Intersection space

In the intersection space (optical probe) of two coherent laser beams, planar interference fringes are formed. These are normal to the plane of beams, parallel to the beam bisector, and of a known uniform distance. 

Migani A, Sinicropi A, Ferr N, Cembran A, Garavelli M, Olivucci M (2004) Structure of the intersection space associated with Z/E photoisomerization of retinal in rhodopsin proteins. Faraday discuss 127 179... 

Figure 5 (a) Typical double-cone topology for a conical intersection, (b) Relation between the branching space (xj, x2) and the intersection space (spanning the remainder of the (n - 2)-dimensional space of internal geometric variables. 

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... 

As reported in the introduction, we have indicated that in some situations there is no transition state connecting an excited state intermediate (M ) to the conical intersection point (sloped conical intersections, see Figures 4c and 8b). In such situations, mechanistic information associated with surface crossings must be obtained by locating the lowest lying intersection point along the n — 2 intersection space of the molecule. 

The general behavior of such an optimization procedure is illustrated in Figure 13, where we report two PES intersecting along the xt and intersection space coordinates (x3,. . x ). Although this example is not realistic because we... 

Here, a topology-adapted representation [55] was chosen, where (Xi,X2) lift the degeneracy at the intersection and thus span the branching plane [74], These modes are obtained by orthogonalizing the modes (X, Xa) of Eq. (10). The third mode Xg is in turn orthogonal to (Xi, ) and carries information on the intersection space, i.e., the X+ component of Eqs. (9)-(10). Alternative construction schemes are possible in particular, the bilinear coupling terms can be eliminated within the three-mode subspace [54,72]. 

Kdppel, 1990), or a more approximate semiclassical trajectory calculation (Herman, 1984). In systems of interest to the organic photochemist, sinmlta-neous loss of vibrational energy to the solvent would also have to be included, and reliable calculations of quantum yields are not yet possible. It is perhaps useful to provide a simplified description in terms of classical trajectories for the simplest case in which the molecule goes through the bottom of the funnel, that is, the lowest energy point in the conical intersection space. 

Intersection Space Hessian for the Analysis of Conical Intersections... 

If the expansion of f and /2 is truncated at first order, one obtains the analog of (3), and the energy splitting occurs only along the branching space vectors. If the second-order terms are included, one obtains the analog of (5). In this case, the conditions of von Neumann and Wigner that define the intersection space are ... 

Equation (27) gives the energy of the intersection seam along the A — 2 curvilinear coordinates. The critical points on the seam can then be characterized with the help of the intersection-space Hessian, the matrix of second derivatives of the seam energy with respect to the curvilinear coordinates fi (i > 3) ... 

Second-Order Analysis at an Intersection Intersection Space of Fulvene... 

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