1. 國立中正大學 化學暨生物化學研究所 博士論文口試 孫翊倫 (Yi-Lun Sun) 指導教授：胡維平 (Wei-Ping Hu) 中華民國 101 年 7 月 10 日

2. Content Chapter 1 Accurate Multi-Coefficient Electronic Structure Methods MLSE(Cn)-DFT for Thermochemical Kinetics Chapter 2 A New Set of Accurate Multi-level Methods Including Parameterization for Heavy Elements Chapter 3 Theoretical Prediction of Stable Noble-Gas Anions XeNO 2  and XeNO 3  with very Short Xenon-Nitrogen Bond Lengths 2 博士論文口試

3. Content Chapter 4 Theoretical Prediction of A New Class of Xenon Containing Molecules and Anions NXeO n F m Chapter 5 Theoretical Study on the Excited State Dynamics of Phenol Chromophores Chapter 6 Theoretical Prediction of A New Type Xe Polymer 博士論文口試 Chapter 2 A New Set of Accurate Multi-level Methods Including Parameterization for Heavy Elements 3

4. Theoretical Study on the Excited State Dynamics of Phenol Chromophores

5. Tyrosine 博士論文口試 Tyrosine, one of the 22 amino acids that are used by cells to synthesize proteins. 5

6. Fluorescence? 博士論文口試 The so-called photostability prevents the undesired photochemical reactions for these molecules upon the irradiation with ultraviolet photons. 6

7. PES of phenol 博士論文口試 Sobolewski, A. L.; Domcke, W. Chem. Phys. 2000, 259, 181. 7

8. 2-hydroxybenzoic acid 博士論文口試 8 2-HBA 3-HBA 4-HBA

9. methods Geometry: B3LYP/6-311+G** PES: TD B3LYP/6-311+G** CAS/6-31+G** Program: Gaussian 03/09 Molpro 2010 博士論文口試 9

10. active space 博士論文口試 CAS(12,12)/6-31+G** 12  electrons and 12 orbitals (6 , 4  *, and 2  *) 10

11. 3-HBA and 4-HBA 博士論文口試 11

12. 3-HBA and 4-HBA 博士論文口試 12 3-HBA 4-HBA

13. 2-HBA 博士論文口試 13

14. 2-HBA-1 博士論文口試 CAS(12,12)/6-31+G** 14

15. 2-HBA-3 博士論文口試 CAS(12,12)/6-31+G** 15

16. HAP, MOBA 博士論文口試 16 2-hydroxyacetophenone (2-HAP) 2-methoxybenzoic acid (2-MOBA)

17. HAP, MOBA 博士論文口試 17

18. 2-HAP-1 博士論文口試 18

19. 2-HAP-2 博士論文口試 19

20. 2-MOBA-1 博士論文口試 20

21. Conclusions Recent theoretical calculations suggested that the low fluorescence quantum yield for phenol was due to dissociation from an excited electronic state potential energy surface. 博士論文口試 21 Sobolewski, A. L.; Domcke, W. Chem. Phys. 2000, 259, 181.

22. 2-hydroxybenzoic acid 博士論文口試 22 2-HBA 3-HBA 4-HBA

23. Conclusions For various conformers of HBA and HAP without intramolecular hydrogen bonding, the second excited state is a repulsive state. It crosses 2A' at short O-H bond distance and crosses 1A' at large O-H bond distance. Hydrogen atom elimination can occur easily on this repulsive potential energy surface. 博士論文口試 23

24. Conclusions For all the MOBA, the second excited state is a repulsive state. It crosses 2A' at short O-C bond distance and crosses 1A' at large O-C bond distance. CH 3 group elimination can occur easily on this repulsive potential energy surface. 博士論文口試 24

25. Conclusions For conformers of 2-HBA and 2- HAP with intramolecular hydrogen bonding, the formation of intramolecular hydrogen bonding reduces the ground state (1A') energy significantly at large O-H distances due to the formation of zwitterionic species and avoids the intersecting with the 1A" state. No H atom elimination analogous to that of phenol was observed 博士論文口試 25

26. A New Set of Accurate Multi-level Methods Including Parameterization for Heavy Elements

27. Schrödinger Equation Electron correlation → Basis set Type 3-21G 6-31+G** aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ HF MP2 MP3 MP4 QCISD(T) … Full CI … … … … … … … ∞ Quantum Chemical Calculations 27 ● ● 博士論文口試

28. Example: MP2/aug-cc-pVDZ QCISD(T)/aug-cc-pVTZ Deficiencies: 1.Low accuracy 2.Cost expensive 28 Single Level Methods 博士論文口試

