指導教授：胡維平 (Wei-Ping Hu) 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 Accurate Multi-Level Electronic Structure Methods, ML(Cn)-DFT for Atomization Energies and Reaction Energy Barriers Chapter 3 Novel Noble Gas Compound 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

Quantum Chemical Calculations Electron correlation → HF MP2 MP3 MP4 QCISD(T) … Full CI Basis set Type Minimal Split-valence Polarized Diffuse High ang. momentum … … … … … … … HF Limit 　 Schrödinger Equation　 ∞ 2017年4月25日 碩士論文口試

Single Level Methods For example: Deficiencies: 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. 2017年4月25日 碩士論文口試

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 2017年4月25日 碩士論文口試

G1 theory E(G1)= Ebase+ ΔE+ +ΔE2df,p + ΔEQCI + ΔEHLC +EZPE 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 2017年4月25日 碩士論文口試

G2 theory E(G2) = E(G1)+ ΔE+2df – ΔE+ – ΔE2df + Δ3d2p + ΔEHLC 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 2017年4月25日 碩士論文口試

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 2017年4月25日 碩士論文口試

Multilevel Methods with Scaled Energies G3S G3X MCG3 MLSEn+d 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

Dunning’s correlation consistent basis sets Dunning-type basis set Pople-type basis sets cc-pVDZ 6-31G(d) aug-cc-pVDZ 6-31++G(d,p) cc-pVTZ 6-311G(d,p) aug-cc-pVTZ 6-311++G(2df,p) 2017年4月25日 碩士論文口試

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 2017年4月25日 碩士論文口試

Density functional theory (DFT) To obtain energies of molecules and their physical properties without solving wave functions. Common functionals: B3LYP、 MPW1B95 、MPW1PW91、 TPSS1KCIS、B1B95 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

Accuracy 2017年4月25日 碩士論文口試

MLSE-DFT Optimized Coefficients 2017年4月25日 碩士論文口試

The MLSE-DFT Computational Cost 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

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 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

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] } 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

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 2017年4月25日 碩士論文口試

Accuracy AE IP EA HTBH NHTBH NHTBH(C) MUE MLSE(C1)-MPWB 0.645 0.698 0.595 0.473 0.483 0.424 0.581 MLSE(C)1-TS 0.633 0.743 0.637 0.508 0.580 0.536 0.605 MLSE(C)2-MPWB 0.640 0.817 0.790 0.451 0.525 0.445 0.599 MLSE(C)2-TS 0.630 0.890 0.782 0.481 0.578 0.614 0.622 MLSE(C)3-MPWB 0.766 0.709 0.665 0.436 0.337 0.662 MLSE(C)3-TS 0.724 0.677 0.692 0.752 0.347 0.648 MCG3-MPWB 0.75 0.670 0.860 0.54 0.97 0.650 0.729 2017年4月25日 碩士論文口試

MLSE(Cn)-DFT Computational Cost MLSE(C1)-MPWB 7396 MLSE(C2)-MPWB 4059 MLSE(C3)-MPWB 2673 MCG3-MPWB 2334 Total CPU time in seconds to calculate C5H5N, C2Cl4, C4H4O, C4H4S, C4H5N, CF3CN, and SiCl4 using Intel E6600 processer. 2017年4月25日 碩士論文口試

Summary Single-Level methods Multilevel 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. 2017年4月25日 碩士論文口試

Summary Scaled Multilevel Methods Scaled Multilevel Methods with DFT 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 1for medium molecules, ~10 heavy atoms. 2017年4月25日 碩士論文口試

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. 2017年4月25日 碩士論文口試

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 2017年4月25日 碩士論文口試

Thanks for your attention 2017年4月25日 碩士論文口試