Woodward and Hoffmann on Secondary Orbital Interactions. How to Make a Fine Two-Course Meal from Leftovers

Abstract

In 1965, R. B. Woodward and Roald Hoffmann published five communications in the Journal of the American Chemical Society that formed the basis for what has been known as the Woodward and Hoffmann (W-H) rules. The last two of these communications applied secondary molecular orbital interactions - that is, interactions that involved atomic orbitals removed from the primary reaction centers - to explain the so-called Alder endo-exo rule of maximum overlap of orbitals for regiochemistry in the Diels-Alder reaction and the then recently noted preference of the chair orientation over the boat orientation in the Cope reaction. This publication presents the back stories of these latter two W-H communications, based on a comprehensive examination of Hoffmann's laboratory notebooks, more than 100 hours of interviews with Hoffmann, interviews with other chemists, and documents found in both Hoffmann's and Woodward's archives.

Keywords: Woodward-Hoffmann rules; history of chemistry; mechanism of pericyclic reactions; molecular orbital theory; secondary orbital interactions.

Figure 1

February – mid‐August 1965 chronology of Hoffmann's research and the submission of the four Woodward‐Hoffmann manuscripts that led to their last four JACS communications of 1965.[ ² , ³ , ⁴ , ⁵ ] The first JACS communication on electrocyclizations was submitted on November 30, 1964, and published in the January 20, 1965, issue of the journal. The term “Solution“ in green font refers to the approximate date that Hoffmann derived the mechanism of the indicated reaction.

Figure 2

Endo IV and exo V transition states for the Diels‐Alder reaction of maleic acid and 1,3‐pentadiene. Chemical pictography are reprinted with permission from: R. B. Woodward, T. J. Katz, Tetrahedron 1959, 5, 70–89. Copyright 1959 Elsevier.

Scheme 1

Chair and boat mechanisms for the Cope reaction of 1,5‐hexadiene (1) and its boat (1 b) and chair (1 c) conformations (eq. 1) as proposed by Doering and Roth in 1962 and 1963. In due course, this mechanistic view would be expanded by Hoffmann with the inclusion of alternative reactions of the diradical species, to bicyclo[2.2.0]hexane and cyclohexane 1,4‐diyl.

Figure 3

Page 89 of 97 of Hoffmann's class notes of Douglas Applequist's course at Harvard, late spring of 1964. This page records some of Applequist's lecture on the Cope rearrangement with a citation to Doering and Roth's review of “Thermal Rearrangements” dealing primarily with Cope reactions. Within this cited review, Doering and Roth included Berry's mechanism reproduced in total in Section 5.2.

Figure 4

Two MOs can interact (or mix) only when they have the same symmetry, have significant geometric overlap, and are reasonably close in energy. (A) Two MOs that are both singly‐occupied interact. There is net stabilization. (B) Two MOs interact. One MO has two electrons (doubly‐occupied), the other has no electrons (unfilled). There is net stabilization. (C) Two MOs interact. Both MO have two electrons. There is net destabilization. (D) Two MOs having significant overlap and similar energies cannot interact when they have different symmetries. (E) Two MOs have the same symmetry and overlap significantly. But they have such very different energies that they interact weakly, if at all. (F) There is an interaction between a doubly‐filled subjacent MO and the LUMO of the other reactant. There is net small stabilization.

Figure 5

This figure shows a progression in sophistication and pedagogy in the depiction of HOMO‐LUMO interactions over time. (A) An excerpt from Michael J. S. Dewar's 1951 publication on π‐complexation. His drawings are essentially HOMO‐LUMO stabilizations. (B) An excerpt from Kenichi Fukui's 1964 chapter in which he proposed an frontier molecular orbital (FMO)‐based interaction diagram/perturbation theory method as the MO explanation for the allowedness of the Diels‐Alder reaction. Compare this graphic with Figure 5C. What Fukui did not explicitly draw was the interaction between the diene's HOMO f and the dienophile's LUMO f’ as shown by the blue dashed lines in (C). The diene's HOMO f and the dienophile's LUMO f’ not only have the same symmetry, they are also reasonably close in energy and overlap in space; therefore, they interact or mix. Consequently, two new MOs are formed, the lower or more stable MO becoming doubly‐occupied. Fukui did not discuss the diene's LUMO interacting with the dienophile's HOMO (shown in Figure 6), likely concluding that the difference in energies of these two MOs was too great, thereby rendering their interaction relatively unimportant. Regarding these HOMO‐LUMO interactions, I refer to these as “Fukui interactions.” (C) A more completely illustrative graphic than (B) shows the interaction of the diene's HOMO with the dienophile's LUMO and the formation of the two MOs. The symmetry plane σ is used herein. MO energy levels are not drawn to scale.

