1. Figure Number: 29-00CO
Title: Vitamin D
Caption: Ball-and-stick model of vitamin D.
Notes: Vitamin D is manufactured in the body from a derivative of cholesterol using UV light from the sun in a pericyclic reaction. The behavior of pericyclic reactions is explained by a combination of orbital symmetry theory and frontier molecular-orbital theory often referred to as the "Woodward–Hoffmann rules." Interestingly, R. B. Woodward (of the Woodward–Hoffmann rules) was the first chemist to do a total synthesis of vitamin D in the lab.

2. Figure Number: 29-01
Title: Figure 29.1
Caption: In-phase and out-of-phase interactions of two atomic p orbitals to give a bonding and an antibonding pi molecular orbital.
Notes: The bonding pi orbital is lower in energy than the atomic p orbitals, whereas the antibonding pi orbital is higher in energy than the atomic p orbitals.

3. Figure Number: 29-02
Title: Figure 29.2
Caption: Pi molecular orbitals of 1,3-butadiene.
Notes: Four atomic p orbitals on the four connected carbons combine to give four pi molecular orbitals.

4. Figure Number: 29-03
Title: Figure 29.3
Caption: Pi molecular orbitals of 1,3,5-hexatriene.
Notes: Six atomic p orbitals on the six connected carbons combine to give six pi molecular orbitals.

5. Figure Number: UN
Title: Conrotatory Ring Closure
Caption: Ring closure which occurs when both orbitals rotate in the same direction to achieve overlap is called conrotatory.
Notes: Conrotatory ring closure occurs when the top lobe of one orbital has the same phase as the bottom lobe of the other orbital involved in forming a sigma bond.

6. Figure Number: UN
Title: Disrotatory Ring Closure
Caption: Ring closure which occurs when the orbitals rotate in opposite directions to achieve overlap is called disrotatory.
Notes: Disrotatory ring closure occurs when the top lobe of one orbital has the same phase as the top lobe of the other orbital involved in forming a sigma bond.

7. Figure Number: UN
Title: Ring Closure With Symmetric HOMO
Caption: Molecules with symmetric HOMOs give disrotatory ring-closure products.
Notes: Molecules with symmetric HOMOs have the top lobe of one orbital in the same phase as the top lobe of the other orbital.

8. Figure Number: UN
Title: Ring Closure with Antisymmetric HOMO
Caption: Molecules with antisymmetric HOMOs give conrotatory ring-closure products.
Notes: Molecules with antisymmetric HOMOs have the top lobe of one orbital in the same phase as the bottom lobe of the other orbital.

9. Figure Number: UN
Title: (2E,4Z,6E)-Octatriene Ring Closure
Caption: (2E,4Z,6E)-Octatriene ring closure is disrotatory, yielding cis-5,6-dimethyl-1,3-cyclohexadiene.
Notes: The HOMO of (2E,4Z,6E)-octatriene is symmetric because MOs of linear conjugated pi systems alternate in symmetry starting with the lowest-energy MO being symmetric. (2E,4Z,6E)-Octatriene has six MOs (from six atomic p orbitals overlapping), half of which (three) are filled in the ground state. The third-lowest-energy orbital has to be the HOMO, and it has to be symmetric rather than antisymmetric.

10. Figure Number: UN
Title: (2E,4Z,6Z)-Octatriene Ring Closure
Caption: (2E,4Z,6Z)-Octatriene ring closure is disrotatory, yielding trans-5,6-dimethyl-1,3-cyclohexadiene.
Notes: The HOMO of (2E,4Z,6Z)-octatriene is symmetric because MOs of linear conjugated pi systems alternate in symmetry starting with the lowest-energy MO being symmetric. (2E,4Z,6Z)-Octatriene has six MOs (from six atomic p orbitals overlapping), half of which (three) are filled in the ground state. The third-lowest-energy orbital has to be the HOMO, and it has to be symmetric rather than antisymmetric.

11. Figure Number: UN
Title: Photochemically induced (2E,4Z,6Z)-Octatriene Ring Closure
Caption: Photochemically induced (2E,4Z,6Z)-octatriene ring closure is conrotatory, yielding cis-5,6-dimethyl-1,3-cyclohexadiene.
Notes: The HOMO of (2E,4Z,6Z)-octatriene which has been excited by light is antisymmetric because MOs of linear conjugated pi systems alternate in symmetry starting with the lowest-energy MO being symmetric. (2E,4Z,6Z)-Octatriene has six MOs (from six atomic p orbitals overlapping), half of which (three) are filled in the ground state. The third-lowest-energy orbital has to be the HOMO in the ground state, and the fourth-lowest-energy orbital has to be the HOMO of the photochemically excited state. This orbital has to be antisymmetric.

