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

Content• Chapter 1

A New Set of Accurate Multi-level Methods Including Parameterization for Heavy Elements

• Chapter 2 & 3Theoretical Prediction of A New Class of Xenon Containing Molecules and Anions

• Chapter 4Theoretical Study on the Excited State Dynamics of Phenol Chromophores

Chapter 5Theoretical Prediction of A New Type Xe Polymer

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SchrödingerEquation 　

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

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●●

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

• Deficiencies:1. Low accuracy2. Cost expensive

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Single Level Methods

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Error of the reaction energy ：CH4 + Cl2 → CH3Cl + HClMP2/aug-cc-pVDZ ： 8.1 kcal/molQCISD(T)/aug-cc-pVTZ ： 1.9 kcal/mol

CH4 → C + 4 H (atomization energy)MP2/aug-cc-pVDZ ： 25.6 kcal/molQCISD(T)/aug-cc-pVTZ ： 6.0 kcal/mol

MP2/aug-cc-pVDZ > 5 kcal/molQCISD(T)/aug-cc-pVTZ > 1 kcal/mol

Single Level Methods

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Cost ：MP2/aug-cc-pVDZTime ： 1 unit

QCISD(T)/aug-cc-pVTZTime ： 288 units~ couple hours

Single Level Methods

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

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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 8

MLSEn+d MethodE(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

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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

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The MLSE-DFT MethodE(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.

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The MLSE(C1)-DFT Method• E(MLSE(C1)-DFT) = CWF { E(HF/pdz) +

CE2 [E2/pdz] +CE34SDQ [E(MP4SDQ/pdz) – E(MP2/pdz)] +CQCID [E(QCISD/pdz) – E(MP4SDQ/pdz)] +CQCI [E(QCISD(T)/pdz) – E(QCISD/pdz)] +CB1E2 [E2/ptz – E2/pdz] +CHF+ [E(HF/apdz) – E(HF/pdz]) +CE2+ [E2/apdz – E2/pdz] +CB2E2 [E2/aptz – E2/apdz] +CB1E34 [E(MP4D/ptz) – E(MP4D/pdz)] } +(1 - CWF ) { E(DFTX/pdz) + CDFT+ [E(DFTX/apdz – DFTX/pdz] } .

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Chem. Phys. Lett. 2009, 475, 141.

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.

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Accuracy

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AE(109)

IP(13)

EA(13)

HTBH(38)

NHTBH(38)

Overall MUE

MLSE(C1)-M06-2X 0.62 0.55 0.63 0.47 0.43 0.56

MLSE(C2)-M06-2X 0.65 0.60 0.69 0.50 0.44 0.59

MLSE(C3)-B3LYP 0.62 0.68 0.82 0.45 0.68 0.62

MLSE-TS 0.62 - - 0.55 0.69 0.61QCISD(T) /aug-cc-pVTZ 10.90 2.05 1.94 0.60 0.73 6.11

Computational Cost

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Cost MUE

MP2/aug-cc-pVDZ 1 15.1

MLSE(C1)-M06-2X 70 0.56

MLSE(C2)-M06-2X 50 0.59

MLSE(C3)-B3LYP 25 0.62

MLSE-TS 25 0.61

QCISD(T)/aug-cc-pVTZ 288 6.11

M06-2X/aug-cc-pVTZ 16 1.89

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CH4 + Cl2 → CH3Cl + HCl

MP2/aug-cc-pVDZ ： 8.1 kcal/molQCISD(T)/aug-cc-pVTZ ： 1.9 kcal/molMLSE(C1)-M06-2X ： 1.0 kcal/mol

CH4 → C + 4 H (atomization energy)

MP2/aug-cc-pVDZ ： 25.6 kcal/molQCISD(T)/aug-cc-pVTZ ： 6.0 kcal/molMLSE(C1)-M06-2X ： 0.13 kcal/mol

Accuracy

For Heavy Elements?

