what theory can do strength and weakness. 2015-7-16 what theory can do 2...

What Theory Can Do

Strength and Weakness

李振华制造23/4/19 What Theory Can Do 2

理论计算起到了非常重要的作用

Fig. 1 The linkages between thermochemical kinetics and other subjects. Ref. Walsh, R. Chem. Soc. Rev. 2008, 37, 686.


Strength

For small and regular moleculesChemical Accuracy:Energetics: Error < 1 kcal/mol

Structures: Error in Bond Lengths < 0.01 Å

Frequencies: A few cm-1


Ref: Hoffman, B.C.; Sherrill, C. D.; Schaefer III, H. F. J. Chem. Phys. 1997, 107(24), 10616.


Ref: Bak K. L. et al. J. Chem. Phys. 2001, 114(15), 6548.


Ref: Abrams, M. L. PhD Thesis, General-Order Single-Reference and Multi-Reference Methods in Quantum Chemistry, 2005


Ref: Abrams, M. L. PhD Thesis, General-Order Single-Reference and Multi-Reference Methods in Quantum Chemistry, 2005

BH, CH+, NH, OH+, HF, C2


Accurate Calculations Can Give Better Results Than Experiment

CCSD(T)/CBSa G3 G3X Literature c

P2 34.4±1.0 35.5 34.3 34.3±0.5d

P4 12.1±2.5 18.2 16.2 14.1±0.05d

PH 56.6±1.0 56.0 55.7 60.6±8.0e 57.4±0.6f

PH2 31.5±1.0 32.6 32.2 26±23g 33.1±0.6f

POi –7.6±1.0 –7.1 –7.7 –5.6±1.0d –6.8±1.9j –7.8k

PO2 –69.7±1.5 –67.5 –69.2 –66.2±3j –70.3k

HOPO –112.0±1.5 –108.3 –110.3 –110.6±3l –112.4k

HOPO2 –170.6±2.0 –164.8 –167.4 –168.8±4l –171.4k

Table VII. Enthalpies of formation at 298 K (in kcal mol–1).Ref: Haworth, N. L.; Bacskay, G. B. J. Chem. Phys. 2002, 117(24), 11175.



Table VII. Average Error in Atomization Energy at 0 K (in kcal mol–1).(H2O,C2H2,CH3,CH4,CH,CO2,CO,F2,HF,N2,NH3,N2O,NO,O2,O3,NO2,Cl2,ClF,CS,H2S,HCl,HOCl,PH3,SO,SO2,OCS,ClCN,C2H4,H2CO,HNO)

Ref: Karton, A.; Rabinovich, E.; Martin J. M. L.; Ruscic, Branko, R. J. Chem. Phys. 2006, 125, 144108.

Method W2.2 W3.2 W4lite W4

MAD 0.44 0.19 0.13 0.10

MAX 3.46 0.7 0.84 0.63

Min 0.02 0.02 0.01 0.00



Table I. Recommended Gas-Phase Heats of Formation at 0 K (in kcal mol–1).Ref: Karton, A.; Martin J. M. L. J. Phys. Chem. A 2007, 111(26), 5936.

element JANAF CODATA OPW9 Theo. Recom.

Be 76.42±1.20 75.8±0.8 76.4±0.6

B 132.6 133.82±1.20 136.2±0.2 135.1±0.2

Al 78.23 78.30±0.96 80.2±0.4

Si 106.5±1.9 108.1±0.5 107.15±0.2



Table 8 Ionization energy and heat of formation of B2F4 at 298 K.Ref: Li, Z. H.; Fan, K. N. J. Phys. Chem. A 2002, 106(28), 6659.

This Work G3 G3S G3SCB Exp.

