Spin-Orbit Coupling and Conical Intersections

When spin-orbit coupling is included in the Hamiltonian, new, qualitatively different effects appear in the radiationless behavior of the system. Two effects are particularly important. First, the spin-orbit interaction can couple states of different spin multiplicity whose intersection otherwise would not be 

Mathematical properties of the time reversal operator relate the matrix elements appearing in the Hamiltonian. More specifically, only two unique off-diagonal matrix elements and two unique diagonal matrix elements exist. The conditions that must be satisfied for degeneracy are as follows  

Using the conditions in Eqs. [47]-[49] and perturbation theory near a conical intersections, algorithms based on the Lagrange multipliers method were developed. These techniques can locate conical intersections when the spin-orbit coupling is included in the Hamiltonian with perturbative methods.  

A system in which this effect has been studied is the reaction of molecular hydrogen with the electronically excited hydroxy radical, 

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