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CH4 + I2 → CH3I + HIQCISD(T)/aug-cc-pVTZ ： 4.7 kcal/molMLSE(C1)-M06-2X ： 2.7 kcal/mol

I2 → 2 IQCISD(T)/aug-cc-pVTZ ： 5.4 kcal/molMLSE(C1)-M06-2X ： 4.3 kcal/mol

New Database

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AE AE IP

I2 35.87 HBr 90.51 I 241.01

HI 73.79 NOBr 181.64 Br 272.43

IBr 42.27 CH3I 369.12 EA

ICl 50.19 CH3Br 380.94 I 70.54

Br2 45.90 C2H5I 662.69 Br 77.60

MLSE(HA-1)

HF MP2 MP4 QCISD(T) MPW1PW91

pdz ●

apdz ● ●

ptz ●

aptz ● ●

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● ● ●

● ● ●

● ●

●

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MLSE(HA-1)

CE2S[(E2aa+E2bb)/pdz] +CE2O [(E2ab)/pdz] +CE2+S [(E2aa+E2bb)/apdz] +CE2+O [(E2ab)/apdz] +CB1E2S [(E2aa+E2bb)/ptz] +CB1E2O [(E2ab)/ptz] +CB2E2S [(E2aa+E2bb)/aptz] +CB2E2O [(E2ab)/aptz] +

The different scaling factors were used to the same spin and opposite spin perturbational terms (MP2).

MLSE(HA-2)

HF MP2 MP4 QCISD(T) MPW1PW91

pdz ● ● ● ●

apdz ● ● ● ●

ptz ● ● ●

aptz ● ●

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●

●

●

New Database

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AE AE IP

I2 35.87 HBr 90.51 I 241.01

HI 73.79 NOBr 181.64 Br 272.43

IBr 42.27 CH3I 369.12 EA

ICl 50.19 CH3Br 380.94 I 70.54

Br2 45.90 C2H5I 662.69 Br 77.60

Accuracy

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(unit : kcal/mol) MUE(225)

HHAE(10)

HHIP(2)

HHEA(2)

MLSE(C1)-M062X(Eso) 0.66 1.84 1.22 2.21

MLSE(C1)-M062X-HA 0.66 1.66 1.21 2.30

MLSE(HA-1) 0.58 0.87 0.49 1.07

MLSE(HA-2) 0.64 0.98 0.48 1.04

Computational Cost

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Cost MUE(211)

MUE(225)

HHAE(10)

MLSE(C1)-M062X 100% 0.56 0.66 1.66

MLSE(HA-1) 162% 0.56 0.58 0.87

MLSE(HA-2) 104% 0.62 0.64 0.98

Results

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CH4 + I2 → CH3I + HIQCISD(T)/aug-cc-pVTZ ： 4.7 kcal/molMLSE(C1)-M06-2X ： 2.7 kcal/molMLSE(HA-1) ： 0.5 kcal/molMLSE(HA-2) ： 1.0 kcal/mol

I2 → 2 IQCISD(T)/aug-cc-pVTZ ： 5.4 kcal/molMLSE(C1)-M06-2X ： 4.3 kcal/molMLSE(HA-1) ： 0.7 kcal/molMLSE(HA-2) ： 0.6 kcal/mol

Results

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CH3I + Cl- → CH3Cl + I-, Erxn = 12.66 kcal/molQCISD(T)/aug-cc-pVTZ ： 2.01 kcal/molMLSE(C1)-M06-2X ： 2.22 kcal/molMLSE(HA-1) ： 0.03 kcal/molMLSE(HA-2) ： 0.58 kcal/mol

CH3Br + Cl- → CH3Cl + Br- , Erxn = 7.90 kcal/molQCISD(T)/aug-cc-pVTZ ： 1.75 kcal/molMLSE(C1)-M06-2X ： 0.91 kcal/molMLSE(HA-1) ： 0.28 kcal/molMLSE(HA-2) ： 0.75 kcal/mol

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.

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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.

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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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Thanks for your attention

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