IP 271.70 271.58 270.94 270.34≤ 282.03 e

278.34 f

ΔHf(298)

B2F4 (D2h) -339.82 -339.71 -339.18 -340.69 -342.20 g


Weakness

Results sensitive to

Basis set,Method

Very Expensive For Reliable Predictions

Wrong conclusion from inaccurate calculations

DFT: Good in geometry, frequency, long way to reliable quantitative predictions

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Everyone uses “Density Functional Theory”Publications from 1980 to 2011 in SCI-Expanded

01000

20003000

40005000

60007000

80009000

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

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2008

2010

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Everyone uses B3LYPPublications from 1994 to 2010 in SCI-Expanded

0

500

1000

1500

2000

2500

3000

1993 1998 2003 2008

B3LYP

PBE

PW91

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DFT: Good in GeometryMUE in Bond Length (Å)Ref: Zhao, Y.; Truhlar, D. G. Theo. Chem. Acc. 2008, 120, 215.

MGBL19 MLBL13 TMBL7

HF 0.035

PBE 0.009 0.010 0.029

B3LYP 0.005 0.010 0.057

B98 0.005 0.011 0.086

TPSSh 0.004 0.010 0.047

M06-HF 0.012

M06 0.007 0.018 0.056

Average (DFT) 0.008 0.017 0.068

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DFT: Not So Bad in Frequency and ZPE

Error in Frequency (cm-1) and ZPE (kcal/mol)Ref: Zhao, Y.; Truhlar, D. G. Theo. Chem. Acc. 2008, 120, 215.

Frequency (Scaled) ZPE (Scaled)

HF 69 0.20

PBE 29 0.08

B3LYP 31 0.08

B98 30 0.08

TPSSh 28 0.09

M06-HF 68 0.22

M06 59 0.16

Average (DFT) 41 0.12

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Bad Thing


Small Vibrational Frequency Very Sensitive to Basis SetTable 1 The lowest harmonic vibrational frequency (cm-1) of the eclipsed (D2h) and staggered (D2d) conformations of B2F4.Ref: Li, Z. H.; Fan, K. N. J. Phys. Chem. A 2002, 106(28), 6659.

HF B3LYP MP2 QCISD

D2h D2d D2h D2d D2h D2d D2h D2d

6-31G(d) -12.5 20.4 15.7 9.4 17.2 -1.2 15.7 3.8

6-31+G(d) 18.2 7.6 14.7 13.6 19.6 -4.0 18.2 -7.4

6-311G(d) 20.7 4.0 20.8 3.9 28.3 -20.6 30.0 -23.1

6-311+G(d) 27.1 8.9 19.7 13.4 27.0 4.7

cc-pVDZ 23.4 -9.0 26.1 -16.9 28.1 -21.1 29.6 -23.1

cc-pVTZ 8.8 -1.4 -4.5 9.1 16.6 -14.9

cc-pVQZ 3.3 -7.2 4.4 6.2


Frequency Calculation: Sensitive to Grid PointThe low harmonic vibrational frequencies (cm-1) of Zn(C2H4)4

2+ by the B3PW91 method. Li, Z. H., unpublished

Frequency (cm-1) qvib(298.15) qvib(800)

Fine Ultrafine Fine Ultrafine Fine Ultrafine

14.9 33.6 14.4 6.7 37.9 17.0

43.1 44.8 5.3 5.1 13.4 12.9

69.2 63.7 3.5 3.8 8.5 9.2

80.4 70.0 3.1 3.5 7.4 8.5

108.8 103.9 2.4 2.5 5.6 5.9

114.1 115.2 2.4 2.3 5.4 5.3

qvib 4871 2696 9.8105 5.4105

Ratio 1.8 1.8

G 0.35 0.94


Very Slow Basis-Set Convergence Ref: Persson, B. J.; Taylor, P. R.; Lee, T. J. J. Chem. Phys. 1997, 107(13), 5051


Wrong Conclusion Can be Drawn from Cheap Calculation Ref: Persson, B. J.; Taylor, P. R.; Lee, T. J. J. Chem. Phys. 1997, 107(13), 5051


Wrong Conclusion Can be Drawn from Cheap CalculationRef: Persson, B. J.; Taylor, P. R.; Lee, T. J. J. Chem. Phys. 1997, 107(13), 5051

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Conclusion by Taylor P. R. in 2000 So, we’ve exhausted our armoury and we disagree with

experiment by 0.03 Å on the bond length and by up to 25 cm−1 (!) in the vibrational fundamentals.

