Valence Bond State Correlation Diagrams for Radical Exchange Reactions

1 Valence Bond State Correlation Diagrams for Radical Exchange Reactions 

Consider a reaction that involves cleavage of a bond A-Y by a radical X (X, A, Y = any atom or molecular fragment)  

As we already argued, the origin of the barrier is G. Since R in Fig. 6.3 is just the VB image of the product HL wave function in the geometry of the reactants, this excited state displays a covalent-bond coupling between the infinitely separated fragments X and A, and an uncoupled fragment Y in the vicinity 

The state R in Equation 6.4 strictly keeps the HL wave function of the product P, and is hence a quasi/spectroscopic state that has a finite overlap with R. If one orthogonalizes the pair of states R and R, by, for example, a Graham—Schmidt procedure (see Exercise 6.3), the excited state becomes a pure spectroscopic state in which the A—Y is in a triplet state and is coupled to X to yield a doublet state. In such an event, one could simply use, instead of Equation 6.5, the spectroscopic gap Gs in Equation 6.6 that is simply the singlet—triplet energy gap of the A—Y bond  

Each formulation of the state R has its own advantages (6,9), Equation 6.6 has the merit of simplicity and is easiest to apply when several bonds are broken—made in a reaction. On the other hand, Equation 6.5, which is more faithful to the sense of the VB correlation, should be preferred when subtle effects are searched for (see Exercises 6.5—6.7). What is essential for the moment is that both expressions use a gap that is either the singlet-to-triplet excitation of the bond that is broken during the reaction, or the same quantity scaled by approximately a constant 0.75. As mentioned above, a useful way of understanding this gap is as a promotion energy that is required in order to enable the A—Y bond to be broken and be replaced by another bond, X—A. 

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