Figure 6

This graphic shows the interaction of the diene's LUMO with the dienophile's HOMO. The symmetry plane σ is used herein. The analogous interaction of the diene's HOMO and the dienophile's LUMO is shown in Figure 5C. This additional interaction results in further stabilization of the Diels‐Alder's transition state. MO energy levels are not drawn to scale.

Figure 7

Illustration of a stabilizing effect of a secondary orbital interaction occurring simultaneously with and further stabilizing the energy of a system due to a set of primary orbital interactions involving the same two interacting MOs. This follows Hoffmann's rule, that “changes in energy levels and wave functions are pairwise additive.” These interacting MOs have the same symmetry. Electron occupancies are not shown, and MO energy levels are not drawn to scale.

Figure 8

(Top) The endo orientation of the Diels‐Alder reaction of 1,3‐butadiene with either p‐benzoquinone or another molecule of 1,3‐butadiene. Primary orbital interactions (HOMO of 1,3‐butadiene with the LUMO of the dienophile) are shown in blue. Secondary orbital interactions are shown in red. The symmetry element is σ, the plane that bisects the central bond of the diene and the dienophile and is perpendicular to the planes containing the reactants. Note that the symmetries of the interacting orbitals are the same (both A) and SOIs are both positive. MO energy levels not drawn to scale. (Bottom) Structure 4 illustrates the diene's HOMO – dienophile's LUMO interaction in the Diels‐Alder dimerization of 1,3‐butadiene. Adapted from Hoffmann and Woodward's 1965 JACS communication on SOIs. See also Figure 9.

Figure 9

(Top) The endo orientation of the Diels‐Alder reaction of 1,3‐butadiene with either p‐benzoquinone or another molecule of 1,3‐butadiene Primary orbital interactions are shown in blue. Secondary orbital interactions are shown in red. The symmetry element is σ, the plane that bisects the central bond of the diene and the dienophile and is perpendicular to the planes containing the reactants. MO energy levels not drawn to scale. (Bottom) Structure 5 illustrates the diene's LUMO – dienophile's HOMO interaction in the Diels‐Alder dimerization of 1,3‐butadiene. Adapted from Hoffmann and Woodward's 1965 JACS communication on SOIs. See Figure 8.

Figure 10

Two early graphics of interaction diagrams from Hoffmann's publications. Compare these interaction diagrams with the interaction diagram in Figure 5. (A) From Hoffmann and Olofson's 1965 JACS publication “The Dependence of Conformational and Isomer Stability on the Number of Electrons in Extended π Systems,” received at the journal offices on September 21, 1965. This was just one month after the submission of Hoffmann and Woodward's fourth and fifth JACS communications on SOIs. (B) Woodward and Hoffmann's interaction diagram of the nonbonding antisymmetric MO levels of the three‐center bond and remnant for the thermal antarafacial [1,7] sigmatropic shift of a hydrogen atom from their 1969 treatise.

Figure 11

(A) Excerpt from page 44 of Hoffmann's Laboratory Notebook 16, ca. February 6, 1965. (B) Excerpt from Hoffmann and Woodward's 1965 communication on secondary orbital effects in the Diels‐Alder reaction.

Figure 12

Page 123 of Hoffmann's Laboratory Notebook 16, ca. March 5, 1965, in which he drew exo (A‐left and D‐left) and endo (A‐right and B‐right) configurations for the Diels‐Alder reaction. (C‐right and D‐left) Hoffmann surely observed that the correlation diagrams for these two Diels‐Alder reactions were identical. In A‐left (with dashes), he drew the primary orbital interactions, namely C(1) with C(6) and C(5) with C(4), using Hoffmann's numbering system in A‐left.

