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Calculating Molecular Binding Energies from Chemical Bonds to van der Waals Interactions

Calculating Molecular Binding Energies from Chemical Bonds to van der Waals Interactions. Thom H. Dunning, Jr. Joint Institute for Computational Sciences University of Tennessee – Oak Ridge National Laboratory Oak Ridge, Tennessee. Joint Institute for Computational Sciences.

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Calculating Molecular Binding Energies from Chemical Bonds to van der Waals Interactions

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  1. Calculating Molecular Binding Energiesfrom Chemical Bonds to van der Waals Interactions Thom H. Dunning, Jr. Joint Institute for Computational Sciences University of Tennessee – Oak Ridge National Laboratory Oak Ridge, Tennessee

  2. Joint Institute for Computational Sciences

  3. Outline of Seminar • Statement of the Problem • Theoretical Methods • Basis Sets and Error Analysis • Correlation Consistent Basis Sets • Errors in Molecular Calculations • Errors in Molecular Binding Energies (for Four Classes) • Intrinsic Errors of Methods • Basis Set Convergence Errors • Statistical Analysis of Errors in Binding Energies • Conclusions

  4. Statement of ProblemWide Range of Binding Energies De (kcal/mol) 0.01 0.1 1.0 10.0 100.0 1000.0 } He2 Ne2 Ar2 (HF)2 N2 Ar-HF H-CO CO N2-HF H-C2H2 Ar-HCl H-CO- H-CHn H-C2Hn

  5. Statement of ProblemImportance of Electron Correlation De (kcal/mol) HF Expt’l HF 100.3 141.6 N2 122.3 228.4 F2 -27.0 39.0 (HF)2 3.7 4.6 N2-HF 1.27 2.22 He2 – 0.0218 Chemical Bonds Hydrogen Bonds Electrostatic “Bonds” van der Waals “Bonds”

  6. Perturbation Theory He = H0 + lH1 Ye = F0 + lF1 + l2F2 + … Ee = E0 + lE1 + l2E2 + … • Most widely used technique for including electron correlation • Assumes that electron correlation is perturbation to the HF hamiltonian • Recent studies have revealed serious convergence problems Theoretical Methods Configuration Interaction Ye = F0 + SCiaFia + SSCijabFijab + … He C = Ee C • Long history in electronic structure theory • Very flexible, e.g., can describe both ground and excited states • Not size extensive/consistent

  7. Theoretical Methods Coupled Cluster Theory Ye = eTF0 T = t1 + t2 + t3 + … t1 = Stiaaa+ai t2 = Stijabab+aa+ajai t3 = ... • Recent addition to electronic structure theory • Includes dominant higher-order terms as products of lower order terms • Rapid convergence if wavefunction is dominated by well localized electron pairs • Convergence problems if HF wave-function provides poor zero-order description of molecule

  8. 260.0 CBS Limit +1s1p1d1f1g 255.0 +1s1p1d1f +1s1p1d HF Orbitals 250.0 245.0 De(CO) 240.0 cc-pVDZ 2 3 4 5 6 cc-pVTZ n (cc-pVnZ) cc-pVQZ Basis Sets and Error AnalysisCorrelation Consistent Basis Sets • cc-Sets based on detailed study of electron correlation in atoms • Correlation functions added in shells • Hartree-Fock orbitals • cc-pVDZ: + (1s1p1d) cc-pVTZ: + (2s2p2d1f) cc-pVQZ: + (3s3p3d2f1g) … • Augmented with diffuse functions for anions, long range interactions, etc. • Molecular properties often exhibit systematic dependence • Possible to extrapolate properties to complete basis set limit

  9. Basis Sets and Error AnalysisDefinition of Errors (Method “M”) • Basis Set Convergence Error DQbsM(n) = Q(M,n) – Q (M,¥) • Intrinsic Error DQM = Q(M,¥) – Q(expt’l) • Calculational Error DQcalc’dM(n) = Q(M,n) – Q (expt’l) = DQbsM(n) + DQM

