Triple conical intersection

Fig. 4. Perspective drawing of a triple conical intersection arising for the PJT potential energy surfaces of Eq. (30). While the upper and lower surfaces (V+ and V ) are identical to the Mexican hat surfaces of Fig. 1, the additional surface (Vb) represents the unperturbed harmonic oscillator potential. For more details see text.

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...

In the nonrelativistic case, at a given the quantity x was shown to be invariant under the hansformation in Eq. (16), for a = y = 0. This invariant, whose value depends on was used to systematically locate confluences, [18-21], intersection points at which two distinct branches of the conical intersection seam intersect. Here, we show that the scalar triple product, gij X is the invariant for q = 3. Since the g t, and h cannot be... 

Surfaces with good description of the conical intersection include work by Mahapatra et al. [252], computed at the MRCI level with a triple zeta basis set, but dissociation is not considered. There is also an effective Hamiltonian by Joyeux et al. [202] to describe the conical intersection region. 

The triple intersection of Eig. 6.7 deserves special mentioning with respect to low-energy vibronic motion. It has been pointed out above that the surface topology near a degeneracy (conical or not) is not of central importance for the strength of the nonadiabatic coupling effects. Eor low-energy motion this shape does matter. 

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