one ν im: transition state saddle point
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1 Hypothetical Potential Energy Surface Ethane conformations Hartree-Fock theory, basis set stationary points all ν s >0: minimum eclipsed one ν im: transition state saddle point multiple ν im: hilltop 1 Source: Hyperchem calculation geometry relaxed at each angle 2 Thermodynamic versus kinetic control Potential Energy Surface for F( 2P3/2, 2P1/2 ) + CH4 FH + CH3 E relates to thermodynamic control. MP2 with G(2df,2pd) basis set Source: Cipriano Rángel, et al., J. Phys. Chem. A, 109 (7), , staggered Ea relates to kinetic control. Engel's Figures 15.4,5,6 3 4
2 E correlation E nonrelativistic E Section 4: Hartree Fock, Configuration Interaction (CI), and Exact Dissociation of H2 is inaccurate for homolytic bond cleavage E.g., H2 (1Σg) 2H (2S1/2) Electron correlation is everything except relativity that is not in. Correlation energy increases in magnitude with increasing number of electrons. R: bad U: poor CI corrects for correlation. Full-CI E > exact E because of small 6-31G(d,p) basis set Ecorrelation (Hartree) Percent CH4 H2O H2O CO source: Lowe's Quantum Chemistry, Tables 11-2 and basis set Hartree-Fock is incorrect for homolytic bond cleavage E (Hartree) Section 6: Correlation energy, continued Section 4: Limiting Hartree-Fock results ΔE (kj/mol) CH3 CH3 CH3 F F F atom or molecule He C F Ar H2 error H2 at R=1.4a0 6-31G(d,p) BeH2 double zeta H2O 39-STO CISD Full CI with the stated basis set same as CISD exact correlation energy with infinite basis source: Modern Quantum Chemistry, by Szabo and Ostlund, Dover, 1996, section 4.3. Hartree-Fock is better for reactions that maintain electron pairs. A+H+ AH+ H+ affinity (kj/mol) ammonia -50 pyridine 29 trimethylamine source: Engel's Tables 15.2 and G(d,p) basis error
3 CI-Singles and Doubles is not size consistent. Density Functional Theory (DFT) Example He monomer and dimer with {1s,2s} basis. CISD for He monomer Figures are from Engel's chapter 15. DFT focuses on ρ(x,y,z) rather than on Ψ(all electrons' x,y,z) Walter Kohn ( ) and Pierre Hohenberg theoretical basis, 1963 CISD for HeaHeb dimer Walter Kohn Nobel Walter Kohn and Lu Sham, 1964 expanded ρ(x,y,z) in electron orbitals (like MO theory) Kohn-Sham equations for orbitals and their energies (SCF) CISD for separated Hea Heb monomers includes four additional double excitations. CIS and full CI are size consistent. [ ZA r RA nuclei A ρ( r ' ) r r ' d r ' + v xc ] KS KS ψks i ( r ) = ϵi ψ i ( r ) 9 10 Kohn-Sham and Hartree-Fock orbitals for ethene Density Functional Theory, results mean absolute errors Bond Lengths1 Method (Angstrom) B3LYP HOMO-LUMO 0.24 Eh HOMO-LUMO 0.55 Eh Dipole3 (Debye) for 32 molecules containing only first-row atoms. Basis set 6-311G(d,p). Cramer, Essentials of Computational Chemistry, Table Atomization energies were calculated for the G2 set: 55 molecules. Basis. Cramer, Essentials of Computational Chemistry, Table Average error in Debye for CO, H2O, H2S, NH3, PH3 and SO Cohen, Chemical Physics Letters, 299, , source: GAMESS, images from wxmacmolplt. Atomization2 (kj/mol)
4 Section 8: model selection Warren Hehre presents four methods Uncorrelated 1 Hartree Fock with the 3-21G basis set basis set is defined for H - Cs (55) Section 8: model selection, continued Most bond lengths are good from all three methods. Tables 15.9 and 15.10, C-X bonds method /3-21G / DFT B3LYP/ 2 Hartree-Fock with the basis set larger and polarized basis set, better than 3-21G basis set is defined for H - Zn (30) Correlated (post-hartree Fock) 3 MP2/ I am skipping MP2. mean absolute error (Å) DFT B3LYP/ about twice as slow as / computation time proportional to N ΔE of bond cleavage is much better with correlated methods. dipole moments (D) reflect geometry and charge distribution reaction energies (kj/mol) 1 debye = C m molecule CO H2O 3-21G DFT B3LYP (CRC) G DFT B3LYP experiment bond cleavage CH3-CH3 2 CH F-F 2 F H2S NH isomerization acetic acid methyl formate PH3 SO ethanol dimethyl ether mean abs err conformational n-butane gauche methylcyclohexane equatorial axial 15 source: Engel, Quantum Chemistry and Spectroscopy, Tables 15.11, 15.12,
5 comparison of and correlated activation energies Section 9: Graphical Models HOMO and LUMO are important in chemical reactivity errors in Ea (kj/mol) for 12 organic elementary gas-phase reactions. average error maximum error 3-21G 6-31(d) DFT B3LYP frontier orbitals for concerted additions HOMO source: Levine, Quantum Chemistry, 5th ed., page 703. activation energies (kj/mol) calculated with the basis set reaction DFT B3LYP CH3NC CH3CN 192 HCO2CH2CH3 HCO2H + C2H LUMO ,184 ethene + butadiene source: Hehre's Table (Engel, Quantum Chemistry and Spectroscopy). 17 but not ethene + ethene Engel's figures and singlet oxygen adds to diphenylisobenzofuran electron density surfaces can show bonds and lone pairs DPBF is used to trap singlet oxygen. O 2 adds across the furan ring. diborane B2H6 molecule e density (0.12 surface) e density (0.08 "bond" surface) LUMO ammonia NH3 pyramidal planar Pictures from Spartan DFT B3LYP 6-31G* HOMO Spartan image 19 Engel's Figure
6 electrostatic potential near H correlates with acidity Spartan. PM3 geometry. electrostatic potential. 21
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