Résumé
Analysis of the space of conical intersection is crucial for the understanding of photochemical and photophysical processes of molecules. This chapter presents our methodology to characterize the critical points of conical intersection and discusses applications to static and dynamic studies. The intersection space is treated as an analog of a Born-Oppenheimer surface. When second-order effects are taken into account (differences between the nuclear Hessians of the intersection states), the seam of intersection lies along curved coordinates, and the critical points are characterized with the second derivatives of the seam energy along these coordinates. This methodology is presented for a simplified three-coordinate model, and the generalization to a multidimensional problem is applied to the study of the intersection space in fulvene, which lies along a double bond isomerization coordinate. Our second-order analysis can also be used for the systematic selection of nuclear coordinates for quantum dynamics with a reduced number of modes. This selection scheme is applied to a quantum dynamics study of the photochemistry of benzene, where we study the competition between unreactive decay and formation of a prefulvenic product. Our study allows us to propose the vibrational modes that have to be stimulated to control the photochemistry.