Accidental conical intersections of three states of the same symmetry. I. Location and relevance

An efficient algorithm for locating conical intersections of three states of the same symmetry is presented. The algorithm, which derives its efficiency from the use of analytic gradient techniques, is used to locate a three state intersection for the excited $3p$ Rydberg states of the ethyl radical. The existence of a seam of three state conical intersections in a $3p$ Rydberg manifold is expected to be a general occurrence.