On the conical intersection and the possibility of a new assignment for molecular systems

In this article we discuss new ideas regarding the effect of conical intersections on a multielectronic adiabatic manifold of eigenfunctions: (a) The conical intersections are used to break up the Hilbert space into sub-Hilbert spaces by demanding that these subspaces do not have common conical intersections with each other (in other words electronic states belonging to different subspaces do not form conical intersections). (b) A new concept, the topological spin, is introduced; it is shown that its value is closely related to the number of (Jahn-Teller) conical intersections in a given sub-Hilbert-space and that the values of the components are related to the possible number of electronic eigenfunctions that flip sign while surrounding the conical intersections. (c) A geometrical description for the above-mentioned sign conversions is introduced, and it is, also, shown that this description agrees nicely with the results obtained from the topological matrix D. This geometrical, qualitative-type picture is supported by a quantitative analysis based again on the line integral.