Comment on "Correct Symmetry Treatment for X + X Reactions Prevents Large Errors in Predicted Isotope Enrichment".

Eli Pollak,Philip Pechukas

doi:10.1021/acs.jpca.0c00210

Abstract

The "Addition" by Goldman et al. to their paper "Correct Symmetry Treatment for X + X Reactions..." is in essence a correction of a serious misreading of our 1978 paper "Symmetry Numbers, Not Statistical Factors, Should Be Used in Absolute Rate Theory..." . This misreading led Goldman et al. to accuse us unjustly of major errors in rate theory. Goldman et al. misread us as recommending an additional factor of 2 in their definition of the rate constant. Naturally, error results. We saw neither the original paper by Goldman et al. nor the subsequent "Addition" before publication. Too bad; this misunderstanding could have easily been avoided.

Highlights

W e appreciate the “Addition”[1] by Goldman et al to their original paper[2] because it is in essence a correction of a serious misreading of our 1978 paper.[3]. This misreading led Goldman et al to accuse us unjustly of major errors in rate theory: “... thermodynamic inconsistencies in the equilibrium constant and ... huge discrepancies in isotopic enrichment ...”2 It is ironic that thermodynamic inconsistencies associated with the use of statistical factors in rate theory are what prompted our
For a bimolecular reaction A + B → product one writes the rate of forward reaction as k′[A][B] and symmetry numbers enter the rate constant k′ through the combination σAσB/σTS where σTS is the symmetry number of the transition state, σA and σB the symmetry numbers of reactants
If A = B, the symmetry number factor in the forward rate k′[A]2 is 2σA2/σTS rather than σA2/σTS, as we pointed out in 1978 by considering the number of physically distinct configurations of reactants in which like atoms are distinguished by labels

Summary

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W e appreciate the “Addition”[1] by Goldman et al to their original paper[2] because it is in essence a correction of a serious misreading of our 1978 paper.[3]. For a bimolecular reaction A + B → product one writes the rate of forward reaction as k′[A][B] and symmetry numbers enter the rate constant k′ through the combination σAσB/σTS where σTS is the symmetry number of the transition state, σA and σB the symmetry numbers of reactants. If A = B (the reactions considered by Goldman et al.), the symmetry number factor in the forward rate k′[A]2 is 2σA2/σTS rather than σA2/σTS, as we pointed out in 1978 by considering the number of physically distinct configurations of reactants in which like atoms are distinguished by labels (see the sentence immediately following eq 5a of our paper). Goldman et al write the forward rate of A + A reactions as 2k[A]2, where the symmetry number factor in k is σA2/σTS, and misread us as recommending an additional factor of 2 in their rate constant k.

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