Figure 13

(A) Enlargement from far right of Figure 12B (from NB16/123). The Diels‐Alder reaction between the central double bond of 1,3,5‐hexatriene, acting as the dienophile, and 1,3‐butadiene, the diene. (B) The primary interactions for the exo and endo Diels‐Alder reactions are shown in 2‐ primary‐ex o and 3‐primary‐endo . The red arrows in (A) and the colored text and blue and red dashes in (C) were added by Seeman. The SOIs are indicated in 3‐secondary‐endo . The red arrows point to two small, inverted U‐shaped curve which Hoffmann drew to represent the atoms involved in potential secondary orbital interactions. (C) Structures 4 and 5 are from Hoffmann and Woodward's fourth JACS communication in 1965 (W−H 4). Compare (C) with (A) and (B‐far right). Compare 4 and 5 in (C) with (A) and (B‐far right), keeping track of the blue and red colors for POIs and SOIs, respectively.

Figure 14

Page 124 from Hoffmann's Laboratory Notebook 16, ca. March 5, 1965. The bottom third of this page focuses on SOIs.

Figure 15

Excerpt from NB16/125, ca. March 5, 1965. Hoffmann was examining the literature relevant to the Alder exo‐endo rule for the Diels‐Alder reaction. In this case, there really are no exo‐endo possibilities. Elsewhere in his laboratory notebooks, though not shown here, Hoffmann also recorded similar exo‐endo studies by Kenneth B. Wiberg, Stanley J. Cristol, and N. A. Belikova.[ ⁷⁸ , ⁷⁹ , ⁸⁰ , ⁸¹ ] While the latter was an English translation from Russian, Hoffmann was also reading other publications in the original Russian – which few American or European chemists would be doing. He learned Russian in advance of his year in Moscow during his graduate school years.

Figure 16

Page 133 of Hoffmann's Laboratory Notebook 16, ca. March 10, 1965. (A) (Left) This correlation diagram may refer to the formation of cubane. The correlation diagram suggests a W−H forbidden reaction. (A) (Right) This correlation diagram looks like a [4+2] cycloaddition, a W−H allowed reaction. (B) The interaction graphic refers to secondary orbital interactions for CBD dimerization. (C) In ink and dark font, Hoffmann asked of himself, “Can one think of an example where interaction hinders?” (D) Two graphics involving potential secondary orbital interactions (a return to secondary orbital interactions). At the left is an interaction diagram of a [4+2] cycloaddition. At the right, the MOs are, for the dienophile, the LUMO+1; for the diene, the HOMO‐1.

Figure 17

(A) Page 134 of Hoffmann's Laboratory Notebook 16, ca. March 10, 1965. (Top) Hoffmann compared the [4+2], the [4+4], and the [6+4] cycloadditions. He then proposed a “necessary condition” for these cycloadditions involving a secondary orbital interaction and a test of that rule “should give reversal of addition rule.” In the middle of (A) in dark font, Hoffmann proposed an answer to the question he posed on NB16/133 (Figure 16), namely, “Can one think of an example where interaction hinders?” At the bottom of (A), Hoffmann drew the correlation diagram for the exo and endo [6+4] cycloadditions, revealing that both reactions are allowed and have identical correlation diagrams that resemble [4+2] cycloadditions. The arrows at the bottom left in (A) represent the phases of (left, for I) the diene's LUMO and the triene's HOMO; and (right, for II) the diene's HOMO and the triene's LUMO. Hoffmann's “mixing 3–3’” and “2’‐4” was his attempt to examine secondary orbital interactions. (B) Chemical pictographs taken from Hoffmann and Woodward's 1965 communication in JACS on secondary orbital interactions in the Diels‐Alder reaction (W−H 4). Symbols in blue (POIs) and in red (for SOIs) font were added by Seeman. Compare the phases of the atomic orbitals in I and II as specified by Hoffmann by the direction of the arrows just below structures I and II in (A) with the phases of the orbitals in VII and VIII in (B). Graphics VII and VIII illustrate the Fukui stabilizations in blue and the SOI destabilization in red. VII and VIII are reprinted with permission from R. Hoffmann, R. B. Woodward, J. Am. Chem. Soc. 1965, 87, 4388–4389. Copyright 1965 American Chemical Society.

