Conical intersections optimization

Run a final state-averaged calculation at the fuUy-optimized conical intersection using the 4-31G basis set and P to predict the energies of the two states and view the configuration coefficients. (This step will not be necessary if you chose to use P for the final conical intersection optimization job you ll find the relevant output in the CAS output for the final optimization step, preceding the table giving the stationary point geometry.)... 

Figure 13 General behavior of a conical intersection optimization procedure. This contrived example was started from an almost planar geometry (much further from the optimum geometry than normal practice). The curve shows the rapid approach to the degenerate situation followed by minimization (retaining the degeneracy).

The optimization of a conical intersection is a constrained optimization in the space orthogonal to the two degeneracy-lifting coordinates, Xj and Xg. The optimization has an additional requirement, namely, the energy difference between the two states at the conical intersection is zero. Thus, the gradient used in our conical intersection optimization algorithm is the sum of two gradients ... 

In Sec. 3 we will mainly concentrate on the discussion of the structure (both geometrical, electronic and topographical) of the chemically relevant (low-lying) conical intersections that have been documented in a number of basic organic chromophores. As we will further point out in Sec. 3.1, the majority of these structures have been computed via conical intersection optimizations and do not strictly correspond to the conical intersection points located at the very bottom of the excited-state path. Nevertheless, their general features are representative of the chemically relevant segment of the intersection space and can be used for the mechanistic rationalization of different photoinduced molecular processes. 

Conical intersection optimization using state-averaged CASSCF. 

The potential surfaces of the ground and excited states in the vicinity of the conical intersection were calculated point by point, along the trajectory leading from the antiaromatic transition state to the benzene and H2 products. In this calculation, the HH distance was varied, and all other coordinates were optimized to obtain the minimum energy of the system in the excited electronic state ( Ai). The energy of the ground state was calculated at the geometry optimized for the excited state. In the calculation of the conical intersection... 

In this exercise, we will examine a small part of this process. We will predici ihe relative energies of the three states at the ground state geometry, and we will locate the conical intersection. We ve provided you with an optimized ground state (cis) structure and a starting structure for the conical intersection in the files 9 06 gs.pclb and 9 06 ci.pdb, respectively. 

We hope that the preceding discussions have developed the concept of a conical intersection as being as real as many other reactive intermediates. The major difference compared with other types of reactive intermediate is that a conical intersection is really a family of structures, rather than an individual structure. However, the molecular structures corresponding to conical intersections are completely amenable to computation, even if their existence can only be inferred from experimental information. They have a well-defined geometry. Like the transition state, the crucial directions governing dynamics can be determined andX2) even if there are now two such directions rather than one. As for a transition structure, the nature of optimized geometries on the conical intersection hyperline can be determined from second derivative analysis. 

In Fig. 3 we show a cross section of the Jahn-Teller surface around the tetrahedral geometry. The simplest Jahn-Teller intersection is of T t2 type (i.e., a triply degenerate electronic state whose components are coupled via a triply-degenerate vibration). Optimization of a triply degenerate conical intersection is not routinely possible at present. The vibrational modes of Td Fe(C0)4 span Qa 2 1 2E T 4T2, so there are clearly several candidate vibrations. This T t type of... 

Figure 14.6 Two electronic states of an arbitrary system having a conical intersection. The inset region illustrates the effect on each curve of optimizing the orbitals for either State A or State B. At the coordinate position marked by an asterisk, the relative energies of the two states depend on which is chosen for orbital optimization, which can lead to root switching problems in an MCSCF calculation. Additionally, geometry optimization can cause root switching as well, if optimization passes through the conical intersection...

Nevertheless, root switching may still be problematic for geometrical reasons in the vicinity of conical intersections. Thus, for instance, any optimization of State B in Figure 14.6 that begins to the left of the asterisk in coordinate q will ultimately proceed to the right until State B falls below State A in energy, at which point it is the first root for chemical reasons, not technical reasons. The only remedy in this situation is careful analysis in the construction of state PESs. 

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