Choose start coefficients for mos 2construct fock

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Choose start coefficients for MO’s 2. Construct Fock Matrix with coefficients 3. Solve Hartree-Fock-Roothaan equations 4. Repeat 2 and 3 until ingoing and outgoing coefficients are the same Self-Consistent-Field (SCF) (SCF)   S F i i i c c
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its.unc.edu 25 Semi-empirical methods (MNDO, AM1, PM3, etc.) Semi-empirical methods (MNDO, AM1, PM3, etc.) Full CI Full CI perturbational hierarchy (CASPT2, CASPT3) perturbational hierarchy (CASPT2, CASPT3) perturbational hierarchy (MP2, MP3, MP4, …) perturbational hierarchy (MP2, MP3, MP4, …) excitation hierarchy (MR-CISD) excitation hierarchy (MR-CISD) excitation hierarchy (CIS,CISD,CISDT,...) (CCS, CCSD, CCSDT,...) excitation hierarchy (CIS,CISD,CISDT,...) (CCS, CCSD, CCSDT,...) Multiconfigurational HF (MCSCF, CASSCF) Multiconfigurational HF (MCSCF, CASSCF) Hartree-Fock (HF-SCF) Hartree-Fock (HF-SCF) Ab Initio Methods Ab Initio Methods
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its.unc.edu 26 Who’s Who
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its.unc.edu 27 Size vs Accuracy Size vs Accuracy Number of atoms 0.1 1 10 1 10 100 1000 Accuracy (kcal/mol) Coupled-cluster, Multireference Nonlocal density functional, Perturbation theory Local density functional, Hartree-Fock Semiempirical Methods Full CI
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its.unc.edu 28 R OO,e = 291.2 pm 96.4 pm 95.7 pm 95.8 pm symmetry: C s Equilibrium structure of (H Equilibrium structure of (H 2 O) O) 2 W.K., J.G.C.M. van Duijneveldt-van de Rijdt, and W.K., J.G.C.M. van Duijneveldt-van de Rijdt, and F.B. van Duijneveldt, F.B. van Duijneveldt, Phys. Chem. Chem. Phys. Phys. Chem. Chem. Phys. 2 , 2227 (2000). , 2227 (2000). Experimental [J.A. Odutola and T.R. Dyke, J. Chem. Phys 72 , 5062 (1980)]: R OO 2 ½ = 297.6 ± 0.4 pm SAPT-5s potential [E.M. Mas et al ., J. Chem. Phys. 113 , 6687 (2000) ]: R OO 2 ½ R OO,e = 6.3 pm R OO,e (exptl.) = 291.3 pm AN EXAMPLE
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its.unc.edu 29 Experimental and Computed Enthalpy Changes H e in kJ/mol Enthalpy Changes H e in kJ/mol Exptl. CCSD(T) SCF G2 DFT CH 4 CH 2 + H 2 544(2) 542 492 534 543 C 2 H 4 C 2 H 2 + H 2 203(2) 204 214 202 208 H 2 CO CO + H 2 21(1) 22 3 17 34 2 NH 3 N 2 + 3 H 2 164(1) 162 149 147 166 2 H 2 O H 2 O 2 + H 2 365(2) 365 391 360 346 2 HF F 2 + H 2 563(1) 562 619 564 540 Gaussian-2 (G2) method of Pople and co-workers is a combination of MP2 and QCISD(T)
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its.unc.edu 30 LCAO Basis Functions LCAO Basis Functions ’s, which are atomic orbitals, are called basis functions usually centered on atoms can be more general and more flexible than atomic orbital functions larger number of well chosen basis functions yields more accurate approximations to the molecular orbitals c
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its.unc.edu 31 Basis Functions Basis Functions Slaters (STO) Gaussians (GTO) Angular part * Better behaved than Gaussians 2-electron integrals hard 2-electron integrals simpler Wrong behavior at nucleus Decrease too fast with r r) exp( 2 n m l r exp * z y x
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its.unc.edu 32 Contracted Gaussian Basis Set Contracted Gaussian Basis Set Minimal STO-nG Split Valence: 3- 21G,4-31G,6- 31G Each atom optimized STO is fit with n GTO’s Minimum number of AO’s needed Each atom optimized STO is fit with n GTO’s Minimum number of AO’s needed Contracted GTO’s optimized per atom Doubling of the number of valence AO’s Contracted GTO’s optimized per atom Doubling of the number of valence AO’s
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