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…
Lindemann-Hinshelwood unimolecular framework: k_uni = k₁·k₂·[M]/(k₋₁·[M] + k₂) (fall-off between 2nd and 1st order)
Lindemann-Hinshelwood unimolecular reaction mechanism: A + M ⇌ A* (rate constants k₁ forward, k₋₁ reverse); A* → products (rate k₂). …
Kramers high-friction barrier-crossing framework: k = (ω_a·ω_b)/(2π·γ)·exp(−E_b/kT) (γ^(−1) Kramers slow-down)
Kramers high-friction escape rate: for a particle in a double-well potential coupled to a heat bath at friction γ, the barrier-crossing…
Landau-Zener non-adiabatic transition framework: P_dia = exp(−2π·H²/(ℏ·v·ΔF)) (velocity-dependent curve-crossing)
Landau-Zener non-adiabatic transition probability: at a curve crossing between two diabatic potentials the probability of remaining on the…
Lindemann unimolecular limits: low-[M] leading term = k₁·[M]; high-[M] asymptote = k₁·k₂/k₋₁ = k_∞
Pressure-limit evaluations: k_uni low-[M] leading term is k₁·[M] (activation-limited, linear in [M]); k_uni high-[M] limit is k₁·k₂/k₋₁…
Kramers high-friction: k(2γ)/k(γ) = 1/2; γ·k = (ω_a·ω_b/2π)·exp(−E_b/kT) is γ-invariant
Friction-scaling evaluations: k(2γ)/k(γ) = 1/2 exactly (doubling friction halves the rate); γ·k is γ-independent: γ·k =…
Landau-Zener transition: P_dia(v→0) = 0 (adiabatic); P_dia(v→∞) = 1 (diabatic); four exact limits
Velocity-limit evaluations: P_dia(v → 0) = 0 (adiabatic limit); P_dia(v → ∞) = 1 (diabatic limit); P_adia(v → 0) = 1 (adiabatic limit);…
RRKM theory (Marcus 1952)
Rice-Ramsperger-Kassel 1928 + Marcus 1952 RRKM: unimolecular rate k(E) from microcanonical density-of-states; basis of master-equation…
Crossed beams (Herschbach-Lee)
Herschbach 1960s + Y T Lee 1980s crossed-molecular-beam (Nobel 1986); state-resolved differential cross-sections; F + H2 -> HF + H…
Femto-chem (Zewail 1980s)
A Zewail 1980s (Nobel 1999) fs-pump-probe of transition state; ICN -> I + CN ~200 fs direct observation; basis of modern ultrafast…
Tully fewest-switches (1990)
J C Tully 1990 fewest-switches surface-hopping (FSSH) algorithm; semi-classical non-adiabatic dynamics; standard photochemistry simulation…
TS spectroscopy (Neumark 1990s)
D Neumark 1990s anion-photoelectron-spectroscopy of transition-state; FH2- + hv -> F-H-H + e-; direct probe of TS region; basis of…
VTST (Truhlar)
D Truhlar 1980s+ variational transition-state-theory: minimize k(T) over reaction-coordinate; semiclassical-tunneling correction;…
Femtochemistry detail (Zewail 1988)
A Zewail 1988 (Nobel 1999) ICN→I+CN 200 fs; modern attoclock + electron-diffraction + UED 4D-imaging chemical-dynamics.
Polanyi rules detail (1962)
J Polanyi 1962 (Nobel 1986) state-correlation early-vs-late-barrier; modern modern HCl + IR-laser-control surface-chem.
Crossed beams detail (Herschbach-Lee Nobel 1986)
D Herschbach-Y Lee 1986 (Nobel 1986) crossed-molecular-beam K+CH3I→KI+CH3; modern velocity-map-imaging + cold-molecule.
RRKM (Marcus 1952)
R Marcus 1952 RRKM unimolecular-reaction; modern variational-TST Truhlar 1985 + master-equation modern combustion-mechanisms.
Variational TST (Truhlar 1985)
D Truhlar 1985 + 2017 variational-TST; modern modern accuracy-rate constants thermal+barrier-tunneling-correction Eckart 1930.
KIE (Bigeleisen 1949)
J Bigeleisen 1949 + Westheimer kinetic-isotope-effect; modern enzymology-tunneling + multiple-isotope-correlation Hammes-Schiffer.