Our current theories on crystal lattice control of organic photochemistry were subjected to studies of type-B rearrangement of bicyclo[3.1.0]hex-3-en-2-ones. A first finding was that the solid state photochemistry differed dramatically from that in solution. One of our past observations in this bicyclic photochemistry in solution was that the six-membered ring, type B, zwitterion was a ubiquitous intermediate. This intermediate invariably underwent a preferential migration of an aryl group to carbon-2 relative to carbon-4 with formation of a 2,3-disubstituted phenol, a result deriving from electronic effects. In contrast, the crystal lattice photochemistry revealed a regioselectivity depending on the surrounding lattice rather than electronics. Perhaps an even more dramatic difference was an observation of the dependence of reactant stereochemistry. Thus, in solution, for 6,6-disubstituted bicyclics with two different groups at C-6, a common zwitterion is formed and the same photoproduct is formed independent of reactant stereochemistry. In crystal lattices the endo and exo stereoisomers of the 6,6-disubstituted bicyclics react differently and the group originally endo tends to migrate after three-ring opening to the zwitterion. The experimental results were paralleled with a theoretical analysis. This consisted of generation of a “mini crystal lattice” with sufficient lattice molecules to completely surround a central, reacting electronically excited state molecule. Then computational extraction of the central molecule and replacement by a transition structure afford a model of the reacting excited state inside the crystal lattice. Overlap of this species with the lattice neighbors and energy computations are then possible. These permit prediction and understanding of excited state crystal lattice reactivity on a quantitative basis.

Four decades ago one of us presented a means of relating, qualitatively, the structures of electronically excited states to many of the known organic reactions. 3 We now describe a method of predicting excited-state reactivity more generally. 4 A particularly intriguing but elusive problem is how excitation energy is distributed in electronic excited states, particularly those exhibiting photochemical reactivity. Using modern quantum mechanical wavefunctions, the present paper not only provides an answer to this question but also provides a method for predicting photochemical reactivity.In very early efforts 5 we reported the use of a "∆D Matrix" (also termed ∆p Matrix) which gives the change in electron densities and bond orders at different molecular sites as a result of electronic excitation. The promise was the ability to predict the molecular consequences of electronic excitation as well as being able to predict and understand photochemical reactions in general. These early studies were limited to the use of a truncated system of basis orbitals, these being in chromophores and bonds involved in a given reaction. However, now with the Weinhold Natural Hybrid Orbitals (NHOs) 6 being available in Gaussian98, 7 it is possible to determine the validity of the concept in virtually any electronically excited state of interest using any of the quantum mechanical methods capable of affording density matrices for ground and excited singlet and triplet electronic states. We define our ∆D matrix elements as in eq 1.Here, the D* rt refers to the excited-state density and D°r t refers to the ground state. The S rt terms are overlap integrals to adjust for distance effects and to maintain proper relative orbital signs.Thus, ∆D might be properly termed an "overlap density matrix"; r and t designate a pair of orbitals.The idea is that, where a ∆D element (e.g., ∆D rt ) is negative, that bond not only is weakened in the excitation process but also is generated by Franck-Condon vertical excitation in a nonminimum geometry with an accumulation of vibrational as well as electronic energy. 8 There may be some bonds which have positive ∆D elements and are stabilized and strengthened, but they will necessarily be fewer, since the molecular electronic energy has risen. 9 Also, the ∆D method gives changes in one-center electron densities, and this portion of our concept has been of value in the literature. 10 The ∆D method not only predicts the occurrence of photochemical reactions but also subtleties such as regioselectivity. Some reactions considered are (a) the Norrish Type I and its regioselectivity, 11a (b) the Yates ring-strained ketone to carbene ring expansion, 11b (c) the cyclopropyl ketone ring opening reactions and regioselectivity, 11c (d) the Norrish Type-II reaction, 11d (e) the butadiene to cyclobutene disrotatory transformation, 11e (f) Type-B bicyclic transformations, 11f (g) p y -orbital hydrogen abstraction, 11g (h) the R-expulsion reaction of R-substituted ketones, 11h (i) meta-electron transmission, 11i (j) ...

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