experiment 9

EXPERIMENT 9預測化學反應途徑與反應速率

化三 49812012 李雨修 49812051 李國禎 49812049 廖偉智

Purpose• Learn the logical of solving Schrödinger equation :• Born–Oppenheimer approximation• Hartree-Fock method

• Predict the optimized structure of transition state and calculate the rate constant:

• Transition State Theory• Eyring Equation

• Use computer program to investigate some chemical phenomena:• Gaussian 03, Gauss view, ChemDraw

Schrödinger Equation

Eigenvalue

Eigenfunction

Eigenvector

The Born-Oppenheimer Approximation• Molecular Hamiltonian (time independent form)

• Electronic Hamiltonian

Kinetic energyof nuclei

Repulsion of nuclei Kinetic energyof electrons

Attractionbetweennuclei andelectrons

Repulsion ofelectrons

The Born-Oppenheimer Approximation

Nucleus

Electron

too heavy to move

moves aroundvery fast

Nucleus and electron have the same momentum(p=mv). While nucleus is massive(Ma>>Me), relate to electron, it just like nucleus at rest.

The Born-Oppenheimer Approximation

By the Born-Oppenheimer approximation,

thus, the Schrödinger Equation can be extended as

Assume we had solved the electronic wavefunction:

Nuclei wavefunction and electrons wavefunction are independent from each other.

The Born-Oppenheimer Approximation

to find out nuclear Hamiltonian, we know

11

Nuclear Hamiltonian

KineticEnergy

PotentialEnergy Surface

The Born-Oppenheimer Approximation

The Born-Oppenheimer Approximation• Limitation

The error comes form the following condition :

1.) The movement of nuclei is too violent.

So nuclei can’t be viewed as “stationary”.

2.) 1st exciting electronic energy level is too low.

Any condition of a little change of nuclear coordinate leading severe alternation of electronic wavefunction makes intolerant errors.

Computational Chemistry• Scheme for solving many-electron system

A molecule

HF

Computational Chemistry ab initio

Semi-Empirical Molecular Mechanics Density Functional Theory (DFT)

A method simulate molecule behaviors only by some basic physical constants and principles instead of by any simplicity coming from experimental experiences.

Hartree–fock Method (HF)

electronindices

spin orbitalindices

Hartree–fock Method (HF)• It contains all possible permutations, all of them are

“indistinguishable” because it’s impossible to distinguish two electron with the difference.

• Interchanging of two rows flips the sign.asymmetry : electron is fermion (Pauli principle)

• If with two identical columns, the determination is always zero.all electrons with different quantum states (Pauli exclusion principle)

Hartree–fock Method (HF)• Purely many-electron Hamiltonian

• HF Mean-field Hamiltonian

Kinetic energy Electron-electronRepulsion

ColumbicAttraction

Hartree–fock Method (HF)

(Linear combination of primitive functrion)

Hartree–fock Method (HF)Split-valence Basis Sets – The Pople Basis Sets • General expression

• Some common types

X – YZ + G*

3-21G 3-21G*3-21+G 3-21+G* 6-21G 6-31G6-31G* 6-31+G*etc.

# basic sets forinert shell orbitals

# basic sets forvalance shell orbitals

with diffuse functions

with polarization functions

John A. Pople (1925-2004)Nobel Prize in Chemistry

(1998)

Gaussian-type

Hartree–fock Method (HF)Self-consistent Field (SCF)

• Self-consistent Field (SCF)

Directly solve the electronic wavefunction is very difficult because, for one electron, the distribution of other electrons we do not know, but it’s necessary to be known if we want to figure out the electronic wavefunction.

What preferable way is guess an initial condition and then using a mathematical method (i.e. Iterative Method) to approach the exact solution gradually.

Hartree–fock Method (HF)Self-consistent Field (SCF)

• Solution process

Choose a basic sets

Work many times.

There seems that we almost could find no more lower energy for the system.

Hartree–fock Method (HF)• Brief conclusions

1.) If the electronic wavefunction can be expressed as a single Slater determinant, we can decompose the many-electron Hamiltonian as the sum of all single-electron Hamiltonian.

i.e. the electron is independent of others, and the correlation and exchanging energy of electrons is neglected.

2.) The electron motion is regarded as on electron under a mean electric field composed by others.

but we do not know any information about the distribution of electrons.

all we can do is guess the value and optimize it.

Eyring Equation

Henry Eyring (1901-1981)

Eyring Equation• Transition State Theory

Reaction Coordinate

Eyring Equation• Derive Eyring eq.

For a reaction

Assume its mechanism: Pre-equilibrium + Transition state

Eyring Equation

By definition, In gaseous phase, the equilibrium const. for this reaction can be written as:

concentration

Eyring Equation

Recall, rate const. of the reaction:

Eyring Equation

Eyring Equation

Eyring Equation

Eyring Equation

Eyring EquationUntil now, we had deduced:

Recall,

#Eyring eq.

Procedure

開啟軟體 Gauss View建構 Gaussian03 之imput ↓ 以水分子為例

點選 Element Fragment

分別點選 O 和 H 並在作圖處點擊

點選 modify bond 和 modify angle

Lable 欲調整的原子

選擇 single bond→”OK”

Lable 三個調整其鍵角

點選“ clean” 可調整分子至較佳形狀儲存成 .gjf 檔

使用軟體 Gaussian03 並開啟GaussView 儲存的 imput 檔更改指令為 HF/6-31G opt freq

開始

計算完成

i2 C CH

H

B

H

H

i4

C C

HH

H B

tsi2i4

H i5

C C BHH

H H

tsi4i5

i8

tsi4i8

C C B

H

H H

H

0.0

kcal/mol

References• Atkins' Physical Chemistry 9/E, Ch24-4• Levine I.N. Quantum Chemistry 4/E, Ch10-Ch13• http://www.iams.sinica.edu.tw/lab/wbtzeng/labtech/

term_calchem.htm, 20120304• http://www.iams.sinica.edu.tw/lab/wbtzeng/labtech/

basis_set.htm, 20120304• http://en.wikipedia.org/wiki/Born

%E2%80%93Oppenheimer_approximation, 20120303• http://www.nobelprize.org/nobel_prizes/chemistry/laureates/

1998/index.html, 20120305• http://www.shodor.org/chemviz/basis/teachers/

background.html, 20120304• http://www.youtube.com/watch?v=EROZXzS51Co, 20120301• http://en.wikipedia.org/wiki/Hartree

%E2%80%93Fock_method, 20120306

THE ENDThank you for your attention.