化学 1935

《化学反应中的活化络合物》

亨利·艾林

每个反应都得先爬到一个转瞬即逝的顶点——正是这道关卡，定下了它的快慢。

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In depth · the introduction

为什么有的反应一瞬间就完了，有的却要等上一千年？艾林在每个反应都必经的那一个瞬间里，找到了答案。

把这个想法拆开看

反应要发生，起始的分子不能直接滑成产物——它们得先被「推上坡」，挤进一个紧绷的、半成半断的构型，就像一个球得先被举过山头，才能滚下另一侧。艾林给那个转瞬即逝的顶点构型起名叫活化络合物，并下了一步大胆的棋：把它当作一个普通分子，看成与反应物短暂地处于平衡。

这样一来，整个反应的快慢，就由两件事定下：在任一瞬间，有多少分子有足够能量待在顶上（由那座山的高度——活化能——决定），以及那些顶点构型翻向产物有多快。而第二个数，竟然是普适的——对每个反应都一样——一个只由温度定下的频率 k_BT/h。

它从哪里来

1930 年代初，在普林斯顿的美国化学家亨利·艾林，一直在描绘反应所穿越的那张「能量地形图」。他与迈克尔·波拉尼一道，为最简单的反应（一个氢原子撞上一个氢分子）画出了最早的几张这种面之一。在 1935 年《化学物理杂志》的一篇论文里，他把那张图变成了一套通用的求速配方。据说，这篇论文，是他在返回普林斯顿途中遭遇车祸、于病床上养伤时写完的。

几乎在同一刻，曼彻斯特的梅雷迪思·埃文斯，与同一个迈克尔·波拉尼，以热力学的外衣发表了同一个想法；这条结果因此有时被称作艾林—波拉尼方程。耐人寻味的是，尽管它重塑了整个化学动力学，却从未得过诺贝尔奖。

它为何重要

在艾林之前，化学家能测出反应有多快，并把它套进阿伦尼乌斯 1889 年的公式——可公式里那个「指前因子」，不过是从数据里凑出的一个数。艾林给了它意义，并且原则上，给了一条仅凭分子的形状与能量去计算反应快慢的路。他还把势垒拆成「焓」的一份（能量）与「熵」的一份（顶点要求多少有序）——这是化学家今天读每一个机理时，仍在拨的两个旋钮。

一个日常的类比

把它想成两座山谷之间的一个山口。要从一谷到另一谷，你不会凿穿大山——你会爬到山脊上最低的那个豁口，也就是山口，再从另一侧下去。反应也一样：活化络合物就是那个山口，活化能是它的高度，而天越冷（温度越低），有力气爬到那儿的人就越少，于是穿越越慢。拖动下方的控件，把山口抬高或压低，感受一下车流如何剧烈地回应。

它在知识谱系里的位置

艾林的理论，补全了一条始于阿伦尼乌斯（1889）的线——后者第一次把速率写成活化能的指数；它也为之后的一切铺了路。马库斯的电子转移理论（1956），就是把过渡态的思路，搬到一个电子的跳跃上；而我们今天对酶如何工作的理解——靠稳定恰恰是这个转瞬即逝的顶点——也是它的直系后代。而要首先知道那张能量地形长什么样，它还得倚仗化学键的量子化学（鲍林）。

The original document

Original source text

H. Eyring · J. Chem. Phys. 3(2), 107–115 · February 1935 · Princeton University (submitted November 1934)

The problem

Arrhenius had shown in 1889 that a rate constant obeys k = A·exp(−E_a/RT): reaction speeds rise steeply with temperature, governed by an activation energy E_a. But the pre-exponential factor A was an empirical number, read off the data, with no theory behind it — and there was no way to compute a rate from the molecules themselves.

Abstract (as published)

The calculation of absolute reaction rates is formulated in terms of quantities which are available from the potential surfaces which can be constructed at the present time. The probability of the activated state is calculated using ordinary statistical mechanics. This probability multiplied by the rate of decomposition gives the specific rate of reaction. The occurrence of quantized vibrations in the activated complex, in degrees of freedom which are unquantized in the original molecules, leads to relative reaction rates for isotopes quite different from the rates predicted using simple kinetic theory.

The activated complex

A reaction traces a path across a potential-energy surface and must cross its lowest pass — a saddle point. The configuration sitting on that col is the activated complex. Eyring treated it as an ordinary molecule, fully in equilibrium with the reactants, with one exception: of its internal degrees of freedom, the motion along the reaction coordinate is not a bound vibration but a loose translation that carries the system over the top toward products.

Its concentration then follows from ordinary statistical mechanics — an equilibrium constant built from molecular partition functions. The rate is that concentration multiplied by the frequency with which each complex falls apart. When the reaction-coordinate mode is separated out of the partition function as a free translation over a small length, that frequency collapses to a single universal quantity, k_BT/h ≈ 6.2×10¹² s⁻¹ at room temperature — the same for every reaction.

[ … ]

The master equation

The result can be written k = κ (k_BT/h)(Q‡/Q_AQ_B) exp(−E₀/RT) in terms of partition functions, or in thermodynamic dress as k = κ (k_BT/h) exp(−ΔG‡/RT) = κ (k_BT/h) exp(ΔS‡/R) exp(−ΔH‡/RT). The transmission coefficient κ (≤ 1) accounts for complexes that slip back; ΔH‡ and ΔS‡ are the enthalpy and entropy of activation.

What followed

Working independently in Manchester, M. G. Evans and Michael Polanyi published the same thermodynamic formulation in 1935 (Trans. Faraday Soc. 31, 875); the equation is often the Eyring–Polanyi equation. Wigner gave it a rigorous dynamical footing in 1938, clarifying that the theory yields an upper bound on the rate. The 1941 textbook of Glasstone, Laidler and Eyring, The Theory of Rate Processes, carried it into general use.

Princeton, New Jersey · 1934–1935