29. 29 Error of the reaction energy ： CH 4 + Cl 2 → CH 3 Cl + HCl, E rxn =  23.1 kcal/mol MP2/aug-cc-pVDZ ： 8.1 kcal/mol QCISD(T)/aug-cc-pVTZ ： 1.9 kcal/mol CH 4 → C + 4 H (atomization energy), E rxn = 420.1 kcal/mol MP2/aug-cc-pVDZ ： 25.6 kcal/mol QCISD(T)/aug-cc-pVTZ ： 6.0 kcal/mol MP2/aug-cc-pVDZ > 5 kcal/mol QCISD(T)/aug-cc-pVTZ > 1 kcal/mol Single Level Methods 博士論文口試

30. 30 Cost ： MP2/aug-cc-pVDZ Time ： 1 unit QCISD(T)/aug-cc-pVTZ Time ： 288 units ~ couple hours Single Level Methods 博士論文口試

31. Popular Multi-level Methods: G1, G2, G3, G4 Multi-level Methods with Scaled Energies: (Multi-coefficient Method) MCG3, G3S, G3SX, MLSEn+d Multi-level Methods 31 博士論文口試

32. G3 & G3S Geometry:MP2(full)/6-31G(d) E base : MP4/6-31G(d) ΔE + : MP4/6-31+G(d)  E base Δ E 2df,p : MP4/6-31G(2df,p) – E base Δ E QCI : QCISD(T)/6-31G(d) – E base Δ E G3Large : MP2(full)/G3Large – [ MP2/6-31G(2df,p) +MP2/6- 31+G(d) – MP2/6-31G(d) ] Δ E HLC : – An β – B(n α – n β ) E(G3)= E base + ΔE + + ΔE 2df,p + ΔE QCI + ΔE G3Large + ΔE HLC + E ZPE Journal of Chemical Physics, 1998, 109, 7764-7776 32 C1 C2 C3 C4 博士論文口試

33. The MLSE(C1)-DFT Method E(MLSE(C1)-DFT) = C WF { E(HF/pdz) + C E2 [E2/pdz] + C E34SDQ [E(MP4SDQ/pdz) – E(MP2/pdz)] + C QCID [E(QCISD/pdz) – E(MP4SDQ/pdz)] + C QCI [E(QCISD(T)/pdz) – E(QCISD/pdz)] + C B1E2 [E2/ptz – E2/pdz] + C HF+ [E(HF/apdz) – E(HF/pdz]) + C E2+ [E2/apdz – E2/pdz] + C B2E2 [E2/aptz – E2/apdz] + C B1E34 [E(MP4D/ptz) – E(MP4D/pdz)] } + (1 - C WF ) { E(DFTX/pdz) + C DFT+ [E(DFTX/apdz – DFTX/pdz] }. 33 Chem. Phys. Lett. 2009, 475, 141. 博士論文口試

34. Database MGAE109 Database. 109 atomization energies (AEs). IP13 and EA13 Database. 13 IPs and 13 EAs HTBH38 Database. 38 transition state barrier heights for hydrogen transfer (HT) reactions. Training sets NHTBH38 Database. 38 transition state barrier heights for non-hydrogentransfer (NHT) reactions. 34 博士論文口試

35. MLSE(C1)-M062X HFMP2MP4QCISD(T)M06-2X pdz ●● apdz ●● ptz ● ● 35 ●●● ● ●● ● 博士論文口試 aptz

36. Computational Cost 36 Cost MUE (kcal/mol) MP2/aug-cc-pVDZ115.1 MLSE(C1)-M06-2X700.56 MLSE(C2)-M06-2X500.59 MLSE(C3)-B3LYP250.62 MLSE-TS250.61 QCISD(T)/aug-cc-pVTZ2886.11 M06-2X/aug-cc-pVTZ161.89 博士論文口試

37. 37 CH 4 + Cl 2 → CH 3 Cl + HCl, E rxn =  23.1 kcal/mol MP2/aug-cc-pVDZ ： 8.1 kcal/mol QCISD(T)/aug-cc-pVTZ ： 1.9 kcal/mol MLSE(C1)-M06-2X ： 1.0 kcal/mol CH 4 → C + 4 H (atomization energy), E rxn = 420.1 kcal/mol MP2/aug-cc-pVDZ ： 25.6 kcal/mol QCISD(T)/aug-cc-pVTZ ： 6.0 kcal/mol MLSE(C1)-M06-2X ： 0.13 kcal/mol Accuracy 博士論文口試