In addition, the heat of the reaction P4 → 2P2 is estimated computationally to be 63.2 kcal/mol, whereas the experimental estimate is around 54 kcal/mol.

NIST thermochemist: “All phosphorus thermochemical results are suspect.”

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New Conclusion by Martin JML in 2007Ref. Karton, A.; Martin, J. M. L. Mol. Phys. 2007, 105(19-22), 2499.

Contrary to previous studies, we find the experimental thermochemistry to be fundamentally sound. The reaction enthalpy for P4 -> 2P2 has a very significant contribution from post-CCSD(T) correlation effects. We derive a gas-phase heat of formation for the phosphorus atom of H0(f) [P(g)] = 75.54 0.1 kcal mol-1 and H298(f) [P(g)] = 75.74 0.1 kcal mol-1, in the upper half of the CODATA uncertainty interval.

CODATA: H0(f) [P(g)] = 75.45 0.24

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Difficult Cases: Open-Shell Systems with Strong Multireference Character

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0.8 1.3 1.8 2.3 2.8 3.3 3.8 4.3 4.8

MP2

MP3

CCSD

CCSD(T)

RCCSD(T)

MRCI(0)

UPBE

RPBE

UPBE/G03

Potential Energy Surface of HF (kcal/mol), basis set: DZP Siesta 1.3f (UPBE, RPBE); 6-311++G(2df,2p) for Others

李振华制造

Difficult Cases: Open-Shell Systems with Strong Multireference CharacterError in Potential Energy Surface of HF (kcal/mol), basis set: DZP Siesta 1.3f (UPBE, RPBE); 6-311++G(2df,2p) for Others

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

1 1.5 2 2.5 3 3.5 4 4.5 5

MP2

MP3

CCSD

CCSD(T)

RCCSD(T)

UPBE

RPBE

UPBE/G03


Potential Energy Surface of N2

Ref: Chan, G.K.; Kállay, M.; Gauss, J. J. Chem. Phys. 2004, 121(13), 6110.

N2 Energy Curve

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Relative Energy of FeO2−

(in kcal/mol)Ref: Li, Z. H.; Gong, Y.; Fan, K. N.; Zhou, M. F. J. Phys. Chem. A. 2008, 112(51), 13641-13649

C2v Dh

Method 2A12B1

4A24B2

6A12g

2g+ 4g

6g+

B3LYP 7.8 8.3 0.2 0.0 2.5 9.5 17.1 1.8 3.7

B3PW91 10.6 11.1 0.2 0.0 0.9 12.5 18.9 2.1 2.1

B97-2 10.6 11.1 1.2 1.2 0.0 12.9 18.4 2.8 0.0

MP2 8.8 9.5 31.6 29.5 c 11.1 24.2 50.5 0.0

MP3 c c 79.3 48.9 c 46.4 66.0 31.8 0.0

CCSD 26.5 26.5 d c c 27.0 39.2 9.7 0.0

CCSD(T) e 10.4 10.6 d c c 12.2 20.1 9.0 0.0

MRCI 0.0 4.6 9.9

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3 Vibrational Frequency of Relative Energy of FeO2-

Ref: Li, Z. H.; Gong, Y.; Fan, K. N.; Zhou, M. F. J. Phys. Chem. A. 2008, in press

C2v Dh

Method 2A12B1

4A24B2

6A12Δg

b 2Σg+ 4g

b 6Σg+

B3LYP 994 998 888 884 850 1002 985 797 854

B3PW91 876 1010 896 895 868 1014 996 800 872

B972 994 997 882 875 850 998 988 778 851

MP2 3751 1103 678 997 c 1054 983 2649i 847

MP3 c c 170 d c 1010 971 19452i 941

CCSD d e d c c 1023 992 696 895

EXP 870.6

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Excitation Energy of Fe2− (Relative to 8g

−Ground State)Ref: Sorkin, A.; Iron, M. A.; Truhlar, D. G. J. Chem. Theo. Comput. 2008, 4(2), 307.