Figure 18

Page 135 of Hoffmann's Laboratory Notebook 16, ca. March 10, 1965. (A) The correlation diagrams for the boat and chair [4+4] dimerization (cycloaddition) of 1,3‐butadiene. (B) The correlation diagrams for the cycloadditions of 1,5‐cyclooctadiene to a tricyclooctane and 1,5‐cyclooctadiene. (C) The photochemical Diels‐Alder reaction “could be boat or chair” and the correlation diagram for the photochemical [2+2] and [4+2] cycloadditions of two molecules of 1,3‐butadiene. Note Hoffmann's graphic of a resonance hybrid of 1,3‐butadiene reacting with the central bond of 1,3,5‐hexatriene, as found in previous pages of his laboratory notebooks (Figure 12, Figure 13, and Figure 16) and in Woodward and Hoffmann's communication on SOIs and the Diels‐Alder reaction (W−H 4). Hoffmann's use of the term “chair” for the Diels‐Alder reaction suggests that he was influenced in his terminology by his contemporaneous research on the Cope rearrangement (see Section 5). Note the flood of correlation diagrams, three on this page alone!

Figure 19

The exo (“chair like”) and endo (“boat”) reaction‐types for [4+4] or two [2+2] cycloadditions. Both pathways are W−H thermally forbidden when suprafacial‐suprafacial and W−H allowed when suprafacial‐antarafacial. Structure 7 is an enlargement from NB16/135 (Figure 18C) and 7 a more clearly illustrates the SOI in 7. The two red arrows in 7 point to the SOIs drawn in very light font by Hoffmann. The [4+4] cycloaddition product could also be derived from the endo conformation, not shown in the graphic.

Figure 20

Page 6 of Hoffmann's Laboratory Notebook 17, ca. March 20, 1965. Hoffmann considered exo‐endo pathways in the [4+2] cycloaddition with cyclopropene and [4+4] cycloaddition, the dimerization of 1,3‐butadiene. The correlation diagram for the endo [4+4] dimerization of 1,3‐butadiene reveals a W−H forbidden reaction, as found previously (NB16/33 and NB16/135). At the bottom right corner, Hoffmann drew several interaction diagrams for the exo and endo dimerization of 1,3‐butadiene. The direction of each arrow refers to the phase of that particular atomic orbital. The interactions appear to be HOMO‐HOMO interactions going to LUMO‐LUMO interactions.

Figure 21

(A) Excerpt from page 8 of Hoffmann's Laboratory Notebook 17, ca. March 21, 1965. Hoffmann recorded the energies of the π‐MOs and the coefficients of the LUMOs of p‐benzoquinone and maleic anhydride. (B) Excerpt from Hoffmann and Woodward's fourth 1965 communication. A comparison of the relative phases of the coefficients in (A) and (B) shows that they are the same. Note the difference in numbering of the atoms between (A) and (B). (C) The π‐MOs of 1,3,5‐hexatriene serve as a model for the extended π‐MOs of maleic anhydride and p‐benzoquinone. In these model reactions, the central double bond of π‐MOs 1,3,5‐hexatriene acts as the dienophile and the β and β’ atomic orbitals are involved in the SOIs (in red, C(3) and C(5), using the numbering scheme that was used in W H 4).

Figure 22

The MOs shown in the figure are to be compared with those in Figure 21. (A) Three‐dimensional molecular orbitals of the π‐system of maleic anhydride using extended Hückel calculations, from Jorgensen and Salem's 1973 monograph The Organic Chemist's Book of Orbitals. The phases and shapes of these MO are worth studying. The MO identifiers in blue bont were added by Seeman. MO3 and MO5 are the MOs relevant to this discussion. (B) The π‐MOs of p‐benzoquinone, from Houk et al. (1981) using STO‐3G x orbital shapes and energies. Reprinted with permission from: Rozeboom, M. D.; Tegmo‐Larsson, I. M.; Houk, K. N. “Frontier molecular orbital theory of substituent effects on regioselectivities of nucleophilic additions and cycloadditions to benzoquinones and naphthoquinones.” J. Org. Chem. 1981, 46, 2338–2345. Copyright 1981 American Chemical Society.

