Three-state conical intersections

Although the importance of two-state conical intersections in nonadiabatic processes has been established [10, 26], the occurrence and relevance of accidental three-state 

Re(S0) Rx(ci12) Rx(ci01) Rx2(ci012) Re(S0) Rx2(ci123 ) Rx(ci01) Rx(ci123) 

The discussion so far has focused on two-state conical intersections, which are the most common conical intersections, and which have been studied extensively. Three-state degeneracies imposed by symmetry have been studied in the context of the Jahn-Teller problem for many decades,but only minor attention had been given to accidental three-state degeneracies in molecules until recently. As most molecular systems in nature have low or no symmetry, these accidental intersections may have a great impact on the photophysics and photochemistry of those molecular systems, as has been found in accidental two-state intersections.Three-state degeneracies may provide a more efficient relaxation pathway when more than one interstate transition is needed. Moreover, they introduce more complicated geometric phase effects,and they can affect the system s dynamics and pathways available for radiationless transitions. 

Extending the noncrossing rule to three states being degenerate can best be understood by inspection of a 3 x 3 electronic Hamiltonian matrix instead of the 2x2 matrix as described earlier 

The first study on accidental three-state conical intersections was done for the CH cation by Katriel and Davidson. In a tetrahedral geometry, the ground state of CH is a T2 state. Therefore, it is triply degenerate as required by symmetry. Only one degree of freedom exists that will preserve Tj symmetry, and the dimensionality of the seam is one because all the requirements for degeneracy are satisfied by symmetry. The authors found additional three-fold degeneracies in this system even when the tetrahedral symmetry was broken. If no symmetry is present, the cation has 9 degrees of freedom and the dimensionality of the seam becomes 9 — 5 = 4. 

Efficient algorithms have recently facilitated the location of three-state conical intersections, and have identified the existence of such intersections 

Three-state conical intersections, like the two-state 

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Figure 11-16. Diagram of the energy levels at the two- and three-state conical intersections in uracil and adenine calculated at the MRCI level, ciIJK represents conical intersection between states Sj, S j, S -. (From Ref. [210])...

Coe JD, Martinez TJ (2005) Competitive decay at two- and three-state conical intersections in excited-state intramolecular proton transfer. J Am Chem Soc 127 4560... 

Coe JD, Martinez TJ (2006) Ab initio molecular dynamics of excited-state intramolecular proton transfer around a three-state conical intersection in malonaldehyde. J Phys Chem A 110 618-630... 

Matsika S, Yarkony DR (2003) Beyond two-state conical intersections. Three-state conical intersections in low symmetry molecules The allyl radical. J Chem Soc 125 10672... 

Matsika S (2005) Three-state conical intersections in nucleic acid bases. J Phys Chem A 109 7538... 

Here we are principally concerned with two-state conical intersections of Hq. However the algorithm discussed in this section is quite general, being applicable to the Af odd with the spin-orbit interaction included case rj = 5, or 3) and three-state conical intersections of Hq (also an rj = 5 problem). This generality is illustrated in the discussion that follows. 

A modified form of Eq. (18a) forms the basis of our algorithm in the case of a three-state conical intersection where... 

Kistler KA, Matsika S (2008) Three-state conical intersections in cytosine and pyrimidinone bases. J Chem Phys 128... 

Gonzdlez-Vdzquez, J., 8c Gonzalez, L. (2010). A time-dependent picture of the ultrafast deactivation of keto-cytosine including three-state conical intersections. A European Journal of Chemical Physics and Physical Chemistry, 11(17), 3617-3624. 

Figure 6 Energy levels at the two- and three-state conical intersection points using MRCI, (a) the So, Si, Si states of uracil and (b) the So, Si, Si, S3, S4 states of adenine. Rx(ciIJ) and Rx(ciIJK) denote conical intetsection between states /,/ ot I,J,K, tespectively. Reproduced with petmission from Ref. 94.

Two-state conical intersections have been well established in many types of molecular systems. In contrast, the study of three-state conical intersections is still in its infancy, and detailed studies are needed to understand the influence of these intersections on the dynamical behavior of molecules. 

S. Matsika,/. Phys. Chem. A, 109, 7538 (2005). Three-state Conical Intersections in Nucleic... 

Intersections. Three-state Conical Intersections in Low Symmetry Molecules The Allyl Radical. 

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