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In this paper we present two new algorithms to study the extended nature of the crossing seam between electronic potential energy surfaces. The first algorithm is designed to optimize conical intersection geometries:  both minima and saddle points. In addition, this method will optimize conical intersection geometries using arbitrary geometrical constraints. We demonstrate its potential on different crossing seams of benzene, z-penta-3,5-dieniminium, and 1,3-butadiene. The second algorithm is designed to explicitly compute the intersection-space minimum energy coordinate. Our computations show how an intersection seam and the energy along it can be unambiguously defined. A finite region of the S0/S1 1,3-butadiene crossing seam has been mapped out, and a new saddle point linked with two lower-lying geometries on the seam.

New Algorithms for Optimizing and Linking Conical Intersection Points