What Theory Can Do

Strength and Weakness

李振华制造2013/10/14 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.

李振华制造2013/10/14 What Theory Can Do 3

Strength

For small and regular molecules

Chemical Accuracy:Energetics: Error < 1 kcal/mol

Structures: Error in Bond Lengths < 0.01 Å

Frequencies: A few cm-1

李振华制造2013/10/14 What Theory Can Do 4

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

李振华制造2013/10/14 What Theory Can Do 5

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

李振华制造2013/10/14 What Theory Can Do 6

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

李振华制造2013/10/14 What Theory Can Do 7

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

李振华制造2013/10/14 What Theory Can Do 8

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

李振华制造2013/10/14 What Theory Can Do 9

Ref: Abrams, M. L. PhD Thesis, General-Order Single-Reference and Multi-Reference

Methods in Quantum Chemistry, 2005

李振华制造2013/10/14 What Theory Can Do 10

Ref: Abrams, M. L. PhD Thesis, General-Order Single-Reference and Multi-Reference

Methods in Quantum Chemistry, 2005

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

李振华制造2013/10/14 What Theory Can Do 11

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.

李振华制造2013/10/14 What Theory Can Do 12

Accurate Calculations Can Give Better Results Than Experiment

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,O

CS,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

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Accurate Calculations Can Give Better Results Than Experiment

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

李振华制造2013/10/14 What Theory Can Do 14

Accurate Calculations Can Give Better Results Than Experiment

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

李振华制造2013/10/14 What Theory Can Do 15

Weakness

Results sensitive to

Basis set,

MethodVery 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

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

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Everyone uses B3LYP

Publications 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

李振华制造2013/10/14 What Theory Can Do 21

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

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Frequency Calculation: Sensitive to Grid Point

The low harmonic vibrational frequencies (cm-1) of Zn(C2H4)42+ 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

DG 0.35 0.94

李振华制造2013/10/14 What Theory Can Do 23

Very Slow Basis-Set

Convergence

Ref: Persson, B. J.; Taylor, P. R.; Lee, T.

J. J. Chem. Phys. 1997, 107(13), 5051

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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

李振华制造2013/10/14 What Theory Can Do 25

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.”

李振华制造

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 DH0(f) [P(g)] = 75.54 0.1 kcal

mol-1 and DH298(f) [P(g)] = 75.74 0.1 kcal mol-1, in

the upper half of the CODATA uncertainty interval.

CODATA: DH0(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

李振华制造2013/10/14 What Theory Can Do 30

Potential Energy Surface of N2

Ref: Robinson, D. J. Comput. Chem. 2013, 34, 2625.

N2 Energy Curve

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Difficult Cases: Open-Shell Systems with Strong Multireference Character

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

6A12Dg

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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Difficult Cases: Open-Shell Systems with Strong Multireference Character

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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Difficult Cases: Open-Shell Systems with Strong Multireference Character

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.

DE

(kcal/mol)Re (Å) we (cm-1)

8Dg

8g

8Dg

8g

8Dg

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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Difficult Cases: Open-Shell Systems with Strong Multireference Character

Excitation Energy of FeO+ (Relative to 6+ Ground State)Ref: Sorkin, A.; Iron, M. A.; Truhlar, D. G. J. Chem. Theo. Comput. 2008, 4(2), 307.

DE (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

李振华制造

Difficult Cases: Open-Shell Systems with Strong Multireference Character

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

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Difficult Cases: Open-Shell Systems with Strong Multireference Character

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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Difficult Cases: Open-Shell Systems with Strong Multireference Character

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.

李振华制造

Difficult Cases (DFT):

Noncovalent

Interactions

Ref: Zhao, Y.; Truhlar, D. G. Acc.

Chem. Res. 2008, 41(2), 157.

李振华制造

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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Don

ald G

. Tru

hlar

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DFT: Reaction Energy and Equilibrium Constants

Error 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 Constants

Equilibrium 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%

李振华制造

DFT: Bad Energy Barriers for Hydrogen Transfer Reactions

Ref: Zhao, Y.; Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 2715.

李振华制造

李振华制造

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

D D

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)

李振华制造

怎样做好的计算

Right Reason for the Right

Answer

李振华制造

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

李振华制造

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

李振华制造

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, 1Dg

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.

李振华制造

理论计算中的常见错误

开壳层 or闭壳层？

李振华制造

理论计算中的常见错误

基本概念错误

如活化能

RTEaAek/D

# 'aE E RTD D

DE0DEe

DEa

李振华制造

理论计算中的常见错误

几种能垒的比较

H + H2 H2 + H

DEe 10.1

DE0 9.3

DEa 9.6

李振华制造

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 D

B

B vib

ln

ln

e

e

F E ZPE k T q

E ZPE k T q

李振华制造

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

李振华制造

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

李振华制造

李振华制造2013/10/14 What Theory Can Do 60

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

李振华制造2013/10/14 What Theory Can Do 61

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