EXPERIMENT 9

1. 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

2. 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

3. Schrödinger Equation Eigenfunction Eigenvector Eigenvalue

4. The Born-Oppenheimer Approximation • Molecular Hamiltonian (time independent form) • Electronic Hamiltonian Kinetic energyof electrons Repulsion ofelectrons Repulsion of nuclei Kinetic energyof nuclei Attractionbetweennuclei andelectrons

5. The Born-Oppenheimer Approximation too heavy to move Electron Nucleus moves around very 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.

6. 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.

7. The Born-Oppenheimer Approximation to find out nuclear Hamiltonian, we know Kinetic Energy Potential Energy Surface 1 1 Nuclear Hamiltonian

8. The Born-Oppenheimer Approximation

9. 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.

10. Computational Chemistry • Scheme for solving many-electron system A molecule HF

11. 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.

12. Hartree–fock Method (HF) electron indices spin orbital indices

13. 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)

14. Hartree–fock Method (HF) • Purely many-electron Hamiltonian • HF Mean-field Hamiltonian Kinetic energy Electron-electron Repulsion Columbic Attraction

15. Hartree–fock Method (HF) (Linear combination of primitive functrion)

16. Hartree–fock Method (HF)Split-valence Basis Sets – The Pople Basis Sets • General expression • Some common types with diffuse functions X – YZ + G* with polarization functions Gaussian-type # basic sets for valance shell orbitals # basic sets forinert shell orbitals 3-21G 3-21G* 3-21+G 3-21+G* 6-21G 6-31G 6-31G* 6-31+G* etc. John A. Pople(1925-2004) Nobel Prize in Chemistry(1998)

17. 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.

18. Hartree–fock Method (HF)Self-consistent Field (SCF) • Solution process Choose a basic sets There seems that we almost could find no more lower energy for the system. Work many times.

19. 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 energyof 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.

20. Eyring Equation Henry Eyring (1901-1981)

21. Eyring Equation • Transition State Theory Reaction Coordinate

22. Eyring Equation • Derive Eyring eq. For a reaction Assume its mechanism: Pre-equilibrium + Transition state

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

24. Eyring Equation Recall, rate const. of the reaction:

25. Eyring Equation

26. Eyring Equation

27. Eyring Equation

28. Eyring Equation

29. Eyring Equation Until now, we had deduced: Recall, Eyring eq. #

30. Procedure 點選“clean”可調整分子至較佳形狀 點選Element Fragment 開啟軟體Gauss View建構Gaussian03之imput ↓ 以水分子為例 點選modify bond 和 modify angle 儲存成 .gjf 檔 選擇single bond→”OK” Lable 欲調整的原子 分別點選O和H並在作圖處點擊 Lable三個調整其鍵角

31. 開始 使用軟體Gaussian03並開啟GaussView儲存的imput檔 計算完成 更改指令為HF/6-31Gopt freq

34. 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

35. THE END Thank you for your attention.