PARAMETERS
k (Arrhenius): —
k (Kramers): —
k (Eyring): —
Half-life t₁/₂: —
Arrhenius (1889): k = A·exp(−Eₐ/RT). The pre-exponential A encodes attempt frequency; the exponential is the Boltzmann probability of surmounting the barrier.
ln k = ln A − Eₐ/(RT)
Kramers (1940) derives the rate from the Fokker-Planck equation — valid for overdamped or underdamped limits.
Eyring / TST (1935): k = (k_BT/h)·exp(−ΔG‡/RT) — uses partition functions at the transition state.
The slope of the Arrhenius plot (ln k vs 1/T) is −Eₐ/R — a straight line reveals the activation energy directly.