E (kcal/mol)

Re (Å) e (cm-1)

8g8g

8g8g

8g

HF 110.5 2.640 2.330 206 297

PBE -15.7 2.209 2.068 281 349

M06-L -2.8 2.212 2.099 299 337

M06 16.6 2.188 2.048 315 375

B3LYP 3.2 2.178 2.046 316 375

CCSD(T) 9.2 2.24 2.12 276 321

MRCI+Q 18.4 2.266 255

Exp 250

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Excitation Energy of FeO+ (Relative to 4+ Ground State)Ref: Sorkin, A.; Iron, M. A.; Truhlar, D. G. J. Chem. Theo. Comput. 2008, 4(2), 307.

E (kcal/mol)

C6v C4v C2v Not Stated

HF 256.4 42.0 -40.6

PBE 21.7 12.0 12.7

M06-L 34.4 22.4 13.8

M06 66.0 39.0 12.9

B3LYP 59.5 29.3 7.6

CCSD(T) 13.1

QMC/B3LYP 8.3

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Bond Length of Cr2Ref: Schultz N. E.; Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2005, 109, 4388.

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Error in the Bond Energies (kcal/mol) of Ag2, AgCu, Cr2, Cu2, Mo2, Ni2, V2, Zr2, ZrVRef: Schultz N. E.; Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2005, 109, 4388.

MSE MAD RMSE

HF -53.5 53.5 58.2

PBE 3.9 7.7 9.3

mPWPW91 0.5 6.5 8.6

B3LYP -16.7 16.7 20.5

B98 -8.9 9.7 13.1

TPSS -1.3 6.1 10.0

B1B95 -21.9 21.9 29.1

TPSSh -11.0 11.0 16.4

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Computed J12 (cm−1) values for [Cu2Cl6]2− on passing from square planar (=0°) to pseudo-tetrahedral geometriesRef: Bencini, A. Inorg. Chimica. Acta 2008, 361, 3820.

Method 0° 45° 70°

Ab initio 36 −58 87

Xa-BS 122 −309 72

LDA-BS 362 −246 191

BP-BS 256 −200 109

B3LYP-BS 271 −95 57

Xa-SD −41 −437 −106

Experiment 0, 40 −80, −90

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Difficult Cases (DFT): Noncovalent Interactions

Ref: Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41(2), 157.

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Difficult Cases: Charge Transfer Excitation Energies

Excitation Energies (eV)Ref: Zhao, Y.; Truhlar, D. G. Theo. Chem. Acc. 2008, 120, 215.

Tetraacene

Valence B2u La

NH3…F2 C2H4…C2F4

HF 3.9 11.1 13.9

PBE 3.0 0.1 5.1

B3LYP 3.4 2.2 7.0

B98 3.5 2.6 6.4

TPSSh 3.4 1.5 10.0

M06-HF 3.8 9.4 12.6

Best Estimate 3.4 9.5 12.6

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Donald G

. Truhlar

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DFT: Reaction Energy and Equilibrium ConstantsError in Reaction Energy at 0 K (kcal/mol) Li Z. H. unpublished.

Difference to G3B3 PBE PW91 B3LYP PBE0 BMK

C3H8 --> H2 + C3H6 7.8 8.0 5.6 11.3 10.2

C3H8+1/2O2-->C3H6+H2O 7.0 6.6 3.7 7.8 4.4

C3H8+CO2 --> C3H6 + H2O + CO 15.1 15.0 6.8 14.4 9.7

H2+CO2 --> HCOOH -6.8 -7.4 -6.0 -9.8 -7.4

C3H8+CO2 --> HCOOH + C3H6 1.0 0.6 -0.4 1.5 2.8

H2+CO2 --> CO + H2O 7.3 7.0 1.2 3.1 -0.6

CO + H2O --> HCOOH -14.1 -14.4 -7.2 -12.9 -6.8

MAD 8.4 8.4 4.4 8.7 6.0

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DFT: Reaction Energy and Equilibrium ConstantsEquilibrium Constant at 298 K (KDFT/KAcc) Li Z. H. unpublished.

