it is the calculation of the scattering-tensor matrix elements which is a matter of greater difficulty, because the eigenfunctions 1 i), l j ) of the molecular vibration-rotation Hamiltonian should be known for such calculations (for the vibrationrotation molecular Hamiltonian see, e.g., Refs 11-13).The effect of vibration-rotation interactions on the Raman scattering line intensities of different polyatomic molecules has been considered previously in a number of papers. A comprehensive review of these papers was given by Brodersen.' In the same paper,' general formulae for precise calculation of the matrix elements (i 1 M l j ) have been discussed for different types of polyatomic molecules. In this case M is a polarizability tensor; 1 i:> are the eigenfunctions of the molecular vibrationratation Hamiltonian: aR ' are the vibrational functions describing the system of non-interacting harmonic oscillators : I Jmk) are the rotational symmetric-top eigenfunctions; A : , , , are the expansion coefficients. These coefficients could be determined by, for example, diagonalization of the H-Hamiltonian matrix constructed on functions 16) I Jmk). However, because of the infinite dimension of the matrix, this problem cannot be solved. It would be possible to use perturbation theory for determining the coefficients However, even the use of this theory does not improve the situation, since one needs to know the parameters of the initial Hamiltonian (in particular, the parameters of the intramolecular potential function, or the parameters describing different electronic states). Therefore, in Ref. 5 and the papers listed there, not exact [Eqn (l)] but approximate functions of the form are used for analysing and calculating matrix elements of the polarizability tenso...