Conical intersections permutational symmetry

In Chapter VIII, Haas and Zilberg propose to follow the phase of the total electronic wave function as a function of the nuclear coordinates with the aim of locating conical intersections. For this purpose, they present the theoretical basis for this approach and apply it for conical intersections connecting the two lowest singlet states (Si and So). The analysis starts with the Pauli principle and is assisted by the permutational symmetry of the electronic wave function. In particular, this approach allows the selection of two coordinates along which the conical intersections are to be found. 

Invariant operators, permutational symmetry, conical intersection, adiabatic state, 735-737... 

Longuet-Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation, 154-155 three-state molecular system, 134-137 two-state molecular system, single conical intersection solution, 98-101 permutational symmetry, degenerate/near-degenerate vibrational levels, 730-733 Polyene molecules ... 

Spin-degenerate systems, geometric phase theory, conical intersections, 6-8 Spin function, permutational symmetry, group theoretical properties,... 

Spin multiplicity, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 706-711 Spin-orbit coupling conical intersections ... 

The second reason is the permutational symmetry. Very often, the system contains the same kinds of nnclei. Any exchange of the positions of such nuclei moves the point representing the system in configuration space to some distant regions, whereas the energy does not change at all. Therefore, any PES has to exhibit the corresponding permutational symmetry. All the details of PES will repeat M times for a system with M identical nuclei. This will multiply the number of conical intersections. 

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