Conical intersection displacement

In the cytosine-guanine Watson-Crick base-pair, radiationless decay occurs instead via an intermolecular charge transfer state, and is triggered by proton transfer. The locally excited states that were studied in the isolated cytosine are rapidly displaced to higher energy along the proton transfer coordinate. Here the protein environment causes a part of the conical intersection seam to become accessible which cannot be reached in the gas phase. 

The energy at the displaced point can be obtained from diagonalization of this Hamiltonian. When the reference geometry is a conical intersection, Eo (Qo) = El (Qo), the energy splitting caused by finite displacements is ... 

Fig. 7 Schematic representation of the conical intersection seam in Mvene along the torsion and pyramidalization modes, including the critical points, the seam normal modes that connect the different structures and the imaginary frequencies in cm (displacement vectors shown only for the hydrogen atoms) (reprinted with permission from [45])...

In an electronically non-adiabatic process the description of the nuclear motion involves more than one PES. Electronic spectroscopy and photochemical reactions involve transitions between two or more PES in critical regions (avoided crossings, conical intersections, crossings) where the nature of the electronic wave function may change rapidly as a function of the nuclear displacement. This is illustrated in Scheme 4 which represents two different... 

As is ISC, IC is very slow for electronic states with similarly shaped potential energy surfaces. When the potential surfaces have very different shapes, there will be a small number of vibrational doorway states that are especially effective in coupling to the bright state. Conical intersections are a special class of potential surfaces of very different shapes. But even when potential surfaces have very different shapes, many normal coordinate displacements and the associated vibrational normal modes will have nearly identical forms on both surfaces. These normal modes are Franck-Condon inactive and do not contribute to IC. The normal coordinate displacements that express the differences in shapes of the potential surfaces are embodied in vibrational normal modes that are Franck-Condon active. These modes are called promoting modes because, when such a mode on one potential surface is plucked from an eigenstate on the other surface, intramolecular dynamics is promoted or initiated. 

Figure 5.17 Suggested potential energy surfaces and pathways. 6 is the C=C twist and a planar CCC bend implying also some phenyl twist (< )). The initial motion on the 2B surface and through the first conical intersection is not time-resolved. The Cl is displaced along (outside the drawing plane), and entering from there into the IB valley...

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... 

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