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國立中正大學 化學暨生物化學研究所 碩士論文口試 孫翊倫 (Yi-Lun Sun) 指導教授：胡維平 (Wei-Ping Hu) 中華民國 97 年 7 月 23 日

國立中正大學 化學暨生物化學研究所 碩士論文口試 孫翊倫 (Yi-Lun Sun) 指導教授：胡維平 (Wei-Ping Hu) 中華民國 97 年 7 月 23 日. Content. Chapter 1 Accurate Multi-Level Electronic Structure Methods (MLSE-DFT) for Atomization Energies and Reaction Energy Barriers in neutral system Chapter 2

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國立中正大學 化學暨生物化學研究所 碩士論文口試 孫翊倫 (Yi-Lun Sun) 指導教授：胡維平 (Wei-Ping Hu) 中華民國 97 年 7 月 23 日

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  1. 國立中正大學 化學暨生物化學研究所 碩士論文口試 孫翊倫(Yi-Lun Sun) 指導教授：胡維平 (Wei-Ping Hu) 中華民國97年7月23日

  2. Content • Chapter 1 Accurate Multi-Level Electronic Structure Methods (MLSE-DFT) for Atomization Energies and Reaction Energy Barriers in neutral system • Chapter 2 Accurate Multi-Level Electronic Structure Methods, ML(Cn)-DFT for Atomization Energies and Reaction Energy Barriers • Chapter 3 Novel Noble Gas Compound 碩士論文口試

  3. Abstract We have developed a set of new multi-level electronic structure methods by including energies calculated from several density functional theory methods. The parameterization of the improved methods MLSE-DFT was based on updated databases of 109 atomization energies, 38 hydrogen-transfer barrier heights, and 22 neutral non-hydrogen-transfer reaction barrier heights. The best method, MLSE-TPSS1KCIS, performed impressively on the above three types of energies with mean unsigned errors of 0.62, 0.55, and 0.69 kcal/mol, respectively. We found that the hybrid versions of DFT are not absolutely necessary, and the performance can be improved significantly using two different basis sets in DFT calculation. 碩士論文口試

  4. Quantum Chemical Calculations Electron correlation → HF MP2 MP3 MP4 QCISD(T) … Full CI Basis set Type Minimal Split-valence Polarized Diffuse High ang. momentum … … … … … … … ∞ 碩士論文口試

  5. Single Level Methods • For example: • MP2/aug-cc-pVDZ • QCISD(T)/aug-cc-pVTZ • Deficiencies: • Low accuracy • MP2/aug-cc-pVDZ: generally more than 5 kcal/mol error. • QCISD(T)/aug-cc-pVTZ: generally more than 1 kcal/mol error. • Cost expensive • The QCISD(T)/aug-cc-pVTZ is more than 100 times the cost of • MP2/cc-pVDZ for medium molecules. 碩士論文口試

  6. Multilevel Methods Base Calculation + Corrections for Incomplete Basis Set Incomplete Electron Correlation Currently Used Multilevel Methods: G2, G3, G4, CBS HF, MP2, MP4, QCISD(T), empirical HLC 6-31G(d), 6-311G(d,p), 6-311+G(d,p) 6-311+G(2df,p), 6-311+G(3df,2p), G3Large Multilevel Methods with Scaled Energies: (Multicoefficient Method) MCG3, G3S, G3X 碩士論文口試

  7. G1 theory • Geometry:MP2(full)/6-31G(d) • Ebase : MP4/6-311G(d,p) • ΔE+ : MP4/6-311+G(d,p) – Ebase • ΔE2df,p : MP4/6-311G(2df,p) – Ebase • ΔEQCI : QCISD(T)/6-311G(d,p) – Ebase • ΔEHLC : –0.00019nα –0.00595nβ • EZPE : ZPE(HF /6-31G(d)) × 0.8929 E(G1)= Ebase+ ΔE+ +ΔE2df,p + ΔEQCI + ΔEHLC +EZPE Journal of Chemical Physics, 1990, 93, 2537-2545 碩士論文口試

