Mini-crystal lattice

The remainder of this chapter will concentrate on the solid-state research carried out in our laboratories at Wisconsin. Our research in this area began in 1984 when it was recognized that with the x-ray coordinates available, one could use methodology not too different from that in ground-state chemistry. Somewhat later we termed a truncated portion of the x-ray data a mini-crystal lattice. At its simplest, it consisted of one central molecule surrounded by one layer of neighbors. However, the number of layers of neighbors is adjustable. This proved to be one of the more important advances permitting the quantitative studies described in this chapter. 

We then define the central molecule as the reactant. A second mini-crystal lattice is generated by replacing the central molecule with a partially reacted species selected as a reasonable model for the transition structure. This species is generated using theoretical generation, optimally by quantum mechanical computation. The reacting species is placed with its atoms as close as possible to those of the reactant molecule... 

Figure 8.1 The mini-crystal lattice reacting the central R is replaced by I.

Table 8.3 summarizes the energetic residts for the five cases as obtained from MM3 molecular mechanics treatment of the first intermediate in the mini-crystal lattice. Again, we note that the species formed by migration of the trans-phenyl... 

The occurrence of a preferential phenyl migration signifies that cavity effects in the mini-crystal lattice cavity override the electronic preference for cyanophenyl migration. 

Thus, this is one dramatic example of how a cavity can change the course of a reaction. However, every attempt to nnder-stand this cavity effect by compntationally constructing a mini-crystal lattice with diradical 1 (i.e., DRl) embedded and comparing this with a mini-lattice with diradical 2 (i.e., DR2) embedded, invariably led to a lower energy for the mini-crystal lattice with the p-cyanophenyl migration intermediate. Initially this failure was ascribed to what seemed to be crystal disorder. 

One of the weaknesses of the treatment of mini-crystal lattices with molecular mechanics is that these computations do not take into account electronic effects, and in the case of open-shell species such as triplets, electronic energy differences between reactants and intermediate and other transformation structures may be appreciable. Yet ab initio and even semi-empirical computations on the entirety of a mini-crystal lattice are formidable. Thus, an alternative was developed. This involved generation of a cavity shell composed of inert gas atoms. The Pairs program was used to identify atoms belonging to the neighboring molecules that were nearest to the reacting central molecule. The number of these nesu est atoms varied. Then, all but these nearest atoms were compu-... 

Table 8.7 ONIOM Energies of Mini-Crystal Lattices with Alternative Migration Intermediates ...

This chapter has had several objectives. One is coverage and review of some of the author s solid-state photochemistry based on the mini-crystal lattice treatment. A second is the demonstration that the Cohen-Schmidt cavity can be put on a quantitative basis. However, probably the main objective is to provide evidence that a very broad spectrum of solid-state photochemistry can be understood and treated with theoretical methods. 

SCHEME 1 The mini-crystal lattice and injection of a reaction intermediate I replacing the central reactant molecule. 

This led the present author to consider ways of dealing quantum mechanically with very large aggregates of molecules. The main impediment to a quantum mechanical computation is the size of a typical mini-crystal lattice. Even with AMI, such a large molecular system cannot be handled practically. 

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