Accidental 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... 

Matsika S, Yarkony DR (2002) Accidental conical intersections of three states of the same symmetry. I. Location and relevance. J Chem Phys 117 6907... 

Intersections are symmetry-required when the two electronic states form the components of a degenerate irreducible representation. The Jahn-Teller intersection of the two lowest electronic states in Nas which correspond to the components of an E irreducible representation of the point group Csv, provides an example of this class of conical intersection. Conical intersections which are not required by symmetry are accidental intersections. Accidental symmetry-allowed different symmetry) intersections correspond... 

The Sx and Sy, Agh and Sgh describe the tilt, asymmetry and pitch of the double cone, and Sy describe the tilt of the principal axis of the cone. Agh describes the asymmetry in the pitch of the cone, which is measured by 6gh- The electronic state symmetry classification of the conical intersection is reflected in these topographical parameters. The syirmietry required double cone characteristic of the extensively studied Jahn Teller problem " has Sx = Sy = 0, and g = hhy symmetry so that q = g and Agh = 0. It is therefore a vertical (non-tilted) symmetric, Agh = 0) cone. For the accidental symmetry-allowed conical intersection only Sy... 

Fig. 6.7 Perspective drawing of a rotationally symmetric three-state ( triple ) conical intersection such as occurs, for example, at an accidental crossing of a doubly degenerate state with a nondegenerate state. The coordinates are the components of a doubly degenerate mode, causing a linear coupling between the electronic states...

Tor example, molecules with higher than twofold symmetry axes may have degenerate states whose wavefunctions necessarily break symmetry, as a consequence of the Jahn-Teller theorem. In these cases singularities (so-called conical intersections) arise as a result of state crossings and are not artifactual. State crossings can also occur accidentally, when only a plane or a twofold axis of symmetry is present, and the Jahn-Teller-type effects that result also create conical intersections on potential energy surfaces. 

Most molecular systems in nature have little or no symmetry, and it is in these systems that accidental conical intersections often exist. Locating accidental points of degeneracy is more difficult than the previous cases because there is no symmetry that can be used for guidance. This difficulty, along with the misinterpretation of the noncrossing rule, delayed the appreciation of accidental conical intersections. One of the early cases where accidental... 

The first accidental conical intersections based on ab initio methods were found for triatomic systems LiNaK, and for CH even before the availability of automatic search algorithms. Later, the availability of algorithms allowed for the study of many small systems. Systems greatly affected by conical intersections are small radicals important in atmospheric and combustion chemistry, and these systems have been studied extensively. Experimental spectroscopic studies of conical intersections are possible for Jahn-Teller systems, and typical radicals like C5H5 and CgH have been studied by Miller et al. " A main advantage of small systems is that they are... 

Conical intersections usually appear in the Jahn-Teller form in inorganic transition metal complexes because the high symmetry of such complexes allows for this symmetry-required type of conical intersection. For example, studies of complexes of metals with carbonyls revealed that conical intersections facilitate the photodissociation of CO. It should be noted, however, that a sufficient amount of work has not been done yet in this area to reveal whether accidental conical intersections exist and what role, if any, they play in photodissociation. As a result of the larger spin-orbit coupling in transition metal systems, there exists a higher probability for spin-forbidden transitions (intersystem crossing) than in nontransition metal systems. Matsu-naga and Koseki have recently reviewed spin-forbidden reactions in this book... 

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. 

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. 

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