1. Transition State Theory
K. Rademann, HU, Chemistry

2. The importance of TST cannot be overestimated

3. IUPAC Definition: TST N

4. Structure of the Seminar
Outline
Structure of the Seminar
Thermodynamic Equilibrium (Thermodynamics):
S=klnΩ(U,V,N) and A(T,V,N)=-kTlnQ(T,V,N)
Quantum Mechanical Calculations Hψ=Eψ
Chemical Statistics (Partition Functions): Ω(U,V,N), Q(T,V,N), q(T,V,N), chemical equilibria in terms of partition functions
Chemical Kinetics

5. Henry Eyring 1935

7. Transition state

8. H3 Surface
Henry Eyring
(1935)
Transition State
(“Lake Eyring”)
Crazy angle of axes means that classical trajectories can be modeled by rolling marble.

9. Make-as-you-break “displacement” is much easier.
H H
Henry
Eyring
(1935)
H H H
Dissociation followed by association requires high activation energy.
SLOW
Make-as-you-break “displacement” is much easier.
FAST
HHH
H H2

10. Potential Energy Surface for Linear Triatomic A-B-C
Plateau
ridge +
minimum
Pass
(Transition State
or Transition Structure)
Valley
maximum
Potential Energy Surface for Linear Triatomic A-B-C
Cliff *
* So 2-D specifies structure

11. C flies away from
vibrating A-B
Reactive Trajectory
Potential Energy Surface for Linear Triatomic A-B-C
A approaches
non-vibrating B-C
“classical” trajectory
(not quantum)

12. Unreactive Trajectory: (A bounces off vibrating B-C)
Potential Energy Surface for Linear Triatomic A-B-C

13. Studying Lots of Random Trajectories Provides Too Much Detail
Summarize Statistically with Collective
Enthalpy (H) & Entropy (S)

14. THE REACTION ENERGY SURFACE
Figure 6-6, pg 239, E&C
“transition state complex”
The reaction is reduced to motion along one dimension: the “reaction coordinate”
P.E.
products
reactants
Reaction coordinate (RC)

15. “steepest descent” path
Slice along this path,
then flatten
and tip up to create…
(not a trajectory)

16. Activated Complex

17. A + B [AB]‡ products
[AB]‡ = activated complex
rate = [AB]‡ (rate of crossover) ()
Rate of crossover = the frequency of decomposition of AB‡
 = "transmission coefficient" = fraction of [AB]‡ crossing forward  1
The frequency of decomposition of the activated complex
The vibrational energy in a bond (one-dimensional harmonic oscillator) of the activated complex is
Evib = kBT = hn (h = planck’s constant = 6.6 x erg.sec; n = frequency of vibration)
n = kBT/h
The activated complex has an energy sufficiently great that the nuclei separate during a single vibration, and the frequency of decomposition is just the vibrational frequency n

18. An estimate of the lifetime of the activated complex:
n = kBT/h = [1.38 x erg-deg][298]/[6.6 x erg-sec = 6.2 x 1012 s-1
The lifetime = 1/n = 1.6 x s !
Back to the problem of determining the rate constant
rate = [AB]‡ (rate of crossover) ()
rate = [AB]‡  (kBT/h)
Because [AB]‡ is assumed to be in thermal equilibrium with the reactants
K‡ = [AB]‡ / [A] [B] [AB]‡ = K‡ [A][B]
rate = (kBT/h)  K‡ [A] [B]
Thus the transition state theory of the rate constant gives
k = (kBT/h)kK‡

19. TST

20. S(U,V,N) = kln Ω Ω (U,V,N) = exp (S/k) A(T,V,N)=-kTlnQ(T,V,N)
Partition functions
S(U,V,N) = kln Ω Ω (U,V,N) = exp (S/k) A(T,V,N)=-kTlnQ(T,V,N)

21. Chemical potential µ(T,V,N)
µ(T,V,N) =- kT ln (q(T,V,N)/N) p(T,V,N)= nRT/V S(T,V,N)=kNln[(q/N)e(5/2)]

23. IUPAC Definition Eyring JCP 3 107 1935 Princeton Evans Manchester
Polyani Fritz Haber 1931
Absolute Rate Constant Calculations
Activated Complex Theory
IUPAC: TST N

24. More effects to be discussed
Isotope effects
Primary
Secondary
Tunneling
Tranmission kappa

26. Complicated Reactions

27. OH radical attachment

28. Energy Profile: ipso,m, o,p

29. Rate constants

30. TST: APPLICATIONS Atmospheric Chemistry Solution Chemistry
Electrochemistry
Enzyme Kinetics
Protein Folding
Surface Chemistry
Catalysis (homogeneous, heterogeneous, bio)