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Color Plates
Color Plates
Figure 3.7 MECI for the 2 þ 2 cycloaddition of two ethylenes63 showing the branchingspace vectors X1 and X2. Note that the arrows shown to represent the branching-space vectors are treated as if they were a molecular vibration. They correspond to the conditions given in Eqn (3.6).
Figure 3.8 Some possible arrangements of 4 orbitals with 4 electrons where {K12 þ K34} (blue) ¼ {K13 þ K24} (red) ¼ {K14 þ K23} (green). Also shown inset, is the point group of each figure and the corresponding labels for the irreducible representations spanned by the vectors X1 and X2, which correspond to the degeneracy motions. In (a) and (b) the conical intersection is a Jahn-Teller degeneracy. In (c) and (d), X1 and X2 span the direct sum of irreducible representations. Accordingly, in (a), the vectors X1 and X2 span the degenerate irreducible representation E in point group Td, while in (c) the vectors X1 and X2 belong to two non-degenerate representations and the degeneracy is “accidental.” Analogously, the conditions for the conical intersection are satisfied by symmetry in (a), while they are achieved in (c) by adjusting the corresponding bond lengths until the inequalities are satisfied. Adapted from Bernardi et al.1
Figure 3.9 Branching-space vector X1 (a) derived from Eqn (3.6) X1 5 (K14 þ K23 ¼ K12 K34). Adapted from Serrano-Perez et al.62
Figure 3.10 Branching-space vector X2 (b) derived from Eqn (3.6) X2 5 {K12 þ K14 þ K23 þ K34 ¼ 2(K13 þ K24)}. Adapted from Serrano-Perez et al.62
Figure 3.11 Distortion of Figure 3.8(a) to give the 2s þ 2s conical intersection of Figure 3.7 (adapted from Serrano-Perez et al.62). In order to reach the 2s þ 2s conical intersection, two motions are required: (1) vertical compression along the z-axis so that all four atoms lie in the plane and (2) rhomboidal distortion (orange arrows) to produce the structure shown on the right-hand side of the figure.
Figure 3.26 VB surfaces for the three VB structures. The VB surfaces for the two-bond addition (purple) and one-bond addition (green) intersect with the product VB structure (orange). They also intersect with each other, which corresponds to the S1 barrier ridge between synchronous and asynchronous paths.
Figure 3.27 The crossing seam between P1 and P2 as a function of the torsional angle around the first-formed bond.
Figure 3.29 Model potential surface for isomerization of a cyanine dye (adapted from Hunt and Robb97). The branching space is shown in Figure 3.28(c). The x-axis corresponds to the reaction coordinate (X3), in this case a complex mixture of conrotatory and disrotatory C]C torsion. Notice that the reaction path is quasi-parallel to the seam itself. From Figure 3.28(c), the branching-space vectors correspond to skeletal deformation rather than torsion. The reaction path encounters the seam at the point MEP-CI where one C]C bond is rotated 90 .
Figure 3.7 MECI for the 2 þ 2 cycloaddition of two ethylenes63 showing the branchingspace vectors X1 and X2. Note that the arrows shown to represent the branching-space vectors are treated as if they were a molecular vibration. They correspond to the conditions given in Eqn (3.6).
Figure 3.8 Some possible arrangements of 4 orbitals with 4 electrons where {K12 þ K34} (blue) ¼ {K13 þ K24} (red) ¼ {K14 þ K23} (green). Also shown inset, is the point group of each figure and the corresponding labels for the irreducible representations spanned by the vectors X1 and X2, which correspond to the degeneracy motions. In (a) and (b) the conical intersection is a Jahn-Teller degeneracy. In (c) and (d), X1 and X2 span the direct sum of irreducible representations. Accordingly, in (a), the vectors X1 and X2 span the degenerate irreducible representation E in point group Td, while in (c) the vectors X1 and X2 belong to two non-degenerate representations and the degeneracy is “accidental.” Analogously, the conditions for the conical intersection are satisfied by symmetry in (a), while they are achieved in (c) by adjusting the corresponding bond lengths until the inequalities are satisfied. Adapted from Bernardi et al.1
Figure 3.9 Branching-space vector X1 (a) derived from Eqn (3.6) X1 5 (K14 þ K23 ¼ K12 K34). Adapted from Serrano-Perez et al.62
Figure 3.10 Branching-space vector X2 (b) derived from Eqn (3.6) X2 5 {K12 þ K14 þ K23 þ K34 ¼ 2(K13 þ K24)}. Adapted from Serrano-Perez et al.62
Figure 3.11 Distortion of Figure 3.8(a) to give the 2s þ 2s conical intersection of Figure 3.7 (adapted from Serrano-Perez et al.62). In order to reach the 2s þ 2s conical intersection, two motions are required: (1) vertical compression along the z-axis so that all four atoms lie in the plane and (2) rhomboidal distortion (orange arrows) to produce the structure shown on the right-hand side of the figure.
Figure 3.26 VB surfaces for the three VB structures. The VB surfaces for the two-bond addition (purple) and one-bond addition (green) intersect with the product VB structure (orange). They also intersect with each other, which corresponds to the S1 barrier ridge between synchronous and asynchronous paths.
Figure 3.27 The crossing seam between P1 and P2 as a function of the torsional angle around the first-formed bond.
Figure 3.29 Model potential surface for isomerization of a cyanine dye (adapted from Hunt and Robb97). The branching space is shown in Figure 3.28(c). The x-axis corresponds to the reaction coordinate (X3), in this case a complex mixture of conrotatory and disrotatory C]C torsion. Notice that the reaction path is quasi-parallel to the seam itself. From Figure 3.28(c), the branching-space vectors correspond to skeletal deformation rather than torsion. The reaction path encounters the seam at the point MEP-CI where one C]C bond is rotated 90 .