  8. G2 theory • ΔE+2df :MP2/6-311+G(2df,p) – MP2/6-311G(d,p) • Δ+ : MP2/6-311+G(d,p) – MP2/6-311G(d,p) • ΔE2df : MP2/6-311G(2df,p) – MP2/6-311G(d,p) • Δ3d2p : MP2/6-311+G(3df,2p) – MP2/6-311+G(2df,p) • ΔEHLC : 0.00114nβ E(G2) = E(G1)+ ΔE+2df –ΔE+ –ΔE2df + Δ3d2p + ΔEHLC Journal of Chemical Physics, 1991, 94, 7221-7230 碩士論文口試

  9. G3 theory • Geometry:MP2(full)/6-31G(d) • Ebase : MP4/6-31G(d) • ΔE+ : MP4/6-31+G(d) - Ebase • Δ E2df,p : MP4/6-31G(2df,p) – Ebase • Δ EQCI : QCISD(T)/6-31G(d) – Ebase • Δ EG3Large : MP2(full)/G3Large – [ MP2/6-31G(2df,p) +MP2/6-31+G(d) – MP2/6-31G(d) ] • Δ EHLC : – Anβ – B(nα –nβ) E(G3)= Ebase + ΔE+ + ΔE2df,p + ΔEQCI + ΔEG3Large +ΔEHLC + EZPE Journal of Chemical Physics, 1998, 109, 7764-7776 碩士論文口試

  10. Multilevel Methods with Scaled Energies • G3S • G3X • MCG3 • MLSEn+d 碩士論文口試

  11. The MCG3 Method E(MCG3/3) = c0E(HF/6-31G(d)) +c1E(HF/MG3S | 6-31G(d)) + c2E(MP2 | HF/6-31G(d)) +c3E(MP2 | HF/MG3S | 6-31G(d)) +c4E(MP4SDQ | MP2/6-31G(d)) +c5E(MP4SDQ | MP2/6-31G(2df,p) | 6-31G(d)) +c6E(QCISD(T) | MP4SDQ/6-31G(d)) + ESO J. Phys. Chem. A 2003, 107, 3898. 碩士論文口試

  12. Dunning’s correlation consistent basis sets 碩士論文口試

  13. The MLSEn+d Method E(MLSEn+d) = CHF × E(HF/cc-pV(D+d)Z) +CHF × [E(HF/cc-pV(T+d)Z )– E(HF/cc-pV(D+d)Z)] + CE2 × [E2/cc-pV(D+d)Z] +CE34 × [E(MP4SDQ/cc-pV(D+d)Z) – E(MP2/cc-pV(D+d)Z)] +CQCI × [E(QCISD(T)/cc-pV(D+d)Z) – E(MP4SDQ/cc-pV(D+d)Z)] +CB × 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] + ESO Chem. Phys. Lett. 2005,412, 430-433 碩士論文口試

  14. Density functional theory (DFT) • To obtain energies of molecules and their physical properties without solving wave functions. • Common functionals: B3LYP、 MPW1B95 、MPW1PW91、 TPSS1KCIS、B1B95 碩士論文口試

  15. The MCG3-DFT Method E(MCG3-DFT) = c8{E[HF/Dd] + c1E[MP2|HF/Dd] + c2E[MP2/DIDZ|Dd] + c3E[MP2/D2dfp|DIDZ] + c4E[MP2/MG3S|D2dfp] + c5E[MP4SDQ|MP2/Dd] + c6E[MP4SDQ/D2dfp|Dd] + c7E[QCISD(T)|MP4SDQ/Dd]} + (1–c8)E(DFTX/MG3S) + ESO Phys. Chem. Chem. Phys. 2005, 7, 43–52. 碩士論文口試

