The Activated Complex in Chemical Reactions
Every reaction must climb to a fleeting summit — and that one barrier sets its speed.
Why is one reaction over in a heartbeat and another takes a thousand years? Eyring found the answer in a single instant that every reaction must pass through.
The idea, unpacked
For a reaction to happen, the starting molecules cannot simply slide into the products. They must first be pushed 'uphill' into a strained, half-made and half-broken arrangement — like a ball that has to be lifted over a hill before it can roll down the far side. Eyring named that fleeting peak arrangement the activated complex, and made a daring move: treat it as if it were an ordinary molecule, momentarily in balance with the reactants.
Once you do that, the speed of the whole reaction comes from two things: how many molecules, at any instant, have enough energy to sit at the top — set by the height of the hill, the activation energy — and how fast those summit arrangements tip over into products. The second number turned out, astonishingly, to be universal: the same for every reaction, a frequency k_BT/h fixed by nothing but the temperature.
Where it came from
In the early 1930s Henry Eyring, an American chemist at Princeton, had been mapping the 'energy landscape' a reaction travels across. With Michael Polanyi he had drawn one of the first such surfaces, for the simplest reaction of all — a hydrogen atom meeting a hydrogen molecule. In a 1935 paper in the Journal of Chemical Physics he turned that picture into a general recipe for speed. The story goes that he finished writing it in a hospital bed, recovering from a car crash on the road back to Princeton.
At almost the same moment, in Manchester, Meredith Evans and that same Michael Polanyi published the same idea in thermodynamic dress; the result is sometimes called the Eyring–Polanyi equation. Curiously, though it reshaped all of chemical kinetics, it never won a Nobel Prize.
Why it mattered
Before Eyring, chemists could measure how fast a reaction went and fit it to Arrhenius's 1889 formula — but the formula's 'pre-factor' was just a number pulled from the data. Eyring gave it a meaning, and in principle a way to calculate a reaction's speed from the shapes and energies of molecules alone. He also split the barrier into an enthalpy part (energy) and an entropy part (how much order the summit demands) — two dials chemists still read off every mechanism today.
An everyday analogy
Think of a mountain pass between two valleys. To cross from one to the other you don't tunnel through the mountain — you climb to the lowest notch in the ridge, the pass, and drop down the far side. A reaction is the same: the activated complex is the pass, the activation energy is its height, and the colder the day (the lower the temperature) the fewer travellers have the energy to reach it, so the slower the crossing. Slide the controls below to raise or lower the pass and feel how violently the traffic responds.
Where it sits
Eyring's theory completed a line that began with Arrhenius (1889), who first wrote rate as an exponential of an activation energy, and it set the stage for what came after. Marcus's theory of electron transfer (1956) is transition-state thinking adapted to the jump of a single electron; the modern picture of how enzymes work — by stabilizing exactly this fleeting summit — descends straight from it. And to know the energy landscape in the first place, it leans on the quantum chemistry of the chemical bond (Pauling).
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.