Symmetry-allowed conical intersections

The ordinary BO approximate equations failed to predict the proper symmetry allowed transitions in the quasi-JT model whereas the extended BO equation either by including a vector potential in the system Hamiltonian or by multiplying a phase factor onto the basis set can reproduce the so-called exact results obtained by the two-surface diabatic calculation. Thus, the calculated hansition probabilities in the quasi-JT model using the extended BO equations clearly demonshate the GP effect. The multiplication of a phase factor with the adiabatic nuclear wave function is an approximate treatment when the position of the conical intersection does not coincide with the origin of the coordinate axis, as shown by the results of [60]. Moreover, even if the total energy of the system is far below the conical intersection point, transition probabilities in the JT model clearly indicate the importance of the extended BO equation and its necessity. 

In Chapter VIII, Haas and Zilberg propose to follow the phase of the total electronic wave function as a function of the nuclear coordinates with the aim of locating conical intersections. For this purpose, they present the theoretical basis for this approach and apply it for conical intersections connecting the two lowest singlet states (Si and So). The analysis starts with the Pauli principle and is assisted by the permutational symmetry of the electronic wave function. In particular, this approach allows the selection of two coordinates along which the conical intersections are to be found. 

Teller19 was the first to point out that in a polyatomic molecule the noncrossing rule, which is rigorously valid for diatomics, fails. Rather, two electronic states, even if they have the same symmetry, are allowed to cross at a conical intersection. Accordingly, radiationless decay from the upper to the lower intersecting state can occur within a single vibrational period when the... 

The photoinduced CO loss from Cr(CO)6 occurs following a symmetry and spin-allowed transition to produce the a 7 u MLCT excited state. A Jahn-Teller active (f2g bending) mode promotes motion to a conical intersection close to the Frank-Condon state. This provides an efficient barrierless transition to the E component derived from the a 7 g state. This process takes approximately 12.5 fs. The E component is unbound with respect to the M-CO interaction. As the M-CO bond lengthens a further conical intersection with the E component derived from the a 7, u state,... 

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... 

In an actual molecule, x and y correspond to molecular motions and can be described in terms of atom centered displacements. Figure 1(a) reports the g and h vectors at a conical intersection of the 1, states in BH2. In Fig. 1(a), the molecule has C v S3munetry and the intersection is a symmetry-allowed conical intersection. The g- or x-direction... 

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... 

We seek conditions under which W x, y, w) will be factorable. Consider the frequently studied case of a symmetry-allowed conical intersection of two states of different S3mimetry. Assume too that the molecule has a plane of symmetry, the least restrictive case. In this case, since x a and y a", where is read transforms as ,... 

In summary, we have demonstrated (a class of) confluences that is intimately related to molecular symmetry. These confluences constitute a subspace of a symmetry-allowed or different symmetry portion of the seam of conical intersection. The symmetry-allowed conical intersection has been over the years the most commonly studied type of conical intersection. Thus the comparatively recent discovery confluences would indicate that they are a rare occurrence. However, very recent work indicates instead that their only recent identification may reflect the limited data on the multidimensional character of conical intersection seams in tetra atomic and larger molecules. ... 

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