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

Accurate Multi-Level Electronic Structure Methods, ML(Cn)-DFT for Atomization Energies and Reaction Energy Barriers

• Chapter 3

Novel Noble Gas Compound

二〇二三年四月二十日 2碩士論文口試

AbstractWe 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.


　　　　　

　　　　　

　　　　　

　　　　　

　　　　　

HFLimit

　　　　　

　

　

　

　

　

SchrödingerEquation 　

Electron correlation →

Basis set Type

Minimal

Split-valence

Polarized

Diffuse

High ang. momentum

HF MP2 MP3 MP4 QCISD(T) … Full CI

… … … … … … …

∞

Quantum Chemical Calculations


• For example:MP2/aug-cc-pVDZQCISD(T)/aug-cc-pVTZ

• Deficiencies:1.Low accuracyMP2/aug-cc-pVDZ: generally more than 5 kcal/mol error.QCISD(T)/aug-cc-pVTZ: generally more than 1 kcal/mol error.

2.Cost expensiveThe QCISD(T)/aug-cc-pVTZ is more than 100 times the cost ofMP2/cc-pVDZ for medium molecules.

Single Level Methods


Base Calculation + Corrections forIncomplete Basis Set Incomplete Electron Correlation

Currently Used Multilevel Methods: G2, G3, G4, CBS

HF, MP2, MP4, QCISD(T), empirical HLC6-31G(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

Multilevel Methods


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


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



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



Multilevel Methods with Scaled Energies

• G3S

• G3X

• MCG3

• MLSEn+d

二〇二三年四月二十日碩士論文口試 10

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.


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)


The MLSEn+d Method

E(MLSEn+d) =

CHF × E(HF/cc-pV(D+d)Z) +

CHF × [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


Density functional theory (DFT)

• To obtain energies of molecules and their physical properties without solving wave functions.

• Common functionals:

B3LYP 、 MPW1B95 、 MPW1PW91 、TPSS1KCIS 、 B1B95


The MCG3-DFT Method

Phys. Chem. Chem. Phys. 2005, 7, 43–52.

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


Databases

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,

Train sets and Test sets

NHTBH22/04 Database. The NHTBH22/04 database consists of 38 transition state barrier heights for non-hydrogentransfer (NHT) reactions.


The MLSE-DFT Method

E(MLSE-DFT) = CWF { E(HF/cc-pV(D+d)Z) +

CHF [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.


Accuracy


MLSE-DFT Optimized Coefficients


The MLSE-DFT Computational Cost


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.


Database for charged system

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,

Train sets and Test sets

NHTBH38/04 Database. The HTBH38/04 database consists of 38 transition state barrier heights for non-hydrogentransfer(NHT) reactions.


The MLSE(C1)-DFT MethodE(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


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.


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] }


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.


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


Accuracy

AE IP EA HTBH NHTBHNHTBH

(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 0.743 0.337 0.662

MLSE(C)3-TS 0.724 0.677 0.692 0.473 0.752 0.347 0.648

MCG3-MPWB 0.75 0.670 0.860 0.54 0.97 0.650 0.729


MLSE(Cn)-DFT Computational Cost

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.


Summary


• Single-Level methodsmethod: QCISD(T)/aug-cc-pVTZaccuracy: >> 1 kcal/molcost1: several hours to several days

• Multilevel Methodsmethod: G3accuracy: 1~2 kcal/molcost1: several minutes to several hours

1for medium molecules, ~10 heavy atoms.

Summary


• Scaled Multilevel Methodsmethod: MLSE1+d, MCG3accuracy: 0.9~1.0 kcal/molcost1: several minutes

• Scaled Multilevel Methods with DFTmethod: MLSE-MPWB, MCG3-MPWBaccuracy: 0.6~0.7 kcal/molcost1: several minutes

1for medium molecules, ~10 heavy atoms.

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.

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


Thanks for your attention


Documents

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