Figure 23

Excerpt from page 10 of Hoffmann's Laboratory Notebook 17, ca. March 21, 1965. Here, Hoffmann recorded the results of and resultant conclusions from eHT calculations on maleic anhydride in which he modified some of the eHT input parameters to modify the molecule's HOMO and LUMO and thereby provide analogues of maleic anhydride having different chemical properties, especially regarding cycloadditions.

Figure 24

Page 9 of Hoffmann's Laboratory Notebook 17, ca. March 21, 1965. Three topics appear on this page. (Top) A literature citation for a possible [1,3] sigmatropic reaction which Hoffmann was simultaneously studying. (Middle) Two references of a cross‐conjugated polycyclic aromatic compound that might undergo a [1,5] hydrogen sigmatropic shift that appears geometrically‐impossible for a concerted reaction, to form pentacene, a polycyclic aromatic hydrocarbon consisting of five linearly‐fused benzene rings. (Bottom) A citation to a Russian journal on “bond alternations in annulenes and polyacetylenes.” Note that Hoffmann was reading the Russian literature in its original Russian.

Figure 25

(A) Page 11 from Hoffmann's Laboratory Notebook 17, ca. March 27, 1965, examined the [4+4] cycloaddition of two benzene rings to the sandwiched 1,1’,4’4’‐dimer of 1,4‐dihydrobenzene. Note Hoffmann's conclusion at the bottom right of the page where he concluded, based on an analysis of the two drawn interaction diagrams, “no 2° interaction here pushes AA down, AS up.” (B) Hoffmann's analysis 47 years later of a number of benzene dimers, compound 4 in this figure being the structure he considered in (A). He called these “jailbreaking benzene dimers.” Colors as in the original. The isomers marked in red remain to be made as of April 2012. Figure reprinted with permission from: Rogachev, A. Y.; Wen, X.‐D.; Hoffmann, R. Jailbreaking benzene dimers. J. Am. Chem. Soc. 2012, 134, 8062–8065. Copyright 2012 American Chemical Society.

Figure 26

Page 47 from Hoffmann's Laboratory Notebook 17, mid‐April 1965. On this page, Hoffmann recorded his ideas regarding SOIs in photochemical reactions. Note the waves and coefficients at lower right. These come from Hoffmann's knowledge of Hückel theory. He used that knowledge to derive the coefficients of the MOs rather than doing the eHT calculation to get them.

Figure 27

Excerpt from page 147 of Hoffmann's Laboratory Notebook 17, ca. August 13, 1965. Hoffmann examined the exo and endo [4+2] cycloaddition of 1,3‐butadiene with allyl carbocation. By this time, he had been at Cornell for about one month.

Figure 28

William von Eggers Doering (1911‐2011), on his 60^th birthday, Harvard University. Doering was wearing a T‐shirt emblazoned with a compound that had added much glory to his chemical reputation, namely bullvalene. Bullvalene, a ten‐carbon compound, is “the archetypal fluxional molecule which, at sufficiently high enough temperature, through endless Cope rearrangements, achieves a state of total degeneracy whereby there are no permanent carbon–carbon bonds. The number of possible valence tautomers of bullvalene is 10!/3=1,209,600, not counting enantiomers.” Photograph courtesy Lauri Robertson.

Figure 29

Chemical pictography from Doering and Roth's 1962 publication on the mechanisms of the Cope reaction (Scheme 1). They examined the stereochemistry of three stereoisomers of 2,6‐octadiene in order to distinguish between the boat and the chair pathways for the reaction. Reprinted with permission from W. von E. Doering., W. R. Roth, Tetrahedron 1962, 18, 67–74. Copyright 1962 Elsevier.

Figure 30

R. Stephen Berry, 1962. Photograph courtesy R. S. Berry.

Figure 31

(Top) The MOs of allyl radical. (Bottom) Basis set for the complex of two interacting allyl radicals in the chair orientation (13 c‐bs). A similar diagram is obtained for the basis set of the complex of two interacting allyl radicals in the boat orientation.