  10. Type I Type II Type III Q(expt’l) DQM QM(¥) DQcalc’dM Note: DQcalc’dM » 0 DQbsM(n) n n n Basis Sets and Error AnalysisConvergence Types

  11. Molecular Binding Energies:Chemical Bonds T. H. Dunning, Jr., J. Phys. Chem. A 104, 9062- 9080 (2000) K. L. Bak, P. Jørgensen, J. Olsen, T. Helgaker, and W. Klopper, J. Chem. Phys. 112, 9229- 9242 (2000)

  12. Intrinsic Errors in DeChemical Bonds CH HF CO N2 De (kcal/mol)a 83.9 141.6 258.6 227.4 MP2 -2.9 4.2 13.0 12.5 MP3 -1.4 -3.1 -8.5 -11.7 MP4 -0.6 1.1 5.7 4.7 MP5 -1.0 CCSD -1.0 -2.2 -8.1 -9.8 CCSD(T) -0.2 -0.1 0.0 -0.3 CCSDT -0.1 -0.2 -0.6 -1.1 a Corrected for core-valence and relativistic effects.

  13. Basis Set Convergence Errors in DeChemical Bonds DDebs(n) (kcal/mol) n n

  14. D = average error Region of “false positives” Statistical Analysis of Binding Energies r(Q) Dstd = error variation 0 DQ (Error in Q)

  15. MP2 CCSD +(T) D 6.0 -8.3 -1.0 Dstd 7.5 4.5 0.5 Intrinsic Errors in DeMP2 , CCSD, CCSD(T) Methods (6Z Set) r(DDe) DDe (kcal/mol)

  16. Basis Set Convergence of DeCCSD(T) Method for Chemical Bonds D = -1.0 kcal/mol Dstd = 0.5 kcal/mol r(DDe) DDe (kcal/mol)

  17. Extrapolation of Binding EnergiesAnalysis of Electron Correlation in He • Principal Expansion E = EHF(1s) + E2(2s2p)corr + E3(3s3p3d)corr + … • Errors in He Atom Klopper et al. [J. Phys. B. 32, R103 (1999)] showed error in truncating series after nth term in principal expansion is • Extrapolation Formula

  18. DT TQ Q5 56 D -3.5 -0.1 0.0 -0.1 Dstd 2.0 0.5 0.3 0.2 Extrapolation of DeCCSD(T) Method for Chemical Bonds 1.6 r(DDe) 5Z-6Z QZ-5Z TZ-QZ DZ-TZ DDe (kcal/mol)

  19. Molecular Binding Energies:Hydrogen Bonds T. H. Dunning, Jr., J. Phys. Chem. A 104, 9062- 9080 (2000) A. Halkier, W. Klopper, T. Helgaker, P. Jørgensen, and P. R. Taylor, J. Chem. Phys.111, 9157 (1999)

  20. Intrinsic Errors in DeHydrogen Bond in HF Dimer (HF)2 De (kcal/mol) 4.56 ± 0.05 a MP2 -0.09 MP3 -0.03 MP4 -0.02 CCSD -0.16 CCSD(T) -0.02 a W. Klopper, M. Quack, and M. Suhm, J. Chem. Phys. 108, 10096 (1998).

  21. Basis Set Convergence Errors in DeHydrogen Bonds in (H2O)2 and Others 0.0 -0.5 (H O) DDebs(n) (kcal/mol) 2 2 -1.0 cc-pV n Z aug-cc-pV n Z d-aug-cc-pV n Z -1.5 2 3 4 5 n n

