Figure 7.6. Calculated potential energy curves'for a twist in the double bond in C H d H , (---) and CH,=NH,@ (-) (by permission from BonaCiC-Koutecky et al.,
1984).
equal to the critical quantity Go the energy gap disappears and the S, and So surfaces touch. According to Figure 7.6 this situation is just attained for the twisted formaldiminium ion CHFNH,@. In this case a thermal equilibrium in S, is not to be expected at the biradicaloid minimum, which corresponds to a funnel instead. Both the conversion of the trans excited state to the cis ground state and the conversion of the cis excited state to the trans ground state would then proceed with dynamical memory and the sum of the quan- tum yields a,,, and cP,-, might therefore reach the limiting values of zero and 2 (Michl, 1972; see also the conversion of azomethines below). These processes are very important for the understanding of the rapid deactivation of excited states of triphenylmethane and rhodamine dyes (Rettig et al., 1992). In cyanine dyes (Momicchioli et at., 1988), for example, 6 can go beyond the critical value do, and it can become very large in TlCT mole- cules. (Cf. Section 5.5.2 and 5.5.3.)
In the case of the retinal Schiff base (6) the efficiency of cis-trans iso- merization of the double bond between C-1 l and C-12 is considerably en- hanced by polar solvents on the one hand and by protonation of the Schiff base on the other hand (Becker and Freedman, 1985). This is rather impor- tant because 6 is the chromophore of rhodopsin and this isomerization rep- resents one of the primary steps in vision.
7.1.6 Azomethines
Syn-anti isomerization about a C=N double bond is intrinsically more com- plicated than cis-trans isomerization of a C=C double bond. This is due to the fact that w n * excitations have to be discussed in addition to n+n*
excitations, and because syn-anti isomerization can be effected by either of two linearly independent kinds of motion or their linear combination, namely twisting and in-plane inversion at the nitrogen atom. (See Figure 7.7.) It is believed that in simple azomethines thermal isomerizations occur through inversion, while photochemical isomerizations proceed along a twisting path (Paetzold et al., 1981).
This has been confirmed by quantum chemical calculations of the poten- tial energy surfaces of the ground state and the lowest excited states of formaldimine in the two-dimensional subspace defined by the twisting and linear inversion motions (Bona6C-Koutecky and Michl, 1985a). Se- lected cuts through these surfaces for different dihedral angles are dis- played in Figure 7.8. Whereas the ground state prefers planar geometries
Figure 7.7. The syn-anti isomerization of formaldimine a) through in-plane inver- sion and b) by rotation. a is the CNH valence angle and 8 the torsional angle.
7.1 CIS-TRANS ISOMERIZATION OF DOUBLE BONDS 375
Figure 7.8. Dependence of the energy of the lowest states of formaldimine on the valence angle a, shown for selected values of the twist angle 0 (by permission from BonaCiC-Koutecky and Michl, 1985a).
( 6 = 0" or 180°), orthogonal geometries (8 = 90") are preferred by the T, and S, states that correspond to n-n* excitation. The very small energy gap between S, and So for orthogonal geometries in the region 100" < a < 120"
can be viewed as a consequence of a conical intersection at a valence angle a = 106.5". Thus, vertical excitation into the S, state should be fol- lowed by vibrational relaxation to an orthogonal twisted geometry and to the funnel in S,, followed by a very rapid radiationless relaxation to So, leav- ing little opportunity for fluorescence or intersystem crossing. Back in the S,, state, the molecule should vibrationally relax rapidly to one of the two symmetry-equivalent planar forms of the imine ("syn" and "anti") with equal probability, and one should have = = 0.5. However, if a significant fraction of the excited molecules reaches the region of the conical intersection without having lost dynamical memory of their original geometry, syn or anti, both quantum yields of isomerization may deviate from 0.5, even in the absence of other competing processes.