  16. Databases Train sets and Test sets MGAE109 Test Set. The MGAE109 test set consists of 109 atomization energies (AEs). HTBH38/04 Database. The HTBH38/04 database consists of 38 transition state barrier heights for hydrogen transfer (HT) reactions, NHTBH22/04 Database. The NHTBH22/04 database consists of 38 transition state barrier heights for non-hydrogentransfer (NHT) reactions. 碩士論文口試

  17. The MLSE-DFT Method E(MLSE-DFT) = CWF { E(HF/cc-pV(D+d)Z) + CHF [E(HF/cc-pV(T+d)Z )– E(HF/cc-pV(D+d)Z)] + CE2 [E2/cc-pV(D+d)Z] + CE34 [E(MP4SDQ/cc-pV(D+d)Z) – E(MP2/cc-pV(D+d)Z)] + CQCI [E(QCISD(T)/cc-pV(D+d)Z) – E(MP4SDQ/cc-pV(D+d)Z)] + CB [E2/cc-pV(T+d)Z – E2/cc-pV(D+d)Z] + CHF+ [E(HF/aug-cc-pV(D+d)Z) – E(HF/cc-pV(D+d)Z]) + CE2+ [E2/aug-cc-pV(D+d)Z – E2/cc-pV(D+d)Z] } + (1 - CWF ) { E(DFTX/cc-pV(D+d)Z) + CB1 [E(DFTX/cc-pV(T+d)Z – DFTX/cc-pV(D+d)Z] } + ESO Chem. Phys. Lett. 2007,442, 220. 碩士論文口試

  18. Accuracy 碩士論文口試

  19. MLSE-DFT Optimized Coefficients 碩士論文口試

  20. The MLSE-DFT Computational Cost 碩士論文口試

  21. For charged system • In order to perfect multi-level electronic structure methods, we development a new series methods for charged system that are not suitable for MLSE-DFT. These series methods are called MLSE(Cn)-DFT. 碩士論文口試

  22. Database for charged system Train sets and Test sets MGAE109 Test Set. The MGAE109 test set consists of 109 atomization energies (AEs). Ionization Potential and Electron Affinity Test Set. These databases are called IP13/3 and EA13/3, respectively. HTBH38/04 Database. The HTBH38/04 database consists of 38 transition state barrier heights for hydrogen transfer (HT) reactions, NHTBH38/04 Database. The HTBH38/04 database consists of 38 transition state barrier heights for non-hydrogentransfer (NHT) reactions. 碩士論文口試

  23. The MLSE(C1)-DFT Method E(MLSE(C1)-DFT) = CWF { E(HF/pdz) +C△HF [E(HF/ptz )– E(HF/pdz)] + CE2 [E2/pdz] +CE34 [E(MP4SDQ/pdz) – E(MP2/pdz)] +CQCI [E(QCISD(T)/pdz) – E(MP4SDQ/pdz)] +CB1MP2 [E2/ptz – E2/pdz] + CHF+ [E(HF/apdz) – E(HF/pdz]) +CE2+ [E2/apdz – E2/pdz] +CHFT+ [E(HF/aptz) － E(HF/apdz)] +CB2MP2 [E2/aptz – E2/apdz] +CB1MP4 [E(MP4D/ptz) － E(MP4D/pdz)] } + (1 - CWF ) { E(DFTX/pdz) + CB1DFT [E(DFTX/ptz – DFTX/pdz] } + ESO 碩士論文口試

  24. Simplification of MLSE(C1)-DFT • The computational cost of MLSE(C1)-DFT is significantly higher than that of MLSE-DFT because of the expensive MP2/aug-cc-pVTZ calculation. • One way to lower the cost would be reducing the size of the aug-cc-pVTZ basis set. We simplify the aug-cc-pVTZ basis sets by omitting the f diffuse functions for the second-row elements, omitting the d,f diffuse functions for the first-row elements, and omitting all diffuse functions for hydrogens. 碩士論文口試

