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Allowed versus forbidden reactions of hydrogen

We have validated eFF on a variety of ground state minima; now, we examine the energetics of allowed and forbidden reactions, and the transition states that connect different minima. As examples, we compute the potential energy surface of $ \mathrm{H + H_{2} \rightarrow H_{2} + H}$, an allowed reaction, and $ \mathrm{H_{2} + H'_{2} \rightarrow H H' + H H'}$, a forbidden reaction (Figure 4.13).

Figure 4.13: eFF distinguishes between allowed and forbidden hydrogen reactions.

For $ \mathrm{H + H_{2}}$, we assume that the atoms are colinear, and find a saddle point at the symmetric geometry $ r_{1} = r_{2} = 1.04 \mathrm{\ \AA}$ with $ \Delta E$ = 42 kcal/mol relative to separated $ \mathrm{H + H_{2}}$. In comparison, quantum Monte Carlo calculations [32] find the transition state to be at $ r_{1} = r_{2} = 0.95 \mathrm{\ \AA}$ with $ \Delta E$ = 9.7 kcal/mol. Although the transition state energy is significantly too high, it is still smaller than the $ \mathrm {H_{2}}$ dissociation energy; that together with the shape of the potential energy curve indicates that the reaction is allowed.

For $ \mathrm{H_{2} + H'_{2}}$, we assume that the atoms are aligned in a square, and we find that there is no low energy path connecting product to reactant -- both of the molecules must break simultaneously in order for the reaction to happen. The potential energy surface is rather flat, and there exists a saddle point at $ r_{1} = r_{2} = 2.21\ \mathrm{\AA}$ with $ \Delta E$ = 132 kcal/mol relative to separated $ \mathrm{H_{2} + H_{2}}$, which makes the reaction forbidden. To compare, we evaluated a potential for $ \mathrm{H_{4}}$ due to Boothroyd [33] derived from MRD-CI calculations over a set of symmetric square geometries, and found a saddle point at $ r_{1} = r_{2} = \mathrm{1.22\ \mathrm{\AA}}$ with $ \Delta E$ = 147 kcal/mol.


next up previous contents
Next: Ionic and multicenter bonds Up: Validation against ground state Previous: Carbocation rearrangements   Contents
Julius 2008-04-29