化學 1935

《化學反應中的活化錯合物》

亨利·艾林

每個反應都得先爬到一個轉瞬即逝的頂點——正是這道關卡，定下了它的快慢。

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In depth · the introduction

為什麼有的反應一瞬間就完了，有的卻要等上一千年？艾林在每個反應都必經的那一個瞬間裡，找到了答案。

把這個想法拆開看

反應要發生，起始的分子不能直接滑成產物——它們得先被「推上坡」，擠進一個緊繃的、半成半斷的構型，就像一個球得先被舉過山頭，才能滾下另一側。艾林給那個轉瞬即逝的頂點構型起名叫活化錯合物，並下了一步大膽的棋：把它當作一個普通分子，看成與反應物短暫地處於平衡。

這樣一來，整個反應的快慢，就由兩件事定下：在任一瞬間，有多少分子有足夠能量待在頂上（由那座山的高度——活化能——決定），以及那些頂點構型翻向產物有多快。而第二個數，竟然是普適的——對每個反應都一樣——一個只由溫度定下的頻率 k_BT/h。

它從哪裡來

1930 年代初，在普林斯頓的美國化學家亨利·艾林，一直在描繪反應所穿越的那張「能量地形圖」。他與麥可·波拉尼一道，為最簡單的反應（一個氫原子撞上一個氫分子）畫出了最早的幾張這種面之一。在 1935 年《化學物理雜誌》的一篇論文裡，他把那張圖變成了一套通用的求速配方。據說，這篇論文，是他在返回普林斯頓途中遭遇車禍、於病床上養傷時寫完的。

幾乎在同一刻，曼徹斯特的梅雷迪思·埃文斯，與同一個麥可·波拉尼，以熱力學的外衣發表了同一個想法；這條結果因此有時被稱作艾林—波拉尼方程。耐人尋味的是，儘管它重塑了整個化學動力學，卻從未得過諾貝爾獎。

它為何重要

在艾林之前，化學家能測出反應有多快，並把它套進阿倫尼烏斯 1889 年的公式——可公式裡那個「指前因子」，不過是從數據裡湊出的一個數。艾林給了它意義，並且原則上，給了一條僅憑分子的形狀與能量去計算反應快慢的路。他還把勢壘拆成「焓」的一份（能量）與「熵」的一份（頂點要求多少有序）——這是化學家今天讀每一個機理時，仍在撥的兩個旋鈕。

一個日常的類比

把它想成兩座山谷之間的一個山口。要從一谷到另一谷，你不會鑿穿大山——你會爬到山脊上最低的那個豁口，也就是山口，再從另一側下去。反應也一樣：活化錯合物就是那個山口，活化能是它的高度，而天越冷（溫度越低），有力氣爬到那兒的人就越少，於是穿越越慢。拖動下方的控件，把山口抬高或壓低，感受一下車流如何劇烈地回應。

它在知識譜系裡的位置

艾林的理論，補全了一條始於阿倫尼烏斯（1889）的線——後者第一次把速率寫成活化能的指數；它也為之後的一切鋪了路。馬庫斯的電子轉移理論（1956），就是把過渡態的思路，搬到一個電子的跳躍上；而我們今天對酶如何工作的理解——靠穩定恰恰是這個轉瞬即逝的頂點——也是它的直系後代。而要首先知道那張能量地形長什麼樣，它還得倚仗化學鍵的量子化學（鮑林）。

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