EXACT TUNNELING CALCULATIONS.
EXACT TUNNELING CALCULATIONS.
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DOI：
10.1021/ja00737a002
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发表时间：
1971
影响因子：
15
通讯作者：
D. Truhlar;A. Kuppermann
中科院分区：
文献类型：
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作者：
D. Truhlar;A. Kuppermann
化学反应的过渡态理论建立在这样的假设之上，即沿反应路径的运动与沿其横向方向的运动是可分离的，并且后者是绝热的，即它们的量子数随着反应的进行而保持不变。这一假设要求在计算量子力学隧穿因子时，将横向运动的零点能量加到沿反应路径的势能中，以提供一个有效的振动绝热屏障，该屏障应用于此类计算。迄今为止报道的所有隧道计算都忽略了这种零点能量修正或对它们使用不切实际的近似值，并且大多数还用近似的解析拟合来取代反应势垒，从而可以解析地确定传输概率。我们用数值方法对H+ h2和D+ d2共线交换反应进行了精确的量子力学计算，得到以下结论：(1)从Eckart势拟合到势能势垒的传输概率和隧穿因子计算结果会导致较大的系统误差，特别是在低温下，因此不应使用。此外，修正Shavitt的计算以消除他的数值近似，使他使用的模型与实验更吻合。(2)忽略横向运动零点能量及其沿反应路径变化的计算结果与包含零点能量的计算结果有显著差异。由于后者符合过渡态理论的绝热推导，而前者不符合，因此后者与气相实验的一致必须被认为是偶然消除误差的结果，而不应被解释为支持理论背后的假设。
The transition state theory of chemical reactions rests on the assumption that motion along a reaction path is separable from motion in directions transverse to it and that the latter are adiabatic, ie, that their quantum numbers are preserved as the reaction proceeds. This assumption requires that, in calculating quantum mechanical tunneling factors, the zero-point energy of the transverse motions be added to the potential energy along the reaction path to furnish an effective vibrationally adiabatic barrier which should be used in such calculations. All tunneling calculations reported so far have neglected such zero-point energy corrections or used unrealistic approximations for them, and most have also replaced the reaction barrier by approximate analytical fits for which transmission probabilities could be determined analytically. We have performed accurate quantum mechanical calculations by numerical techniques for the collinear exchange reactions of H+ H 2 and D+ D 2 and reached the following conclusions.(1) The results of transmission probability and tunneling factor calculations from Eckart potential fits to the potential energy barrier lead to substantial systematic errors, especially at low temperatures, and therefore should not be used. Further, correcting Shavitt's calculations to eliminate his numerical approximations brings the model he used into better agreement with experiment.(2) The results of calculations ignoring the zero-point energy of the transverse motion and its variation along the reaction path are dramatically different from the ones including it. Since the latter are in accord with the adiabatic derivation of transition state theory and the former are not, agreement of the latter with gas-phase experiments must be considered the result of fortuitous cancellations of errors and should not be construed as support for the assumption behind the theory.