11. Range of Molecular Mechanics and Quantum Methods Method Range (heavy atoms)‏ Molecular Mechanics > 1000 Semi-Empirical < 200 Ab initio Hartree-Fock(HF) < 50 Ab initio Correlated < 20 Density Functional (DFT) < 100

12. Relative Computation Times Methylcyclohexane (C 7 H 14 )‏ 14 2 pBP/DN* ( DFT )‏ .06 8 54 - f 1 7 100 AM1 ( Semi-Empirical )‏ HF/3-21G ( Ab initio )‏ HF/6-31G* ( Ab initio )‏ MP2/6-31G* ( Ab initio Correlated )‏ f f MMFF94 ( MM )‏ Geometry Optimization Single-Point Energy Level of Calculation

13. Comparison of the Performance of Molecular Mechanics( MM ) and Quantum Methods( QM ) S= satisfactory; U= unsatisfactory Task MM Semi- Ab initio DFT Empirical HF Correlated Geometry S S S S S Transition-state - S S S S Geometry Conformation S U S S S Thermochemistry - U S S S

19. Relation between Dihedral Angle and Relative Conformer Energy in 1,3-Butadiene s- trans s- cis twisted Order of stability: s- trans > s- cis > twisted

25. Determination of Absolute Configuration in A Macrocyclic System by a Combination of Computational Chemistry and Another Method

26. The distance between H-2 and H-13 is 4.0 Å in 13( R )configuration . This is not consistent with information based on NOESY.

27. The distance between H-2 and H-13 is 2.4 Å in 13( S )configuration. This is consistent with information based on NOESY.

28. CD Spectrum Negative Cotton Effect - CD also supports 13( S )configuration.

32. Imidazole: Where is the Basic Site ? The N-3 is negatively charged , and thus is the basic site . Electrostatic Potential Map

33. Acidities of Alcohols stronger stronger weaker weaker 15.5 Methanol 15.9 Ethanol 7.2 4-Nitrophenol 10.0 Phenol 12.4 2,2,2-Trifluoroethanol pKa’s (acidities)‏

42. HOMO of the Enolate HOMO Map of the Enolate The color near red indicates minimum value, and the color near blue indicates maximum value of HOMO. The terminal carbon,where HOMO shape (value) is larger , generally reacts with electrophile .

45. Nucleophilic Additions to Dioxanone Ring LUMO map for the axial face LUMO map for the equatorial face Nucleophililes preferentially attack from the axial face.

46. Nucleophilic Additions to Dithianone Ring LUMO map for the axial face LUMO map for the equatorial face Nucleophililes preferentially attack from the equatorial face.