Orbital Interaction Theory of Organic Chemistry

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Figure 15.1. Potential energy surfaces for bound states, S0 and S1, and a dissociative state, S2.

inversely on the moment of inertia. For large molecules (more than a few ®rstor higher row atoms) or in solution, the rotational structure is not resolved, although at room temperature, a number of rotational levels will be populated. The range of structures in the ground vibrational state is given by the vibrational wave function shown for the lowest vibrational level of S0 in Figure 15.1. The time required to excite the electron (10ÿ15 s) is very short compared to vibrational periods (>10ÿ13 s). The shaded area in Figure 15.1 represents the range of structures from which vertical excitation may take place if the energy of the photon corresponds to the approximate energy di¨erence between the ground-state lowest vibrational level and some vibrational level of an excitedstate potential energy surface. In general, the excited state reached by vertical excitation from the ground state will be hot (vibrationally excited) and may dissociate if the vibrational mode of the excited state corresponds to bond stretching. A more detailed representation of the sequence of events after photoexcitation is given by a Jablonski diagram.

JABLONSKI DIAGRAM

A generic Jablonski diagram for a molecular system is shown in Figure 15.2. Singlet states and triplet states are shown as separate stacks. Associated with each electronic state is a vibrational/rotational manifold. The vibrational/rotational manifolds of dif-

Figure 15.2. Modi®ed Jablonski diagram: A ˆ absorption; F ˆ ¯ourescence; P ˆ phosphorescence; IC ˆ internal conversion; ISC ˆ intersystem crossing; VC ˆ vibrational cascade.

ferent electronic states will in general overlap each other. Straight lines represent photon absorption (A) or emission, the latter as ¯uorescence (F) or phosphorescence (P). Wavy lines correspond to radiationless transitions which involve vibrational relaxation via a vibrational cascade (VC) to the zero vibrational level of the same electronic state. Energy is carried away through collisions with solvent. If vibrational/rotational levels of two electronic states overlap, then it is possible to move from one state to the other (lower) without a change in energy. If a change in spin multiplicity is not involved (S ! S or T ! T), the process is called internal conversion (IC); if a change in spin multiplicity is involved (S ! T or T ! S), the process is called intersystem crossing (ISC). Both IC and ISC are immediately followed by VC.

FATE OF EXCITED MOLECULE IN SOLUTION

The fate of an excited molecule depends on the rates (time scales) of competing processes. As already mentioned above, the time scale for photon absorption (A) is very

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fast, 10ÿ15 s. For molecules containing elements with atomic number less than about 50, electron spin is strongly conserved. As a result, only singlet states are accessible in the primary excitation process. The time scale for the vibrational cascade and for internal conversion between higher excited states is governed by vibrational motions or collision frequencies in dense medium. Both are about 10ÿ12 ±10ÿ13 s. Internal conversion between S1 and S0 may be substantially slower, 10ÿ6 ±10ÿ12 s, of the same magnitude approximately as ¯uorescence, 10ÿ5 ±10ÿ9 s. Ultimately, useful photochemistry is limited by the ¯uorescence lifetime, tF, which for absorptions in the near UV may be estimated from the molar extinction coe½cient as [314]

tF …s†A 10ÿ4 emax

A photochemical transformation can be accomplished only if the photoexcited molecule has a chance to do something before it ¯uoresces. Intersystem crossing time scales may vary considerably, 10±10ÿ11 s. Return to the ground state by means of phosphorescence is comparatively slow, 102 ±10ÿ4 s. The rates of chemical processes depend on the magnitudes of barriers hindering the change. Intermolecular processes depend additionally on collision frequency between reactant (the photoexcited molecule) and substrate as well as possible orientational (stereoelectronic) criteria. E¨ective barriers hindering reaction tend to be lower in photochemical processes, partly because bonding in the excited molecule is weaker and partly because the excited molecule may be vibrationally excited (hot). The collision frequency for intermolecular reactions may be maximized if the substrate can function as the solvent or if the reaction is intramolecular.

DAUBEN±SALEM±TURRO ANALYSIS

The following very useful approach for the analysis of photochemical reactions is due to Dauben, Salem, and Turro [13]. A bond, aÐb, made from fragment orbitals fa and fb of molecular fragments, a and b, is broken in the process under consideration. The relationship to the orbital interaction diagram is transparent (see Figure 15.3). The orbitals fa and fb are the leftand right-hand sides of the interaction diagram, while the assembly aÐb is the middle. The ``middle'' constitutes the reactant. The noninteracting rightand left-hand sides constitute the products. Assume that the orbital fb is lower in energy than fa. The two electrons originally in the bonding orbital may be distributed in

four distinct ways between the two fragment orbitals, fa and fb, yielding four states,

Z1 ˆ . . .…fb†2…fa†0, Z2 ˆ . . .…fb†0…fa†2, 1D ˆ . . .…fb†1…fa†1, and 3D ˆ . . .…fb†1…fa†1. The ®rst two states are zwitterionic, since the bond dissociates heterolytically. Also, since

both electrons occupy the same orbital, both zwitterionic states are singlet states and will be totally symmetric with respect to any symmetry operation which may be preserved in the dissociation. By our assumption that E…fb† < E…fa†, it is expected that E…Z1† < E…Z2†. The remaining two states arise from homolytic dissociation of the bond and therefore are diradical in character. Both singlet and triplet states arise. If any residual interaction persists (i.e., if the bond broken was a p bond or the products are held together in a solvent cage), then the triplet diradical state is lower than the singlet diradical state. Otherwise the two have the same energy. Since the electrons end up in di¨erent orbitals, the spatial symmetry of the diradical states is determined by the symmetry properties of fa and fb. The diradical is symmetric (S) if fa and fb are both