  25. The MLSE(C2)-DFT Method • E(MLSE(C2)-DFT) = CWF { E(HF/pdz) + C△HF [E(HF/ptz )– E(HF/pdz)] + CE2 [E2/pdz] + CE34 [E(MP4D/pdz) – E(MP2/pdz)] + CQCI [E(QCISD(T)/pdz) – E(MP4D/pdz)] + CB1MP2 [E(MP2/ptz) – E(MP2/pdz)] + CHF+ [E(HF/apdz) – E(HF/pdz]) + CE2+ [E2/apdz – E2/pdz] + CB2MP2 [E(MP2/aptz) – E(MP2/apdz)] + CB1MP4 [E(MP4D/ptz) －E(MP4D/pdz)] } + (1 - CWF ) { E(DFTX/pdz) + CB1DFT [E(DFTX/ptz – DFTX/pdz] } 碩士論文口試

  26. Simplification of MLSE(C2)-DFT • Two large basis sets, ptz and the simplified aptz, are still used in the MP2 calculation, and the MP4D/ptz calculation is also very expensive. To make the method even more affordable, we eliminate the calculation using the ptz basis set completely in the following MLSE(C3)-DFT method. 碩士論文口試

  27. The MLSE(C3)-DFT Method • E(MLSE(C3)-DFT) = CWF { E(HF/pdz) + CE2 [E2/pdz] + CE34 [E(MP4SDQ/pdz) – E(MP2/pdz)] + CQCID [E(QCISD/pdz) －E(MP4SDQ/pdz)] + CQCI [E(QCISD(T)/pdz) – E(QCISD/pdz)] + CHF+ [E(HF/apdz) – E(HF/pdz]) + CE2+ [E2/apdz – E2/pdz] + CHFT+ [E(HF/aptzs) －E(HF/apdz)] + CB2MP2 [E(MP2/aptz) – E(MP2/apdz)] + CBMP4+ [E(MP4SDQ/apdz) －E(MP4SDQ/pdz)] } (1 - CWF ) { E(DFTX/pdz) } + ESO 碩士論文口試

  28. Accuracy 碩士論文口試

  29. MLSE(Cn)-DFTComputational Cost Total CPU time in seconds to calculate C5H5N, C2Cl4, C4H4O, C4H4S, C4H5N, CF3CN, and SiCl4 using Intel E6600 processer. 碩士論文口試

  30. Summary • Single-Level methods • method: QCISD(T)/aug-cc-pVTZ • accuracy: >> 1 kcal/mol • cost1: several hours to several days • Multilevel Methods • method: G3 • accuracy: 1~2 kcal/mol • cost1: several minutes to several hours • 1for medium molecules, ~10 heavy atoms. 碩士論文口試

  31. Summary • Scaled Multilevel Methods • method: MLSE1+d, MCG3 • accuracy: 0.9~1.0 kcal/mol • cost1: several minutes • Scaled Multilevel Methods with DFT • method: MLSE-MPWB, MCG3-MPWB • accuracy: 0.6~0.7 kcal/mol • cost1: several minutes • 1for medium molecules, ~10 heavy atoms. 碩士論文口試

  32. Concluding Remarks • We have developed a set of new multi-level electronic structure methods by including energies calculated from several density functional theory methods, we called it MLSE-DFT method. • For neutral system, MLSE-TPSS1KCIS, performed on 169 atomization energies and reaction energy barriers with overall mean unsigned errors(MUE) of 0.61 kcal/mol. We recommend this method for neutral system. • Overall MUEs of MLSE(C2)-MPWB is 0.599 kcal/mol, it’s lower than MCG3-MPWB about 0.13 kcal/mol, cost is also acceptable, so it provides us another choice for charged system. 碩士論文口試

  33. 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 碩士論文口試

  34. Thanks for your attention 碩士論文口試

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