Conical intersection

In quantum chemistry, a conical intersection of two or more potential energy surfaces is the set of molecular geometry points where the potential energy surfaces are degenerate (intersect) and the non-adiabatic couplings between these states are non-vanishing. In the vicinity of conical intersections, the Born–Oppenheimer approximation breaks down and the coupling between electronic and nuclear motion becomes important, allowing non-adiabatic processes to take place. The location and characterization of conical intersections are therefore essential to the understanding of a wide range of important phenomena governed by non-adiabatic events, such as photoisomerization, photosynthesis, vision and the photostability of DNA. The conical intersection involving the ground electronic state potential energy surface of the C₆H₃F₃⁺ molecular ion is discussed in connection with the Jahn–Teller effect in Section 13.4.2 on pages 380-388 of the textbook by Bunker and Jensen.^[1]

Conical intersections are also called molecular funnels or diabolic points as they have become an established paradigm for understanding reaction mechanisms in photochemistry as important as transitions states in thermal chemistry. This comes from the very important role they play in non-radiative de-excitation transitions from excited electronic states to the ground electronic state of molecules.^[2] For example, the stability of DNA with respect to the UV irradiation is due to such conical intersection.^[3] The molecular wave packet excited to some electronic excited state by the UV photon follows the slope of the potential energy surface and reaches the conical intersection from above. At this point the very large vibronic coupling induces a non-radiative transition (surface-hopping) which leads the molecule back to its electronic ground state. The singularity of vibronic coupling at conical intersections is responsible for the existence of Geometric phase, which was discovered by Longuet-Higgins^[4] in this context.

Degenerate points between potential energy surfaces lie in what is called the intersection or seam space with a dimensionality of 3N-8 (where N is the number of atoms). Any critical points in this space of degeneracy are characterised as minima, transition states or higher-order saddle points and can be connected to each other through the analogue of an intrinsic reaction coordinate in the seam. In benzene, for example, there is a recurrent connectivity pattern where permutationally isomeric seam segments are connected by intersections of a higher symmetry point group.^[5] The remaining two dimensions that lift the energetic degeneracy of the system are known as the branching space.