PBE PW91 B3LYP PBE0 BMK

C3H8 --> H2 + C3H6 2.010-6 1.410-6 8.310-6 5.110-9 3.210-8

C3H8+1/2O2-->C3H6+H2O 7.610-6 1.510-5 2.010-3 1.810-8 6.310-4

C3H8+CO2 --> C3H6 + H2O + CO 8.310-12 1.010-11 1.010-5 2.710-11 8.410-8

H2+CO2 --> HCOOH 1.0105 2.7105 2.4104 1.6107 2.7105

C3H8+CO2 --> HCOOH + C3H6 0.20 0.38 2.0 8.210-2 8.710-3

CO2+H2 --> CO + H2O 4.210-6 7.210-6 0.13 5.310-3 2.6

CO + H2O --> HCOOH 2.31010 3.71010 1.9105 3.0109 1.0105

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Reaction Energy at 0 K (kcal/mol)

PBE PW91 B3LYP PBE0 BMK G3B3

H2+CO2 --> HCOOH -1.1 -1.7 -0.2 -4.1 -1.7 6.9

HCOOH --> CO + H2O 19.9 20.2 12.9 18.7 12.6 5.8

H2+CO2 --> CO + H2O 18.8 18.5 12.7 14.6 10.9 11.5

Free energy change (kcal/mol) at 800 K

PBE PW91 B3LYP PBE0 BMK G3B3

C3H8 --> H2 + C3H6 11.9 12.1 9.7 15.4 14.3 4.1

C3H8+CO2 --> C3H6 + H2O + CO 23.3 23.1 14.9 22.6 17.8 8.2

K2/K1 0.08% 0.1% 3.6% 1.1% 11% 7.9%

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DFT: Bad Energy Barriers for Hydrogen Transfer ReactionsRef: Zhao, Y.; Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 2715.

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Prediction on Selectivity?Figure From: Somorjai, G. A.; Park, J. Y. Angew. Chem. Int. Ed. 2008, 47, 9212.

# '/( ) v G RTBr

k Tk V e

h

298 800

80%:20% 0.8 2.2

90%:10% 1.3 3.5

99%:1% 2.7 7.3

不同的选择性对应的自由能垒的差别 (kcal/mol)

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怎样做好的计算 Right Reason for the Right

Answer

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怎样做好的计算了解所研究的体系建立合理的模型选择合适的方法

理论方法： HF, MP2, DFT, 半经验，经验基组可靠性性价比

分析结果得到结论

Right Reason for the Right Answer

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理论计算中的常见错误随便选择一个方法就进行计算

B3LYP, DFT 计算不够细致

开壳层，闭壳层 Grid, k 点，基组大小

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理论计算中的常见错误开壳层 or 闭壳层？O2: 基态， triplet, 3g

-, 第一激发态， singlet, 1g

B3LYP CCSD MRCI Exp

RHF 38.5 33.1 22.9 22.6

UHF 10.0 11.7 -

O2 第一激发能 (kcal/mol), basis set: 6-311+G(3df)

Li, Z.H. unpublished.

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理论计算中的常见错误开壳层 or 闭壳层？

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理论计算中的常见错误基本概念错误

如活化能

RTEaAek /# 'aE E RT

E0Ee

Ea

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理论计算中的常见错误几种能垒的比较H + H2 H2 + H

Ee 10.1

E0 9.3

Ea 9.6

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理论计算中的常见错误基本公式错误JACS

( ) (0 )eF E T TS E ZPE E T TS

B

B vib

ln

lne

e

F E ZPE k T q

E ZPE k T q

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理论计算中的常见错误计算细节语焉不详，无法重复计算结果

基组方法程序

随意调整计算方法中的参数，凑实验结果溶液模型基组： BSSE 的问题

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理论计算中的常见错误得出结论非常大胆：用了很多近似，却推出非常新颖的结

论

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what theory can do strength and weakness. 2015-7-16 what theory can do 2...

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