  22. Errors in DeHydrogen Bonds De(n) (kcal/mol) BSSE BSCE De(n=∞) n

  23. Extrapolation of DeHydrogen Bond in HF Dimer De(n) (kcal/mol) Calculated Extrapolated n

  24. Molecular Binding Energies:Electrostatic Interactions T. H. Dunning, Jr., J. Phys. Chem. A 104, 9062- 9080 (2000)

  25. Intrinsic Errors in DeElectrostatic Interactions N2-HF Ar-HF Ar-FH Ar-HCl Ar-ClH De (cm-1) 776±30a 211±4b 109±10b 176±5c 148±10c MP2 35 -10 -16 31 33 MP3 -36 -31 -31 MP4 38 7 -10 10 7 CCSD -52 -45 -36 CCSD(T) 17 0 -15 0 7 a R. J. Bemish, E. J. Bohac, M. Wu, and R. E. Miller, J. Chem. Phys. 101, 9457 (1994) and references therein. b J. M. Huston, J. Chem. Phys. 96, 6752 (1992) and references therein. c J. M. Huston, J. Chem. Phys. 89, 4550 (1988); J. M. Hutson, J. Chem. Phys. 96, 4237 (1992) and references therein.

  26. Basis Set Convergence Errors in DeElectrostatic Interactions DDebs(n) (cm-1) n n

  27. Molecular Binding Energies:van der Waals Interactions T. H. Dunning, Jr., J. Phys. Chem. A 104, 9062- 9080 (2000)

  28. Intrinsic Errors in Devan der Waals Interactions He2 Ne2 Ar2 De(cm-1) 7.59 a 29.4 b 99.6 c MP2 -2.7 -10.5 13.4 MP3 -1.1 -7.1 -17.6 MP4 -0.5 -1.9 0.4 MP5 -0.2 CCSD -1.1 -6.8 -27.6 CCSD(T) -0.2 -1.0 -2.6 CCSDT -0.0 a R. A. Aziz and M. J. Slaman, J. Chem. Phys. 94, 8047 (1991); R. A. Aziz, A. R. Janzen, and R. Moldover, Phys. Rev. Lett. 74, 1586 (1995). b R. A. Aziz, W. J. Meath, and A. R. Allnatt, Chem. Phys. 78, 295 (1983); R. A. Aziz and M. J. Slaman, Chem. Phys. 130, 187 (1989). c R. A. Aziz and M. J. Slaman, Mol. Phys. 58, 679 (1986); R. A. Aziz, J. Chem. Phys. 99, 4518 (1993).

  29. Basis Set Convergence Errors in Devan der Waals Interactions DDebs(n) (cm-1) n n

  30. Conclusions • Critical Assessment of Methods • Coupled cluster method provides reliable means of computing molecular properties for molecules well described by single configuration • Perturbation method is poorly convergent or even non-convergent; often does not achieve chemical accuracy for chemical bonds • Critical Assessment of Basis Sets • Correlation consistent basis sets systematically approach complete basis set limit, extrapolation possible • Choice of cc-basis set family depends on molecular system • Chemically bound covalent molecules—standard sets

  31. Conclusions (cont’d) • Chemically bound ionic, hydrogen-bonded, and electrostaticly bound molecules—singly augmented sets • van der Waals bound molecules—doubly augmented sets • Convergence with basis set is slow • Difficult to describe coulomb hole using expansions in one-electron functions • Rate of convergence depends on molecular details • Single, double or triple bonds • Chemically bound, hydrogen-bonded, electrostatically bound or van der Waals bound • Extrapolation substantially improves convergence rate

  32. Acknowledgements It is a pleasure to acknowledge contributions of … Kirk Peterson, David Woon, David Feller, Ricky Kendall, Tanja van Mourik, and Angela Wilson to this work It is also a pleasure to acknowledge work of … Poul Jørgensen, Trygve Helgaker, Wim Klopper, Jeppe Olsen and coworkers, whose work has also contributed greatly to calibrating the methods used for molecular calculations Finally, I would like to thank … Division of Chemical Sciences, Office of Science, U.S. Department of Energy for their support of this work.

  33. End of Presentation

  34. DefinitionsDe and D0 Separated Atoms A+B E De D0 Zero Point Energy AB Molecule

  35. 10.0 1.0 -0.32 K 0.1 V(R) (K) T-(T) 0.01 -0.015 K FCI-T 0.001 0.0001 3 4 5 6 7 8 9 10 11 12 R (bohr) Higher Order Effects in He2

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