We present the ability to coherently control triatomic chemical reactions with pulsed-laser techniques. We show that one can control the final state probability distribution of triatomic chemical reactions with nearly 100% selectivity. We develop the population transfer by adiabatic passage theory to coherently control the chemical reaction with the ability of choosing the translational energies of the final reaction products. We also show a new way to achieve the creation of both homonuclear and heteronuclear diatomic molecules at an ultracold temperature using laser catalysis.

We also generalize the treatment of the geometric phase effect in a triatomic system which includes a seam of conical intersections. We derive generally how to include the geometric phase effect with nonlinear conical intersections in the C2v geometries with the Numerov propagation method. We develop a Mixed-Odd-Even-State method to simplify the conventional treatment of the generally complex Hamiltonian. We are the first group to develop the theoretical derivation of how to include geometric phase in a triatomic system where the seam of conical intersection are located in the collinear geometries. We show that the vector potential, for the collinear conical intersections, not only depends on the three internal coordinates but also on one of the Euler angles. The resultant Hamiltonian in the internal coordinates, after the integration of the three Euler angles, is a real Hamiltonian when the nuclear total angular momentum J is assumed to be zero.