12. Figure Number: UN
Title: (2E,4Z)-Hexadiene Ring Closure
Caption: (2E,4Z)-Hexadiene undergoes conrotatory ring closure to yield cis-3,4-dimethylcyclobutene.
Notes: The HOMO of (2E,4Z)-hexadiene has to be antisymmetric because this compound has to have four pi MOs, two of which are filled. The HOMO has to be the second-lowest-energy orbital. Since the lowest-energy orbital has to be symmetric, the HOMO has to be antisymmetric.

13. Figure Number: UN
Title: (2E,4E)-Hexadiene Ring Closure
Caption: (2E,4E)-Hexadiene undergoes conrotatory ring closure to yield trans-3,4-dimethylcyclobutene.
Notes: The HOMO of (2E,4E)-hexadiene has to be antisymmetric because this compound has to have four pi MOs, two of which are filled. The HOMO has to be the second-lowest-energy orbital. Since the lowest-energy orbital has to be symmetric, the HOMO has to be antisymmetric.

14. Figure Number: UN
Title: Suprafacial vs. Antarafacial Bond Formation
Caption: In a cycloaddition reaction, bond formation is called suprafacial if both sigma bonds form on the same side of the pi system, and antarafacial if the sigma bonds form on the opposite side of the pi system.
Notes: Antarafacial cycloadditions result in strained transition states for small rings, as one of the fragments undergoing cycloaddition must simultaneously bond to the top face of one side of its partner and the bottom face of the other side of the partner, forming a strained-ring transition state. Generally, a seven-membered or larger ring needs to be formed by a cycloaddition reaction in order to observe antarafacial ring formation.

15. Figure Number: 29-05
Title: Figure 29.5
Caption: Frontier molecular-orbital analysis of a [4 + 2] cycloaddition reaction.
Notes: The HOMO of either of the reactants used with the LUMO of the other gives the same results as switching the reactant which contributes the HOMO with the reactant which contributes the LUMO. Both cases require suprafacial overlap for bond formation. In the normal situation, the four-electron system contributes the HOMO and the two-electron system contributes the LUMO, but this situation can be reversed.

16. Figure Number: 29-06
Title: Figure 29.6
Caption: Frontier MO analysis of a [2 + 2] cycloaddition reaction under thermal and photochemical conditions.
Notes: Under thermal conditions, this cycloaddition would have to be antarafacial, which is impossible for a [2 + 2] cycloaddition (forms a four-membered ring). Under photochemical conditions, this reaction allows suprafacial ring formation.

17. Figure Number: UN
Title: Suprafacial and Antarafacial Sigmatropic Rearrangements
Caption: A sigmatropic rearrangement in which a migrating group remains on the same face of the pi system as it migrates is suprafacial. If the migrating group moves from one face of the pi system to the opposite face, the migration is antarafacial.
Notes: Suprafacial migrations normally occur when the HOMO of the pi system is symmetric, and antarafacial migrations normally occur when the HOMO of the pi system is antisymmetric and the migration transition state is a ring with seven or more atoms in it.

18. Figure Number: UN
Title: Migration of Hydrogen
Caption: Migration of hydrogen in a suprafacial and antarafacial rearrangement.
Notes: Since hydrogen's s orbital has only one phase, the phase of the lobe of the developing p orbital of the atom it migrates from and the lobe of the p orbital of the atom it migrates to must have the same phase. Thus, hydrogen is forced to migrate suprafacially in cases where there is an odd number of electron pairs involved in the migration (symmetric HOMO) and antarafacially in cases where there is an even number of pairs of electrons involved in the migration (antisymmetric HOMO).

19. Figure Number: UN
Title: Migration of Carbon Using One Lobe
Caption: Suprafacial and antarafacial migration of carbon with carbon using the same lobe to bond to its destination position that it uses to bond to its original position.
Notes: When carbon uses only one lobe to migrate in a sigmatropic rearrangement, it must migrate suprafacially when an odd number of electron pairs are involved in the migration (symmetric HOMO) and antarafacially when an even number of electron pairs are involved in the migration (antisymmetric HOMO). This type of migration results in retention of configuration at the migrating carbon.

20. Figure Number: UN
Title: Migration of Carbon Using Both Lobes
Caption: Suprafacial and antarafacial migration of carbon with carbon using the opposite lobe to bond to its destination position from the one that it uses to bond to its original position.
Notes: When carbon uses both lobes to migrate in a sigmatropic rearrangement, it must migrate antarafacially when an odd number of electron pairs are involved in the migration (symmetric HOMO) and suprafacially when an even number of electron pairs are involved in the migration (antisymmetric HOMO). This type of migration results in inversion of configuration at the migrating carbon.

21. Figure Number:
Title: Table Woodward-Hoffmann Rules for Electrocyclic Reactions
Caption:
Notes:

22. Figure Number:
Title: Table Configuration of the Product of an Electrocyclic Reaction
Caption:
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23. Figure Number:
Title: Table Woodward-Hoffmann Rules for Cycloaddition Reactions
Caption:
Notes:

24. Figure Number:
Title: Table Woodward-Hoffmann Rules for Sigmatropic Rearrangements
Caption:
Notes: