An index-1 saddle point on the energy landscape defines the transition state between reactants and products. The Arrhenius law k = A·exp(−Eₐ/kT) connects barrier height to reaction rate via mean first-passage time.
1.00
Barrier Eₐ
0.368
Rate k (arb.)
2.72
MFPT τ
1.00
k_B T
Controls
Theory
Arrhenius rate:
k = A · exp(−Eₐ/k_BT)
Kramers (1940):
k = (ω_min·ω_sad)/(2πζ)
· exp(−Eₐ/k_BT)
MFPT = 1/k
Index-1 saddle:
∇V=0, one neg. eigenvalue
Hessian: (+,+,...,−,...)