Conical intersection of potential energy surfaces

Figure 4.2. Conical intersection of potential energy surfaces with different symmetries with respect to a symmetry element which is present only along the X, axis a) cross section along this x, axis b) three-dimensional representation, with symmetry lowering along the x axis (adapted from Lorquet et al..

Bearpark MJ, Larkin SM, Vreven T (2008) Searching for conical intersections of potential energy surfaces with the ONIOM method application to previtamin D. J Phys Chem A 112 7286-7295... 

The stoi7 begins with studies of the molecular Jahn-Teller effect in the late 1950s [1-3]. The Jahn-Teller theorems themselves [4,5] are 20 years older and static Jahn-Teller distortions of elecbonically degenerate species were well known and understood. Geomebic phase is, however, a dynamic phenomenon, associated with nuclear motions in the vicinity of a so-called conical intersection between potential energy surfaces. 

The import of diabatic electronic states for dynamical treatments of conical intersecting BO potential energy surfaces is well acknowledged. This intersection is characterized by the non-existence of symmetry element determining its location in nuclear space [25]. This problem is absent in the GED approach. Because the symmetries of the cis and trans conformer are irreducible to each other, a regularization method without a correct reaction coordinate does not make sense. The slope at the (conic) intersection is well defined in the GED scheme. Observe, however, that for closed shell structures, the direct coupling of both states is zero. A configuration interaction is necessary to obtain an appropriate description in other words, correlation states such as diradical ones and the full excited BB state in the AA local minimum cannot be left out the scheme. 

More generally, the integral may also equal a multiple of tt in view of the trigonometric functions in Eq. (9), and the diabatic wavefunctions (10) still be well defined. A value of tt is expected when encircling a conical intersection between potential energy surfaces in order to compensate for the singularity of the adiabatic wavefunctions (see also Chapters 1 and 7 in this book). In the ideal case, Eq. (22) is generalized as ... 

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. 

At minimum of the conical intersection on the upper sheet of potential energy surface. Rotation about the axis perpendicular to the plane of the molecule. 

Commonly, it is asserted that upward transitions from the lower adiabat to the upper one should be less likely than downward transitions because of the funneling property of the intersection [144,145]. This is clearly seen in the usual model conical intersection—as seen, for example, in Fig. 1 of Ref. 146, where there is (a) a well, or funnel, in the upper adiabat which guides the wavepacket to the intersection and (b) a peak on the lower adiabat which tends to guide the wavepacket away from the intersection. The potential energy surfaces shown in Fig. 7 differ from this canonical picture, and in particular it is not at all clear that the wavepacket on the lower adiabatic state will be funneled away from the intersection. For the conditions chosen in our calculations, we... 

At minimum of the conical intersection on the upper sheet of potential energy surface. 

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