1. A New Set of Accurate Multi-level Methods Including Parameterization for Heavy Elements 演講者：孫翊倫 (Yi-Lun Sun) 指導教授：胡維平 (Wei-Ping Hu) 中華民國 101 年 6 月 11 日

2. Content Chapter 1 A New Set of Accurate Multi-level Methods Including Parameterization for Heavy Elements Chapter 2 & 3 Theoretical Prediction of A New Class of Xenon Containing Molecules and Anions Chapter 4 Theoretical Study on the Excited State Dynamics of Phenol Chromophores Chapter 5 Theoretical Prediction of A New Type Xe Polymer 2

3. 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 3 ● ●

4. Example: MP2/aug-cc-pVDZ QCISD(T)/aug-cc-pVTZ Deficiencies: 1.Low accuracy 2.Cost expensive 4 Single Level Methods

5. 5 Error of the reaction energy ： CH 4 + Cl 2 → CH 3 Cl + HCl MP2/aug-cc-pVDZ ： 8.1 kcal/mol QCISD(T)/aug-cc-pVTZ ： 1.9 kcal/mol CH 4 → C + 4 H (atomization energy) 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

6. 6 Cost ： MP2/aug-cc-pVDZ Time ： 1 unit QCISD(T)/aug-cc-pVTZ Time ： 288 units ~ couple hours Single Level Methods

7. Popular Multi-level Methods: G1, G2, G3, G4 Multi-level Methods with Scaled Energies: (Multi-coefficient Method) MCG3, G3S, G3X, MLSEn+d Multi-level Methods 7

8. G3 theory 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 8

9. MLSEn+d Method E(MLSEn+d) = C HF × E(HF/cc-pV(D+d)Z) + C  HF × [E(HF/cc-pV(T+d)Z )– E(HF/cc-pV(D+d)Z)] + C E2 × [E2/cc-pV(D+d)Z] + C E34 × [E(MP4SDQ/cc-pV(D+d)Z) – E(MP2/cc-pV(D+d)Z)] + C QCI × [E(QCISD(T)/cc-pV(D+d)Z) – E(MP4SDQ/cc-pV(D+d)Z)] + C B × γE2 × [E2/cc-pV(T+d)Z – E2/cc-pV(D+d)Z] + C + × [E2/aug-cc-pV(D+d)Z – E2/cc-pV(D+d)Z] + E SO Chem. Phys. Lett. 2005, 412, 430-433 9

10. Density functional theory (DFT) To obtain energies of molecules and their physical properties without solving wave functions. Common functionals: B3LYP 、 MPW1B95 、 MPW1PW91 、 TPSS1KCIS 、 B1B95 、 M06-2X 10

11. The MLSE-DFT Method E(MLSE-DFT) = C WF { E(HF/cc-pV(D+d)Z) + C  HF [E(HF/cc-pV(T+d)Z )– E(HF/cc-pV(D+d)Z)] + C E2 [E2/cc-pV(D+d)Z] + C E34 [E(MP4SDQ/cc-pV(D+d)Z) – E(MP2/cc-pV(D+d)Z)] + C QCI [E(QCISD(T)/cc-pV(D+d)Z) – E(MP4SDQ/cc-pV(D+d)Z)] + C B [E2/cc-pV(T+d)Z – E2/cc-pV(D+d)Z] + C HF+ [E(HF/aug-cc-pV(D+d)Z) – E(HF/cc-pV(D+d)Z]) + C E2+ [E2/aug-cc-pV(D+d)Z – E2/cc-pV(D+d)Z] } + (1  C WF ) { E(DFTX/cc-pV(D+d)Z) + C B1 [E(DFTX/cc-pV(T+d)Z – DFTX/cc-pV(D+d)Z] } + E SO Chem. Phys. Lett. 2007, 442, 220. 11

12. 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] }. 12 Chem. Phys. Lett. 2009, 475, 141.

13. 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. Train sets and Test sets NHTBH38 Database. 38 transition state barrier heights for non-hydrogentransfer (NHT) reactions. 13

14. Accuracy 14 AE (109) IP (13) EA (13) HTBH (38) NHTBH (38) Overall MUE MLSE(C1)-M06-2X0.620.550.630.470.430.56 MLSE(C2)-M06-2X0.650.600.690.500.440.59 MLSE(C3)-B3LYP0.620.680.820.450.680.62 MLSE-TS0.62--0.550.690.61 QCISD(T) / aug-cc-pVTZ 10.902.051.940.600.736.11

15. Computational Cost 15 CostMUE 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

16. 16 CH 4 + Cl 2 → CH 3 Cl + HCl 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) 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

17. For Heavy Elements? 17 CH 4 + I 2 → CH 3 I + HI QCISD(T)/aug-cc-pVTZ ： 4.7 kcal/mol MLSE(C1)-M06-2X ： 2.7 kcal/mol I 2 → 2 I QCISD(T)/aug-cc-pVTZ ： 5.4 kcal/mol MLSE(C1)-M06-2X ： 4.3 kcal/mol

18. New Database 18 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

19. MLSE(HA-1) HFMP2MP4QCISD(T)MPW1PW91 pdz ● apdz ●● ptz ● aptz ●● 19 ●●● ●●● ●● ●

20. 20 MLSE(HA-1) 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).

21. MLSE(HA-2) HFMP2MP4QCISD(T)MPW1PW91 pdz ●●●● apdz ●●●● ptz ●●● aptz ●● 21 ● ● ●

22. New Database 22 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

23. Accuracy 23 (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

24. Computational Cost 24 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

25. Results 25 CH 4 + I 2 → CH 3 I + HI 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 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

26. Results 26 CH 3 I + Cl  → CH 3 Cl + I , E rxn = 12.66 kcal/mol QCISD(T)/aug-cc-pVTZ ： 2.01 kcal/mol MLSE(C1)-M06-2X ： 2.22 kcal/mol MLSE(HA-1) ： 0.03 kcal/mol MLSE(HA-2) ： 0.58 kcal/mol CH 3 Br + Cl  → CH 3 Cl + Br , E rxn = 7.90 kcal/mol QCISD(T)/aug-cc-pVTZ ： 1.75 kcal/mol MLSE(C1)-M06-2X ： 0.91 kcal/mol MLSE(HA-1) ： 0.28 kcal/mol MLSE(HA-2) ： 0.75 kcal/mol

27. Concluding Remarks 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. 27

28. Concluding Remarks We recommend MLSE(HA-1) method for the heavy halogens containing systems. The simplified, but reasonably accurate, MLSE(HA- 2) method is an economical alternative for larger systems. 28

29. 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 29

30. Thanks for your attention 30