Développement complet du moment dipolaire des molécules tétraédriques. Application aux bandes triplement dégénérées et à la diade ν2 et ν4

Abstract

Using a coupling scheme in the Td group, we determine all the vibration–rotation operators of the dipole moment of XY4 molecules up to any order of approximation. We give the matrix elements for these operators and general formulas for the calculation of the infrared transition intensities. This general formalism is available for any transition between vibrational sublevels of any symmetry. It can be used for the analysis of isolated bands and for the simultaneous analysis of interacting bands as well. We show that this method can be applied to the calculation of Raman intensities and to XY6 molecules.In some cases, it is possible to carry out a tensorial extension from the Td group to the O(3) group. We have constructed the operators of the dipole moment adapted to this process using a coupling scheme in O(3). In particular, we give the matrix elements for a triply degenerate band.We use the contact transformation technique to explain the parameters introduced in the formal expansion of the dipole moment. We define the contact transformation operators in a tensorial form. We apply this method in the case of the two interacting bands ν2 and ν4.