An overview is given of various results of ab initio quantum dynamical simu
lations on conically intersecting potential energy surfaces. Here, the nona
diabatic coupling effects are typically very strong, leading to a femtoseco
nd (fs) population decay of the upper electronic state and to a diffuse app
earance of the corresponding band in the electronic spectrum. For the lower
electronic state we demonstrate the possibility of a bifurcation of the wa
vepacket that can lead to a manifestation of the geometric phase. The examp
les chosen to illustrate these phenomena are triatomic hydrogen, sulfur dio
xide, and the radical cation of benzene. The latter systems features a comp
lex "web" of different multidimensional, partly coalescing, conical interse
ctions between up to eight potential energy surfaces. The resulting stepwis
e femtosecond decay processes give rise to a highly complex vibronic dynami
cs that is currently being modeled to an increasing degree of sophisticatio
n. (C) 2000 John Wiley & Sons, Inc.