Location of Energy Barriers. II. Correlation with Barrier Height

In Paper I of this series a hypothetical potential‐energy surface was used in order to examine the effect on the dynamics of exchange reactions A + BC→AB + C of moving the energy barrier from an “early” to a “late” position along the reaction coordinate (i.e., from the entry valley to the exit valley of the energy surface). In the present work an attempt has been made to correlate barrier location with other properties of the energy surface, as a step toward the application of the generalizations of Paper I to real cases. Related families of reactions have been examined in the London–Eyring–Polanyi–Sato (LEPS) and bond‐energy bond‐order (BEBO) approximations. The principal generalizations may be summarized as follows: (1) For substantially exothermic reactions the barrier is in the entry valley, and for substantially endothermic reactions the barrier is in the exit valley. In the light of Paper I this implies that the cross sections for these exothermic reactions will rise most steeply with increasing translational energy in the reagents, whereas the cross sections for the endothermic reactions will rise most steeply with increasing vibrational energy in the bond under attack. (2) For decreasing barrier height in related exothermic reactions the barrier moves to successively earlier positions along the entry valley, with increasing percentage “attractive energy release.” (3) In general [i.e., if (4), below, is obeyed even qualitatively], for increasing barrier height in related endothermic reactions the barrier moves to successively later positions along the exit valley. (4) The correlation between the classical barrier height $E_C$ and reaction energy $q_c$ , written ${\mathrm{\Delta E}}_C{\mathrm{\hspace{0.17em}=\hspace{0.17em}-\alpha \; \Delta q}}_c$ by Ogg and Polanyi (OP) was found to be a weaker correlation than (2), above. For families where barrier height did decrease with increasing reaction energy, a logarithmic relationship, $\Delta \log E_C{\mathrm{\hspace{0.17em}=\hspace{0.17em}-\alpha }}^l{\mathrm{\Delta q}}_c$ , was preferable for the exothermic reactions. The same relationship encompassed members of the family with $q_c\text{\hspace{0.17em}<\hspace{0.17em}0}$ (endothermic reactions). With the proviso that (4) shall be applicable, (1)–(3) are summarized in the proposition that the barrier moves to successively later positions along the reaction coordinate with increasing barrier height. This progressive shift of the barrier is embodied in the following approximate relationships: $\Delta \log E_C{\mathrm{\hspace{0.17em}=\hspace{0.17em}-\beta }}_1^l{\mathrm{\Delta r}}_1^{\text{‡,0}}\mathrm{,\; \Delta }\log r_2^{\text{‡,0}}{\mathrm{\hspace{0.17em}=\hspace{0.17em}-a\Delta r}}_1^{\text{‡,0}}{\mathrm{\hspace{0.17em}+\hspace{0.17em}c\Delta [(r}}_1^{\text{‡,0}}{)}^{\text{−1}}]$ , where $r_1^{\text{‡,0}}$ and $r_2^{\text{‡,0}}$ are the extensions of AB and BC, from their equilibrium separation, at the crest of the barrier. In view of (4), ${\mathrm{\Delta q}}_c{\mathrm{\hspace{0.17em}=\hspace{0.17em}(\beta }}_1^l{\mathrm{\hspace{0.17em}/\hspace{0.17em}\alpha }}^l{\mathrm{)\Delta r}}_1^{\text{‡,0}}$ , a relationship which encompasses both exothermic and endothermic reactions. The fraction of attractive energy release alters from one exothermic reaction to the next by approximately ${\mathrm{\Delta (\alpha \perp )\hspace{0.17em}=\hspace{0.17em}\gamma }}_1{\mathrm{\Delta r}}_1^{\text{‡,0}}$ ; hence, $\Delta \log E_C{\mathrm{\hspace{0.17em}=\hspace{0.17em}-(\beta }}_1^l{\mathrm{\hspace{0.17em}/\hspace{0.17em}\gamma }}_1{\mathrm{)\; \Delta \; (\alpha }}_{\perp })$ .