Accidental symmetry-allowed

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 electronic state symmetry classifications described in the Introduction are contained in the properties of G and W. The intersection is symmetry required if Eqs. (6a) and (6b) are satisfied, provided only that X has the correct symmetry. The intersection is accidental symmetry-allowed, provided Eq. (6b) is satisfied when X has the correct symmetry. The intersection is accidental same-symmetry, provided symmetry does not guarantee that Eq. (6b) is satisfied. 

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... 

Deforming the geometry of Coulomb sources adiabatically is an allowed process, since these are classical variables the electronic energy, eq.(4), can only increase, but there cannot be a change of electronic state. The energy of two electronic states with the same space symmetry for a given a can be accidentally equal. Still, they cannot produce an "avoided crossing" in the sense of the BO picture. If each state represents, for instance, the reactants ( 1R>) and products ( 1P>), respectively, and the system is prepared as reactants, the matrix element... 

Symmetry operations apply not only to the unit cells shown in Fig. 2-3, considered merely as geometric shapes, but also to the point lattices associated with them. The latter condition rules out the possibility that the cubic system, for example, could include a base-centered point lattice, since such an array of points would not have the minimum set of symmetry elements required by the cubic system, namely four 3-fold rotation axes. Such a lattice would be classified in the tetragonal system, which has no 3-fold axes and in which accidental equality of the a and c axes is allowed. 

It was the Harvard physicist Meyer who in 1974 first recognized that the symmetry properties of a chiral tilted smectic would allow a spontaneous polarization directed perpendicular to the tilt plane [61]. In collaboration with French chemists, he synthesized and studied the first such materials [62]. These were the first polar liquid crystals recognized and as such something strikingly new. As mentioned before, substances showing a smectic C phase had been synthesized accidentally several times before by other groups, but their very special polar character had never been surmised. Meyer called these liquid crystals ferroelectric. In his review from 1977 [43] he also discussed the possible name antiferroelectric, but came to the conclusion that ferroelectric was more appropriate. 

The relatively low symmetry of the Ci, capped octahedron allows it to be oblate, prolate, or accidentally spherical depending on the L-M-L bond angles. 

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... 

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