Dunning_BasisSets_Correlated - Solution of the Electronic...

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Unformatted text preview: Solution of the Electronic Schrödinger Equation Using Basis Sets to Solve the Electronic Schrödinger Equation with Electron Correlation Errors in HF Predictions: Binding Energies De (kcal/mol) HF HF 100.3 141.6 N2 122.3 228.4 F2 Chemical Bonds Expt’l -27.0 39.0 Hydrogen Bonds (HF)2 3.7 4.6 Electrostatic “Bonds” N2-HF 1.27 2.22 van der Waals “Bonds” He2 NB Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation 0.0218 Mathematical Models for Electron Correlation Configuration Interaction e = 0+ C ia Cijab i R Long history in electronic structure theory + a ij ab +… H e C = Ee C R Number of configurations grows rapidly with excitation level R Truncated CI not size extensive Perturbation Theory R Most widely used technique for including electron correlation H e = H0 + H 1 e = 0 + R Very flexible, e.g., can describe both ground and excited states 1 + Ee = E0 + E1 + 2 2E 2 2 + … R H0 usually taken to be the HF +… Hamiltonian R Recent studies have revealed serious convergence problems Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation Models for Electron Correlation (cont’d) Coupled Cluster Theory e = eT 0 T = t1 + t2 + t3 + … t1 = tiaaa+ai t2 = t3 = tijabab+aa+ajai ... R Recent addition to electronic structure theory R Includes dominant higher-order terms as products of lower order terms R Rapid convergence if wavefunction is dominated by well localized electron pairs, e.g., CCSD is exact if electron pairs are completely separate R Convergence problems if HF wavefunction provides a very poor zeroorder description of molecule Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation Notation for Correlated Calculations Perturbation Theory Methods MP2 MP3 MP4 ... He = H0 + H 1 = 0 + 1 + 2 2 + ... Coupled Cluster Methods T2 T1+ T2 T1+ T2+ T3 ... = eT 0 T = T1 + T2 + T3 + ... Variational Methods = 0+ Ca i {ai} a i + Cabij ij ab + ... {ab}{ij} Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation CCD CCSD CCSDT ... SDCI SDTCI ... MRCI SDCI Calculations on the Oxygen Atom -100.0 En,n+1 (mEh) En,n-1 = Ecorr(n, l) - Ecorr(n-1, l) -10.0 (nsnp) (ng) -1.0 (1h) -0.1 1 (nf) 2 3 (nd) 4 Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation Contributions to Correlation Energy (SDCI) Basis Function Groupings Contributions of basis functions to the correlation energy for the first row atoms fall into distinct groups with E1,0(sp) E1,0(d) E2,1(d) E1,0(f) E2,1(sp) E3,2(sp) E3,2(d) E2,1(f) E1,0(g) These grouping form the foundation for the construction of correlation consistent basis sets: -100.0 cc-pVDZ cc-pVTZ -10.0 cc-pVQZ cc-pV5Z -1.0 cc-pVDZ: HF Orbitals + (1s1p1d) cc-pVTZ: HF Orbitals + (2s2p2d1f) cc-pVQZ: HF Orbitals + (3s3p3d2f1g) where to balance the errors cc-pVDZ: HF Set = (9s4p) cc-pVTZ: HF Set = (10s5p) cc-pVQZ: HF Set = (12s6p) -0.1 1 Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation 2 3 Nbf 4 Atomic Calculations with cc-Sets -50.0 -100.0 B J H Ecorr (mEh) P B B B J J J B H H H -150.0 F B C N B J H -200.0 P P P O Exponential Convergence J Ecorr(n) = Ecorr( ) + Ecorr(2)eH Inverse Powers of lmax (=n) P R B P Ecorr(n) = Ecorr( ) + A/n3 F F -250.0 F R -300.0 -350.0 2 R 3 4 R 5 F Ne F R 6 Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation (n-2) Errors in Molecular Calculations Basis Set Convergence Error QbsM(n) = Q(M,n) – Q (M, ) Intrinsic Error QM = Q(M, ) – Q(expt’l) Calculational Error Qcalc’dM(n) = Q(M,n) – Q (expt’l) = QbsM(n) + QM Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation Illustration of Types of Errors in Calculations Type I Type II Type III Q(expt’l) QM( QM ) Qcalc’dM QbsM(n) n Note: Qcalc’dM 0 n Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation n Confusion: Convergence of De(N2) with MPn De (kcal/mol) 240.0 230.0 228.4 kcal/mol 220.0 210.0 Basis set: cc-pVTZ 200.0 MP2 MP3 MP4 Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation Resolution of the N2 Problem Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation Binding Energies: Chemically Bound Molecules CH HF N2 CO De(expt’l)a De(core-valence) De(valence-only) 83.9 -0.2 83.7 141.6 -0.2 141.4 228.4 -0.8 227.6 259.3 -0.9 258.4 CCSD CCSD(T) CCSDT -0.8 0.0 0.1 -2.0 0.1 0.0 -9.9 -0.3 -0.9 -7.5 0.1 -0.3 MP2 MP3 MP4 MP5 -2.7 -1.2 -0.4 4.4 -3.3 1.3 -0.8 12.4 -11.8 4.2 13.6 -7.9 5.9 a Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules; Van Nostrand,; Princeton, 1979. Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation Binding Energies: Hydrogen-bonded Molecules (HF)2 De(expt’l)a, kcal/mol 4.56 CCSD CCSD(T) -0.16 -0.02 MP2 MP3 MP4 -0.09 -0.03 -0.02 a Cayton, D. C.; Jucks, K. W.; Miller, R. E. J. Chem. Phys. 1989, 90, 2631; Klopper, W.; Quack, M.; Suhm, M. A. J. Chem. Phys. 1998, 108, 10096. Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation Binding Energies: Weakly Bound Molecules N2-HFa Ar-HFb Ar-FHb Ar-HClc Ar-ClHc De(expt’l), cm-1 776.±30 211.±4 109.±10 176.±5 148.±10 CCSD CCSD(T) -52 17 -45 0 -36 -15 — 0 — -1 MP2 MP3 MP4 35 -36 38 -10 -31 7 -16 -31 -10 31 — 10 33 — 7 a Lovejoy, C. M.; Nesbitt, D. J. J. Chem. Phys. 1987, 86, 3151; Nesbitt, D. J.; Child, M. S. J. Chem. Phys. 1993, 98, 478; Nesbitt, D. J.; Lindeman, T. G.; Farrell, J. T., Jr.; Lovejoy, C. M. J. Chem. Phys. 1994, 100, 775; Bemish, R. J.; Bohac, E. J.; Wu, M.; Miller, R. E. J. Chem. Phys. 1994, 101, 9457; Farrell, J. T.; Sneh, O.; Nesbitt, D. J. J. Phys. Chem. 1994, 98, 6068; Tang, S. N.; Chang, H-C.; Klemperer, W. J. Phys. Chem. 1994, 98, 7313. b Hutson, J. M. J. Chem. Phys. 1992, 96, 6752 and references therein. c Hutson, J. M. J. Chem. Phys. 1988, 89, 4550; Hutson, J. M. J. Phys. Chem. 1992, 96, 4237; and references therein. Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation Binding Energies: Very Weakly Bound Molecules He2a De(expt’l), cm-1 De(core-valence) De(valence-only) Ne2b Ar2c 7.59 29.4 +0.05 29.4 99.6 -0.8 98.8 CCSD CCSD(T) CCSDT -1.1 -0.2 0.0 -6.8 -1.0 -26.8 -1.8 MP2 MP3 MP4 MP5 -2.7 -1.1 -0.5 -0.2 -10.5 -7.1 -1.9 13.2 -16.8 1.2 a Aziz, R. A.; Slaman, M. J. J. Chem. Phys. 1991, 94, 8047. Aziz, R. A.; Janzen, A. R.; Moldover, R. Phys. Rev. Lett. 1995, 74, 1586. b Aziz, R. A.; Meath, W. J.; Allnatt, A. R. Chem. Phys. 1983, 78, 295. Aziz, R. A.; Slaman, M. J. Chem. Phys. 1989, 130, 187. c Aziz, R. A.; Slaman, M. J. Mol. Phys. 1986, 58, 679. Aziz, R. A. J. Chem. Phys. 1993, 99, 4518 Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation References 1. “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen,” T. H. Dunning, Jr., J. Chem. Phys. 90, 10071023 (1989). 2. “Electron affinities of the first-row atoms revised. Systematic basis sets and wave functions,” R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, J. Chem. Phys. 96, 6796-6806 (1992). 3. “Gaussian basis sets for use in correlated molecular calculations. III. The second row atoms, Al-Ar,” D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 980,13581371 (1993). 4. “Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties,” D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 100, 2975-2988 (1994). 5. “Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon,” D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 103, 4572-4585 (1995). Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation References (cont’d) 6. “Gaussian basis sets for use in correlated molecular calculations. VI. Sextuple-zeta correlation-consistent sets for boron through neon,” A. K. Wilson, T. van Mourik, and T. H. Dunning, Jr., J. Molec. Struct. (Theochem) 388, 339-349 (1996). 7. “Gaussian basis sets for use in correlated molecular calculations. VII. The atoms aluminum through argon revisted,” T. H. Dunning, Jr., K. A. Peterson, and A. K. Wilson, J. Chem. Phys. 114, 9244-9253 (2001). 8. “Gaussian basis sets for use in correlated molecular calculations. VIII. Standard and augmented sextuple zeta correlation consistent basis sets for aluminum through argon,” T. van Mourik and T. H. Dunning, Jr., Intern. J. Quant. Chem. 76, 205-221 (2000). 9. “Gaussian basis sets for use in correlated molecular calculations. IX. Correlation consistent sets for the atoms gallium through krypton,” T. H. Dunning, Jr., J. Chem. Phys. 110, 7667-7676 (1999). 10. “Accurate correlation consistent basis sets for molecular core-valence effects: The second row atoms, Al-Ar, and the first row atoms B-Ne revisited,” K. A. Peterson and T. H. Dunning, Jr., J. Chem. Phys. 117, 10548-10560 (2002). Using Basis Sets to Solve the Schrödinger Equation with Electron Correlation ...
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This note was uploaded on 12/07/2011 for the course CHEM 350 taught by Professor Duanejohnson during the Summer '06 term at University of Illinois, Urbana Champaign.

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