The Born-Oppenheimer separation of electronic and nuclear motions is a widely used approximation in molecular physics. Nonetheless, transitions between different electronic surfaces (non Born-Oppenheimer or non-adiabatic dynamics) represent a field of growing interest, because they appear to govern a large variety of fundamental processes, such as internal conversion, intersystem crossing, electron transfer and photoinduced reactions. Compared to Born-Oppenheimer dynamics, the study of non-adiabatic systems is made somewhat more complex by the fact that the Hamiltonian is a matrix instead of a scalar. For example, a 2x2 matrix is needed to describe two coupled electronic surfaces : the diagonal elements of the matrix are the Hamiltonians of the uncoupled electronic surfaces, while the off-diagonal terms account for the coupling between the two surfaces.

In this context, the conical intersection between the two lowest electronic surfaces of NO₂, which takes place at about 10000 cm^-1 above the quantum mechanical ground state (see figure below), has already attracted much attention from both the experimental and theoretical points of view. In particular, most of the experimental spectra were recorded in our University, in the group of R. Jost. My work in this field was precisely motivated by the need for a model, which would satisfactorily reproduce the experimental vibronic spectrum of NO₂ up to and above the region of the conical intersection.

For this purpose, we first derived a Canonical Perturbation procedure for non-adiabatic systems, which provided us with a good insight into the non Born-Oppenheimer coupling mechanism. Based on the conclusions of this study, we then proposed an efficient method for calculating the eigenstates and adjusting the parameters of an effective Hamiltonian in good agreement with the experimental spectrum.

We are now studying the non-adiabatic dynamics of NO₂ on the basis of this effective model.