| Summary: | This thesis concerns the theoretical development and implementation of a second-oider description of conical intersections. Several novel methodologies are presented and new aspects of the field are discussed. The conditions leading to a Born-Oppenheimer failure are outlined and a general formulation ofthe second-order description of conical intersections is introduced. Topological features of the two crossing potential energy hypersurfaces are investigated, and an analytical description of the crossing energy is proposed. This formulation yields an analytical definition ofthe intersection-space seam energy Hessian. A set of examples is then presented to demonstrate the applicability of the intersection-space frequency analysis to photochemical and Jahn-Teller problems. The definition of an intersection-space Hessian has allowed us to develop a new and more efficient conical intersection optimization algorithm. Aspects of its implementation and performance on different crossing seams are discussed in detail. As a consequence of using a better defined Hessian, a smother and faster convergence is achieved. Moreover, the possibility of optimizing saddle points on the crossing hyperline is also investigated. A novel algorithm to compute the minimum energy coordinate within the space of intersection is presented. This coordinate connects three points uniquely within the intersection space: two minima through a saddle point. The efficiency ofthe algorithm has been analysed and its possible applications to photochemical problems are discussed. Finally, a new methodology to select the relevant modes in a photochemical reaction is described, which exploits the second-order description of conical intersections. Theoretical predictions are shown to be consistent with dynamics studies on the internal conversions of ketene and benzene.
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