Interstate coupling

Different topological situations are possible for unavoided crossings between surfaces. One can have intersections between states of different spin multiplicity [an (n - l)-dimensional intersection space in this case, since the interstate coupling vector vanishes by symmetry], or between two singlet surfaces or two triplets [and one has an n - 2)-dimensional conical intersection hyperline in this case]. We have encountered situations in which both types of... 

In this transformed Hamiltonian Hq again describes uncoupled system and bath the new element being a shift in the state energies resulting from the system-bath interactions. In addition, the interstate coupling operator is transformed to... 

The polaron transformation, executed on the Hamiltonian (12.8)-( 12.10) was seen to yield a new Hamiltonian, Eq. (12.15), in which the interstate coupling is renormalized or dressed by an operator that shifts the position coordinates associated with the boson field. This transformation is well known in the solid-state physics literature, however in much of the chemical literature a similar end is achieved via a different route based on the Bom-Oppenheimer (BO) theory of molecular vibronic stmcture (Section 2.5). In the BO approximation, molecular vibronic states are of the form (/) (r,R)x ,v(R) where r and R denote electronic and nuclear coordinates, respectively, R) are eigenfunctions of the electronic Hamiltonian (with corresponding eigenvalues E r ) ) obtained at fixed nuclear coordinates R and... 

We have thus found that the interstate coupling (12.17) associated with the... 

Note that Ea(.R ) is the height of the curve-crossing energy above the bottom of the reactant well a. It is also noteworthy that in the non-adiabatic limit the rate depends explicitly on the interstate coupling Vab (in additional to its dependence on the characteristic frequency a>a and the slopes at the crossing point via AF). In the adiabatic limit dependence on Vab enters only indirectly, through its effect on the adiabatic barrier height. 

Figure 2.6 Energy profiles at a peaked conical intersection along (a) gradient difference and (b) interstate coupling coordinates.

The intersection between the two states (Cl-S/Sg) was optimized together with the TS between the two minima, which lies along the interstate coupling vector for CI-S/S2. (The fourth critical point of the three-electron model discussed... 

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