Figure 15.3. (a) Orbital interaction diagram for the formation of a bond between molecule fragments a and b. (b) Orbitals for Dauben±Salem±Turro analysis of the rupture of the aÐb bond: lefthand side, orbitals of the bond with other occupied and unoccupied MOs of the reactant (molecule aÐb); right-hand side, con®gurations which arise from the orbitals which made up the bond (other orbitals of fragments a and b not shown).

symmetric (S) or both antisymmetric (A) with respect to a preserved symmetry operation. If fa and fb have di¨erent symmetry properties, one S and the other A, then the spatial symmetry of the diradical states is A. Notice that the latter case could not arise if fa and fb are the orbitals involved in the original bond, since they could not have interacted to form the bond if they were of di¨erent symmetry. It will generally happen that one or more of the orbitals of the fragments a and b will be comparable in energy to fa and fb so that other diradical and zwitterionic states must be considered and the situation of di¨erent symmetries may occur among these. The same holds true for the reactant excited states.

As mentioned earlier, heterolytic cleavage of a bond to form charged species is never observed in the gas phase and is very unlikely in nonpolar solvent. Thus the expected overall order of the energies of the product states arising from the bond rupture is E…3D† U E…1D† < E…Z1† < E…Z2†. If the energy separation of fa and fb is large, or if fa and/or fb are di¨use, that is, the Coulomb repulsion of two electrons in the same MO (neglected in HuÈckel theory) is not large, the energy separation of the diradical states from Z1 may not be very large and may indeed be reversed if the dissociation is carried out in a highly polar solvent like water. Examination of several reactions of carbonyl compounds will serve to exemplify the principles of Dauben±Salem±Turro analysis.

NORRISH TYPE II REACTION OF CARBONYL COMPOUNDS

A common photochemical reaction of carbonyl compounds is the transfer of a hydrogen atom to the carbonyl oxygen atom:

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Figure 15.4. (a) Frontier orbitals of the fragments; (b) electronic con®gurations with two electrons; (c) order of the energies of the electronic states.

The lower electronic states of the reactants (left-hand side) are those of the carbonyl group shown in Figure 14.8c, since the sCH and sCH orbitals are too far apart to participate in the lower electronic states. In other words, the light will be absorbed by the carbonyl compound. The local group orbitals of the product fragments and the states which arise from them are shown in Figure 15.4. The reaction is considered to take place in the plane of the carbonyl group, and the orbitals are symmetry typed according to their behavior with respect to re¯ection in this plane.

A Dauben±Salem±Turro state correlation diagram for the photochemical step of the Norrish Type II hydrogen abstraction reaction is shown in Figure 15.5. The reactant (carbonyl) states are classi®ed in point group Cs and also as S or A. The placement of the reactant and product states on the same energy diagram need only be approximate. The singlet and triplet np states are located by virtue of the observed lowest electronic transition in the UV spectra of carbonyls, about 250 nm or 5 eV relative to the ground state. The pp states are higher, with a larger singlet±triplet gap. Assuming the ground states of reactants and products to be of similar energy, the diradical states may be placed at about the energy required to dissociate a CÐC or CÐH bond, about 360 kJ/mol or 4 eV.

The state correlation diagram indicates that the reaction should proceed via the np states which correlate directly with the product states of the respective multiplicity. The pp states of the carbonyl group correlate with higher electronic states of the products. The carbonyl ground state correlates with the Z1 state of products. Both singlet and triplet np states cross with the ascending ground state at the regions marked by shaded circles. At the crossing of singlet states, IC may allow a substantial fraction of the reaction to revert to the reactants. Intersystem crossing is usually much less e½cient, and therefore a higher quantum yield would result if the reaction were carried out on the triplet potential energy surface.

The e½ciency of photon capture to form the 1…np † state is very low since the excitation is electric dipole forbidden in the local C2v point group of the carbonyl. Direct

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Figure 15.6. (a) Frontier orbitals of the fragments of a Norrish Type I cleavage; (b) electronic con®gurations with two electrons; (c) order of the energies of the electronic states.

Figure 15.7. Dauben±Salem±Turro analysis of the photochemical step of the Norrish Type I reaction for (a) saturated carbonyls and (b) conjugated carbonyls. The reaction is most e½cient on the 3…pp † surface to yield triplet diradical products. It is also e½cient on the 3…np † surface since IC permits formation of products in their ground state.

orbitals of the product fragments and the states which arise from them are shown in Figure 15.6. The reaction is again considered to take place in the plane of the carbonyl group and the orbitals are symmetry typed according to their behavior with respect to re¯ection in this plane.

A Dauben±Salem±Turro state correlation diagram for the photochemical step of the Norrish Type I a cleavage reaction is shown in Figure 15.7. The reactant (carbonyl) states are classi®ed in point group Cs and also as S or A. The state correlation diagram indicates that the reaction should proceed most e½ciently via the triplet pp state which correlates directly with the ground state of the products. The 3…np † state of the carbonyl group also cleaves relatively e½ciently via internal conversion at the crossing of the triplet surfaces. Reaction via 1…np † also occurs since the 1…np † state correlates with a higher singlet electronic state of the products and can then undergo internal conversion and vibrational cascade to the lowest singlet state of products. However, in this case, recombination of the radical pair is very fast if the radicals have been held together in a solvent cage or within the same fragment, as in the case of a-cleavage of cyclic ketones. The carbonyl ground state correlates with the 1D1 state of products. This reaction corresponds to thermal cleavage of the a CÐC bond.