Transition State Theory K. Rademann, HU, Chemistry

The importance of TST cannot be overestimated

IUPAC Definition: TST N

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

Henry Eyring 1935

Transition state

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

Make-as-you-break “displacement” is much easier. H2 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

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

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)

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

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

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)

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

Activated Complex

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 10-27 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

An estimate of the lifetime of the activated complex: n = kBT/h = [1.38 x 10-16 erg-deg][298]/[6.6 x 10-27 erg-sec = 6.2 x 1012 s-1 The lifetime = 1/n = 1.6 x 10-13 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‡

TST

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)

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)]

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

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

Complicated Reactions

OH radical attachment

Energy Profile: ipso,m, o,p

Rate constants

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