### Exp9

```實驗九 預測化學反應途徑與反應速率
49912001 趙珮鈞
49912044 鄭宇娟

• 趙珮鈞：目的、原理
• 鄭宇娟：原理、實驗流程、數據處理

1.以電腦為工具探討化學反應。
2.解分子之electronic Schrödinger equation 藉以預測

3.熟悉分子計算程式：Gaussian 03,Gauss View,以及分

4.計算反應速率常數，並得出產量。

• Born-Oppenheimer approximation
• Hatree-Fock method
• Basis set：6-31G
• Reaction rate constant (Eyring equation)

Schrödinger equation
Eigenfunction
Eigenvector
Eigenvalue
Born-Oppenheimer approximation

i
j

Time-independent

Born-Oppenheimer
approximation
electron
Nuclear

electronic Schrödinger equation
U= electronic energy including internuclear repulsion

Born-Oppenheimer approximation 總結：
1. 可用於處理多電子系統。
2. 分子實際的值，較難精準得到，此方法是原子核不動，取得

3. 此方法最重要的目的就是簡化處理波函數，將原子核與電子

。
Hatree-Fock method

function

function
(2n)!為2n個電子在不同軌域中的任意排列。

(1)

Coulomb integrals：電子與電子間的庫倫作用力
Exchange integrals ：電子間交換的能量
Hatree- Fock Equation

HF能量收斂

Hatree- Fock energy

K：basis set
Hatree-Fock method 總結
1.將複雜的

2. HF 方法只考慮了電子間的平均作用力，並未計算原子核能量，

3. HF 方法提供一些很有用的定性預測與最佳化的分子軌域，對於

Basis set

Slater-type orbital (STO)
A
Gaussian-type functions (GTO)
B

Contracted Gaussian-type functions (CGTF)

29)，但具有不同的 exponents(Z)，可稱為
primitive Gaussians
minimal basis set
CGTF 的數目與其在週期表中同週期原子可用之原子軌域數相同。
C
STO-3G basis set
1S
2S
2P
double-zeta (DZ) basis set

split-valence double-zeta basis set

Gaussians 所組成的一個 CGTF。

6-31G

Gaussians 所組成其中一個 CGTF。
Eyring Equation
A+B
2
A+B⇌
‡

‡

transition state
‡ : transition state or activated
complex
potential
energy
reactant
A,B
products
Reaction coordinate
1
○
A + B ⇌ ‡
if in gas :  ‡ =
‡

Θ
Θ

Θ

( assuming ideal gas :  =  ⇒  =  )
⇒
‡
⇒
‡
‡ Θ
‡
Θ
=
=
⋅
⋅

‡
= Θ

2
○
‡
v=
‡

=  ‡  ‡ = Θ  ‡ ‡

∵  =
⇒ 2 =
‡ ‡

Θ
(A+B
2
)
to get ‡
Products can be formed if transition state is passed
If the vibration-like motion along reaction coordinate has a frequency ν
⇒ frequency of  ‡ approaching P is also ν
‡ ∝ ν
⇒  ‡ =
κ : transmission coefficient
to get ‡
K=

‡ =
Θ
,

Θ‡
Θ Θ

−Δ0
−Δ0

( where Δ0 = 0  ‡ − 0  − 0

Θ : standard molar partition function )
Note : we look at vibration mode of  ‡ along reaction coordinate
1
for this special mode q =
−ℎ
1−
∵ ν here is very low ⟹
ℎ

≪1
(  = 1 +  + ⋯ )
1

≈
ℎ
ℎ
1− 1−
+⋯

⟹q=
⟹
⇒
Θ‡
‡
Θ
=
‡
ℎ
=
Θ‡
Θ Θ
−Δ0
=
⋅
Θ
‡ ⋅  −Δ0
ℎ
Θ Θ
‡ ‡
‡
2 = Θ   = Θ ⋅  ⋅

ℎ
‡
=

ℎ
( Eyring equation )

‡
=

ℎ
( let
‡

=
‡

Θ
)

• Atkin’s Physical Chemistry (ch22)
• Levine. Quantum Chemistry 13.1節
• 影片：量子化學 Born-Oppenheimer approximation