1、What Theory Can DoStrength and Weakness2022/7/11What Theory Can Do2理論計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, 686.2022/7/11What Theory Can Do3StrengthFor small and regular moleculesChemical Accuracy:Energetics: Error

2、 1 kcal/molStructures: Error in Bond Lengths 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 un

3、certainty interval. CODATA: H0(f) P(g) = 75.45 0.24 Difficult Cases: Open-Shell Systems with Strong Multireference CharacterPotential Energy Surface of HF (kcal/mol), basis set: DZP Siesta 1.3f (UPBE, RPBE); 6-311+G(2df,2p) for OthersDifficult Cases: Open-Shell Systems with Strong Multireference Cha

4、racterError in Potential Energy Surface of HF (kcal/mol), basis set: DZP Siesta 1.3f (UPBE, RPBE); 6-311+G(2df,2p) for Others2022/7/11What Theory Can Do31Potential Energy Surface of N2Ref: Chan, G.K.; Kllay, M.; Gauss, J. J. Chem. Phys. 2004, 121(13), 6110.N2 Energy CurveDifficult Cases: Open-Shell

5、Systems with Strong Multireference CharacterRelative 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), 13641-13649C2vDhMethod2A12B14A24B26A12g2g+4g6g+B3LYP7.88.30.20.02.59.517.11.83.7B3PW9110.611.10.20.00.912.518.92.12.1B97-210.611.11.21.2

6、0.012.918.42.80.0MP28.89.531.629.5c11.124.250.50.0MP3cc79.348.9c46.466.031.80.0CCSD26.526.5dcc27.039.29.70.0CCSD(T) e10.410.6dcc12.220.19.00.0MRCI0.04.69.9Difficult Cases: Open-Shell Systems with Strong Multireference Character3 Vibrational Frequency of Relative Energy of FeO2-Ref: Li, Z. H.; Gong,

7、Y.; Fan, K. N.; Zhou, M. F. J. Phys. Chem. A. 2008, in pressC2vDhMethod2A12B14A24B26A12g b2g+4g b6g+B3LYP9949988888848501002985797854B3PW9187610108968958681014996800872B972994997882875850998988778851MP237511103678997c10549832649i847MP3cc170dc101097119452i941CCSDdedcc1023992696895EXP870.6Difficult Ca

8、ses: Open-Shell Systems with Strong Multireference CharacterExcitation Energy of Fe2 (Relative to 8gGround State)Ref: Sorkin, A.; Iron, M. A.; Truhlar, D. G. J. Chem. Theo. Comput. 2008, 4(2), 307.DE (kcal/mol)Re ()we (cm-1)8Dg8Sg8Dg8Sg8DgHF110.5 2.640 2.330 206297PBE-15.7 2.2092.068281349M06-L-2.8

9、2.2122.099299337M0616.6 2.1882.048315375B3LYP3.2 2.1782.046316375CCSD(T)9.2 2.242.12276321MRCI+Q18.4 2.266255Exp250Difficult Cases: Open-Shell Systems with Strong Multireference CharacterExcitation Energy of FeO+ (Relative to 4+ Ground State)Ref: Sorkin, A.; Iron, M. A.; Truhlar, D. G. J. Chem. Theo

10、. Comput. 2008, 4(2), 307.E (kcal/mol)C6vC4vC2vNot StatedHF256.442.0-40.6PBE21.7 12.012.7M06-L34.422.413.8M0666.039.012.9B3LYP59.5 29.37.6CCSD(T)13.1QMC/B3LYP8.3Difficult Cases: Open-Shell Systems with Strong Multireference CharacterBond Length of Cr2Ref: Schultz N. E.; Zhao, Y.; Truhlar, D. G. J. P

11、hys. Chem. A 2005, 109, 4388.Difficult Cases: Open-Shell Systems with Strong Multireference CharacterError 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.MSEMADRMSEHF-53.553.558.2PBE3.97.79.3

12、mPWPW910.56.58.6B3LYP-16.716.720.5B98-8.99.713.1TPSS-1.36.110.0B1B95-21.921.929.1TPSSh-11.011.016.4Difficult Cases: Open-Shell Systems with Strong Multireference CharacterComputed J12 (cm1) values for Cu2Cl62 on passing from square planar (=0) to pseudo-tetrahedral geometriesRef: Bencini, A. Inorg.