Relatively little is known about the E-Z isomerization of N-alkylimines (7a). The reversible photoisomerization of anils (7b), however, has been studied in some detail. Since the quantum yield of intersystem crossing a,,,
376 ORGANIC PHOTOCHEMISTRY
I 7.1 CIS-TRANS ISOMERIZATION OF DOUBLE BONDS
is relatively large, it is assumed to be a triplet reaction. (Cf. Paetzold et al., 1981.)
7.1.7 Azo Compounds
Finally, azoalkanes (8) have lone pairs of electrons on both nitrogen atoms, and additional w n * transitions and additional kinds of motion have to be considered in discussing cis-trans isomerization. The effect of the n orbitals is apparent from the orbital correlation diagram shown in Figure 7.9. In con- structing this diagram use has been made of the fact that the orbitals n, and n, of the lone pairs of electrons on the two nitrogen atoms split due to an appreciable interaction, and that the orbital ordering is the natural one in the cis isomer, with the combination n + = (n, + n,)/fl below the combination n- = (n, - n,)/*, while in the trans isomer orbital interaction produces the opposite ordering.
From PE spectroscopy results for azomethane (Haselbach and Heilbron- ner, 1970) the energy of the n MO is known to lie between those of the n + and n- orbitals. Thus, a HOMO-LUMO crossing results and the trans-cis
Figure 7.9. Orbital correlation diagram for the cis-trans isomerization of diimide HN=NH.
Figure 7.10. Computed potential energy surfaces of the ground state So and the (n,n*) excited states TI and S, for the cis-trans isomerization of diimide as a function of the twist angle 6 and the valence angle a at one of the nitrogen atoms.
isomerization is forbidden in the ground state and allowed in the first excited singlet and triplet states, as in the case of olefins. In con- trast to the olefins, however, the lowest excited states of azoalkanes are the (n,llr) excited states. On the (n,n*) excited singlet and triplet surfaces the reaction encounters a correlation-imposed barrier. For in- stance, the configuration (n-)2(n)1(n +),(+)' of the trans isomer correlates with the doubly excited configuration (n +)'(n)2(n..)'(n*)2 of the cis isomer.
The computed potenti;ll energy surfaces of Figure 7.10 confirm these con- cepts. From these calculations it is also seen that isomerization by motion of the substituent in the molecular plane (variation of a) is energetically pref- erable to twisting the N=N bond (variation of 8) in the ground state, while the opposite is true in the 'v3(n,+) excited states.
In agreement with the theoretical results, the photoisomerization of sim- ple azoalkanes is found to be rather effective. For azomethane in benzene at 25°C quantum yields of @,+,. = 0.42 and @,,, = 0.45 have been observed (Thompson et al., 1979). Cis-azo compounds are moderately stable. Only tertiary cis-azoalkanes are thermally unstable and decompose to nitrogen and radicals. (See Section 7.2.2.)
Example 7.3:
In azobenzene the cis-trans isomerization in the '(n.9) state apparently pro- ceeds along a twisting path whereas in the '(n,n*) state it proceeds along the inversion path. This has been suggested by the fact that for azobenzenes such
OKC,r\l\llC I'HO'I'OCHEMISI KY
Figure 7.11. Schematic state correlation diagram for the cis-trans isomeriza- tion of azobenzene for two reaction paths that correspond to a twist mecha- nism and an inversion mechanism, respectively (adapted from Rau, 1984).
as the bridged crown ether 9, for which twisting is inhibited for steric reasons, the quantum yield @,-, of trans-cis isomerization is independent of the exciting wavelength. In azobenzene itself, however, n + 9 excitation (A = 436 nm) and n-n* excitation ( A = 3 13 nm) give different quantum yields a,,,.. According to the schematic state correlation diagram of Figure 7.1 1, inversion, which is preferred in the '(n,9) state, is forbidden in the ( n , ~ ) state. However, from this state a funnel for a 90" twisted geometry may be reached, followed by a rapid transition to the ground-state surface (Rau, 1984).