Quantitative valence bond computations of curve-crossing diagrams for model atom exchange reactions

Curve-crossing diagrams are presented and computed for the exchange reactions X + X-X → X-X + X, X = H, Li, by use of a multistructure VB approach. The computations provide the essential diagram quantities G,f, and B. These parameters are 156.8 kcal/mol, 0.37, and 42.4 kcal/mol, respectively, for X = H, and 22.4 kcal/mol, 0.13, and 6.6 kcal/mol for X = Li. The quantitative analyses confirm the qualitative deduction that all these quantities are related to a fundamental property of X, the singlet-triplet splitting ΔE_st(X-X) of the dimer. It is possible therefore to predict the height of the barrier and the mechanistic modality of the exchange reaction by reliance on ΔE_st; as ΔE_st decreases in a series the barrier decreases and eventually the X₃ species is converted to a stable intermediate. The B quantity is the quantum mechanical resonance energy (QMRE) of the X₃ species. The values of 42.4 kcal/mol for H₃ and 6.6 kcal/mol for Li₃ are computed as energy differences between a variational bonding scheme and the variational adiabatic and delocalized (X-X-X) state.