13、Chimica. Acta 2008, 361, 3820.Method04570Ab initio365887Xa-BS12230972LDA-BS362246191BP-BS256200109B3LYP-BS2719557Xa-SD41437106Experiment0, 4080, 90 Difficult Cases (DFT): Noncovalent InteractionsRef: Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41(2), 157.Difficult Cases (DFT): Noncovalent Interac

14、tionsRef: Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41(2), 157.Difficult Cases (DFT): Noncovalent InteractionsRef: Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41(2), 157.Difficult Cases: Charge Transfer Excitation EnergiesExcitation Energies (eV)Ref: Zhao, Y.; Truhlar, D. G. Theo. Chem. Acc.

15、 2008, 120, 215.TetraaceneValence B2u LaNH3F2C2H4C2F4HF3.911.113.9PBE3.00.15.1B3LYP3.42.27.0B983.52.66.4TPSSh3.41.510.0M06-HF3.89.412.6Best Estimate3.49.512.6Donald G. TruhlarDFT: Reaction Energy and Equilibrium ConstantsError in Reaction Energy at 0 K (kcal/mol) Li Z. H. unpublished.Difference to G

16、3B3PBEPW91B3LYPPBE0BMKC3H8 - H2 + C3H67.8 8.0 5.6 11.3 10.2 C3H8+1/2O2-C3H6+H2O7.0 6.6 3.7 7.8 4.4 C3H8+CO2 - C3H6 + H2O + CO15.1 15.0 6.8 14.4 9.7 H2+CO2 - HCOOH-6.8 -7.4 -6.0 -9.8 -7.4 C3H8+CO2 - HCOOH + C3H61.0 0.6 -0.4 1.5 2.8 H2+CO2 - CO + H2O7.3 7.0 1.2 3.1 -0.6 CO + H2O - HCOOH-14.1 -14.4 -7.

17、2 -12.9 -6.8 MAD8.48.44.48.76.0DFT: Reaction Energy and Equilibrium ConstantsEquilibrium Constant at 298 K (KDFT/KAcc) Li Z. H. unpublished.PBEPW91B3LYPPBE0BMKC3H8 - H2 + C3H62.010-6 1.410-6 8.310-65.110-93.210-8C3H8+1/2O2-C3H6+H2O7.610-61.510-52.010-31.810-86.310-4C3H8+CO2 - C3H6 + H2O + CO8.310-12

18、1.010-111.010-52.710-118.410-8H2+CO2 - HCOOH1.01052.71052.41041.61072.7105C3H8+CO2 - HCOOH + C3H60.200.382.08.210-28.710-3CO2+H2 - CO + H2O4.210-67.210-60.135.310-32.6CO + H2O - HCOOH2.310103.710101.91053.01091.0105Reaction Energy at 0 K (kcal/mol)PBEPW91B3LYPPBE0BMKG3B3H2+CO2 - HCOOH-1.1 -1.7 -0.2

19、-4.1 -1.7 6.9HCOOH - CO + H2O19.920.212.918.712.65.8H2+CO2 - CO + H2O18.818.512.714.610.911.5Free energy change (kcal/mol) at 800 KPBEPW91B3LYPPBE0BMKG3B3C3H8 - H2 + C3H611.9 12.1 9.7 15.4 14.3 4.1C3H8+CO2 - C3H6 + H2O + CO23.323.114.922.617.88.2K2/K10.08%0.1%3.6%1.1%11%7.9%DFT: Bad Energy Barriers

20、for Hydrogen Transfer ReactionsRef: Zhao, Y.; Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 2715.Prediction on Selectivity?Figure From: Somorjai, G. A.; Park, J. Y. Angew. Chem. Int. Ed. 2008, 47, 9212.29880080%:20%0.8 2.2 90%:10%1.3 3.5 99%:1%2.7 7.3 不同的選擇性對應的自由能壘的差別 (kcal/mol)DFT: Be Careful to Select a Good MethodGrid pointMultireference system: Metal-Metal BondEnergy barrierWeak interactionExcitation energyAccuracy still need to be improvedNo systematic way to improve results怎樣做好的計算Right Reason for the Right Answer怎樣做好的計算了解所研究的體系建立合理的模型選擇合適的方法