过渡态理论

硬球碰撞模型：没有给出准确的速率常数

合适的模型：考虑反应分子之间真实的分子间力，由反应分子到产物分子其结构的变化。

A + B-C →A-

B + C

反应过程中，能量在各个键间重新再分配，旧键断裂，新键生成

1930-1935 H. Eyring& M. Polanyi

在量子力学和统计力学的基础上提出：

反应速率的过渡态理论/ 活化络合物理论

Problems to be solved

1 What is the physical meaning of the Activated Complex, and the Transition State?

2 How to express thermodynamic relation between the reactant and the activated complex ?

3 How to treat the rate of reaction?

Zero point energy E 0= D e -D 0

D e V r

E 0

)]}

(exp[2)](2{exp[)(00r r a r r a D r V e −−−−−=r = r 0, V(r = r 0) = -D e

r →∞, V(r →∞) = 0

AB(ν=0) →A + B

D 0光谱离解能

Morse equation

1 Transition State

1931, Eyring and M.Polanyi

φ= 180 o ,线性碰撞

the potential energy surface 势能面can be plotted in a three dimensions system.

V = V (r AB , r BC )

Activated complex Transition state

To calculate E

= E b+ (1/2)[hν0≠-hν0(rectant)] E

the freedom f or molecule with n atoms

translational freedom: 3 rotational freedom (linear): 2 rotational freedom (no-linear): 3 vibrational freedom (linear): 3n-5 vibrational freedom (no-linear): 3n-6

Absolute rate theory

Example

For elementary equation:

H2+F →H…H …F →H+HF Theoretical: k = 1.17 ×1011exp(-790/T) Experimental: k = 2 ×1011exp(-800/T)

θ

m

r

a H RT E ≠Δ+=For liquid reaction: Δ(PV) = 0

∑ν≠:反应物形成活化络合物时气态物质的物质量的变化

A +

B = [AB]≠

∑ν≠= 1-2 = -1 n: 气态反应物系数之和n = (1-∑ν≠) = 2

nRT

H RT H E m r

B

B m r

a +Δ=−+Δ=≠≠≠∑θ

θ

ν)1(For gaseous reaction: Δ(PV) = ∑ν≠RT

Conclusion:

1 The rate of reaction depends on both activation energy and activation entropy.

2 The pre-exponential factor depends on the standard entropy of activation and related to the structure of activated complex.

Summary on TST:

1 过渡态理论基本点

2 活化络合物& 过渡态

3 The statistical expression for the k of TST 4Thermodynamic treatment for the k of TST: activation energy and activation entropy

Summary

Comparison between STC and TST

作业：

p.305 Ex. 3, 4, SCT

6, 8,10 TST p.306 13,14,15