Reaction dynamics — the microscopic / state-resolved / single-trajectory study of how chemical reactions actually happen, distinct from the ensemble-averaged rate-law phenomenology of chemical-kinetics. Foundations: (1) Arrhenius 1889…
reaction-dynamics
Arrhenius framework: k = A·exp(-E_a/RT) and Arrhenius-plot slope
The Arrhenius framework — the empirical two-parameter temperature dependence k(T) = A·exp(-E_a/RT) that underlies every phenomenological…
Eyring transition-state theory: k = (k_B·T/h)·exp(-ΔG‡/RT)
Eyring 1935 transition-state theory (TST) — the statistical-mechanical reformulation of Arrhenius. Central assumption: the reactants are…
Detailed balance & van 't Hoff: K_eq = k_f/k_r = exp(-ΔG_rxn/RT)
The detailed-balance principle — at equilibrium, every elementary forward process is exactly balanced microscopically by its reverse…
Arrhenius: k(T → ∞) = A; k(T → 0⁺) = 0; ln[k(T)/k(2T)] = -E_a/(2RT)
Sympy-exact symbolic witness of the two Arrhenius-law limiting behaviours plus the T-doubling log-ratio fingerprint. Setup: k(T) =…
Eyring: thermoneutral ΔG‡ = 0 ⇒ k = k_B·T/h (universal frequency ceiling)
Sympy-exact symbolic witness of the Eyring TST universal-frequency anchor. Setup: k = k_B·T/h · exp(-ΔG‡/(R·T)) as a sympy expression with…
Detailed balance: K_eq(ΔG_rxn = 0) = 1; ln K_eq = -ΔG_rxn/RT
Sympy-exact symbolic witness of the detailed-balance / van 't Hoff equilibrium-constant relation. Setup: K_eq = exp(-ΔG_rxn/(R·T)) as a…