38. MLSE(Cn)-DFT 博士論文口試 38

39. For Heavy Elements? 39 CH 4 + I 2 → CH 3 I + HI, E rxn = 13.1 kcal/mol QCISD(T)/aug-cc-pVTZ ： 4.7 kcal/mol MLSE(C1)-M06-2X ： 2.7 kcal/mol I 2 → 2 I, E rxn = 35.9 kcal/mol QCISD(T)/aug-cc-pVTZ ： 5.4 kcal/mol MLSE(C1)-M06-2X ： 4.3 kcal/mol 博士論文口試

40. New Database 40 unit: kcal/mol AE IP I2I2 35.87HBr90.51I241.01 HI73.79NOBr181.64Br272.43 IBr42.27CH 3 I369.12EA ICl50.19CH 3 Br380.94I70.54 Br 2 45.90C2H5IC2H5I662.69Br77.60 博士論文口試

41. MLSE(C1)-M062X 博士論文口試 41 (unit : kcal/mol) MUE (225) HHAE (10) HHIP (2) HHEA (2) MLSE(C1)-M062X(Eso)0.661.841.222.21 MLSE(C1)-M062X-HA0.661.661.212.30

42. 42 SCS-MP2 C E2S [(E2aa+E2bb)/pdz] + C E2O [(E2ab)/pdz] + C E2+S [(E2aa+E2bb)/apdz] + C E2+O [(E2ab)/apdz] + C B1E2S [(E2aa+E2bb)/ptz] + C B1E2O [(E2ab)/ptz] + C B2E2S [(E2aa+E2bb)/aptz] + C B2E2O [(E2ab)/aptz] + The different scaling factors were used to the same spin and opposite spin perturbational terms (MP2). 博士論文口試

43. MLSE(HA-1) HFMP2MP4QCISD(T)MPW1PW91 pdz ● apdz ●● ptz ● aptz ●● 43 ●●● ●●● ●● ● 博士論文口試

44. MLSE(HA-2) HFMP2MP4QCISD(T)MPW1PW91 pdz ●●●● apdz ●●●● ptz ●●● aptz ●● 44 ● ● ● 博士論文口試

45. New Database 45 unit : kcal/mol AE IP I2I2 35.87HBr90.51I241.01 HI73.79NOBr181.64Br272.43 IBr42.27CH 3 I369.12EA ICl50.19CH 3 Br380.94I70.54 Br 2 45.90C2H5IC2H5I662.69Br77.60 博士論文口試

46. Accuracy 46 (unit : kcal/mol) MUE (225) HHAE (10) HHIP (2) HHEA (2) MLSE(C1)-M062X(Eso)0.661.841.222.21 MLSE(C1)-M062X-HA0.661.661.212.30 MLSE(HA-1)0.580.870.491.07 MLSE(HA-2)0.640.980.481.04 博士論文口試

47. Computational Cost 47 (unit : kcal/mol)Cost MUE (211) MUE (225) HHAE (10) MLSE(C1)-M062X100%0.560.661.66 MLSE(HA-1)162%0.560.580.87 MLSE(HA-2)104%0.620.640.98 博士論文口試

48. Results 48 CH 4 + I 2 → CH 3 I + HI, E rxn = 13.1 kcal/mol QCISD(T)/aug-cc-pVTZ ： 4.7 kcal/mol MLSE(C1)-M06-2X ： 2.7 kcal/mol MLSE(HA-1) ： 0.5 kcal/mol MLSE(HA-2) ： 1.0 kcal/mol I 2 → 2 I, E rxn = 35.9 kcal/mol QCISD(T)/aug-cc-pVTZ ： 5.4 kcal/mol MLSE(C1)-M06-2X ： 4.3 kcal/mol MLSE(HA-1) ： 0.7 kcal/mol MLSE(HA-2) ： 0.6 kcal/mol 博士論文口試

49. Conclusions The MLSE(C1)-M06-2X method provided the lowest overall MUE of 0.56 kcal/mol on the training set. Both MLSE(C1)-M06-2X (Eso) and MLSE(C1)-M06-2X-HA methods performed unsatisfactorily on the 10 heavy halogen containing atomization energies(>1 kcal/mol). 博士論文口試 49

50. Conclusions MLSE(HA-1) and MLSE(HA-2) performed 0.58 and 0.64 kcal/mol on the MUE(225), with the MUE of HHAE(10) both less than 1 kcal/mol. MLSE(HA-1) method required 62% cost more than the MLSE(C1)-M06-2X method. But MLSE(HA-2) method only cost 4% more than the MLSE(C1)-M06- 2X method. 50 博士論文口試

51. Acknowledgement Prof. Wei-Ping Hu Our group members. ( Tsung-Hui Li, Jien-Lian Chen et al.) Department of Chemistry & Biochemistry, National Chung Cheng University National Science Council National Center for High-Performance Computing 51 博士論文口試

52. Thanks for your attention 52 博士論文口試