1. 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

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
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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.
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4. Quantum Chemical Calculations
Electron correlation →
HF MP MP MP QCISD(T) … Full CI
Basis set Type
Minimal
Split-valence
Polarized
Diffuse
High ang. momentum
… … … … … … … HF
Limit 　
Schrödinger
Equation　 ∞
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5. 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.
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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), G(d,p)
6-311+G(2df,p), G(3df,2p), G3Large
Multilevel Methods with Scaled Energies:
(Multicoefficient Method)
MCG3, G3S, G3X
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7. 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 : – nα – nβ
EZPE : ZPE(HF /6-31G(d)) ×
E(G1)= Ebase+ ΔE+ +ΔE2df,p + ΔEQCI + ΔEHLC +EZPE
Journal of Chemical Physics, 1990, 93,
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8. 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 : nβ
E(G2) = E(G1)+ ΔE+2df – ΔE+ – ΔE2df + Δ3d2p + ΔEHLC
Journal of Chemical Physics, 1991, 94,
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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,
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10. Multilevel Methods with Scaled Energies
G3S
G3X
MCG3
MLSEn+d
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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.
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12. 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
G(2df,p)
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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,
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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
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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.
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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.
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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.
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18. Accuracy
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19. MLSE-DFT Optimized Coefficients
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20. The MLSE-DFT Computational Cost
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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.
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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.
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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
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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.
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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] }
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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.
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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
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28. 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
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29. 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.
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30. 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.
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31. 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.
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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 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.
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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
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34. Thanks for your attention
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