Figure 32

A graphical exposition of R. Stephen Berry's explanation of the chair preference for the Cope reaction,[ ³⁰ , ³¹ ] in the form of an interaction diagram for the reaction of two allyl radicals approaching each other from infinity as if they were to react and form 1,5‐hexadiene. Columns A−E refer to the boat‐like transit of the Cope reaction; Columns A’‐E’ refer to the chair‐like transit. Columns A and A’ refer to the complex of two allyl radicals at infinite distance, i. e., no interactions between their respective MOs, for the boat and chair orientations of the Cope reaction, respectively. When the allyl radicals are far apart, their respective MOs will have the same energies (i. e., will be degenerate), as shown in Columns B and B’. As the two allyl radicals approach each other (Columns D and D’), the MOs interact in both a bonding and antibonding fashion, that is, when a dark lobe faces another dark lobe (or two white lobes face each other), there is bonding (the in‐phase interaction). Antibonding is one dark lobe facing one white lobe (out‐of‐phase interactions). In a sense, we are adding and subtracting the MOs in Column A (and Column A’) from each other to derive the MOs in Column D (and Column D’). Columns E and E’ show the MO energy levels and symmetries, e. g., SS and SA, of the interacting MOs. The symmetry elements S and A for the boat and the chair mechanisms are shown at the top of the graphic. (To avoid confusion with the use of “C” in other places in this graphic, there is no “Column C” in this figure.) As illustrated, MO(Bt)‐2 is more destabilized relative to MO(Ch)‐2 compared to the stabilization of MO(Bt)‐1 relative to MO(Ch)‐1. (The symbol “‐” in MO(Bt)‐2” should be read as a “dash” and not as a “minus.” “Bt” and “Ch” refer to the boat and chair orientations, respectively.) See the curved red arrow pointing to the antibonding interaction indicated by the three parallel red lines in MO(Bt)‐2. The key observation is, |ΔE₂| > ||ΔE₁|.

Figure 33

The handwritten text in this figure is from page 48 of Hoffmann's Laboratory Notebook 16. Hoffmann recorded the total energies and bond orders and energies of the HOMO, HOMO‐1, LUMO, LUMO+1, and LUMO+2 for the complexes consisting of two allyl radicals in parallel planes with atom‐to‐atom overlap approaching each other from 5.0 Å to 2.0 Å in the boat orientation (left set of numbers) and chair orientation (right set of numbers). The calculations actually modelled eq. 1‐bicyclo and eq. 1‐dirad, to bicyclo[2.2.0]hexane (14) and cyclohexane 1,4‐diyl (15), respectively (Scheme 2). The first five lines of data reported the total energies of the boat and the Mulliken overlap populations,[ ⁶¹ , ¹⁰⁶ ] a measure of bond orders (on the left) and chair complexes from 1.0 to 5.0 Å separations of the two planes containing the two radicals. At 2.0 Å apart, the chair is lower in energy. The next five lines of data represent the energies of five of the complex's MOs, again from 1.0 to 5.0 Å separations of the two planes containing the two radicals. The horizontal line between MO17 and MO18 represents the nonbonding region; below that line are bonding MOs, and above that line are antibonding MOs. The identification of the MOs is shown in the ChemDraw graphics at the bottom‐right of this figure added by Seeman. Hoffmann did not record the energies of the most stable MO of the π‐complex, namely MO20. The arrows for each pair of interacting allyl radicals represent the positive or negative coefficients of the atomic orbitals at each carbon atom, i. e., they provide the phases of each MO, as in Figure 20 and Steve Berry's mechanism shown in Figure 32.

Scheme 2

Hoffmann applied eHT to the formation of 1,5‐hexadiene from two allyl radicals coming together from infinity to distances in which the two allyl radicals interact (Figure 33). From the boat orientation of the two allyl radicals, bicyclo[2.2.0]hexane (14) is the product (eq. 1‐bicyclo). From the chair orientation of the two allyl radicals, cyclohexane 1,4‐diyl (15) is the product (eq. 1‐dirad).

Figure 34

(A and B) Page 49 from Hoffmann's Laboratory Notebook 16. The correlation diagrams on this page were constructed by Hoffmann immediately after he performed eHT calculations on two allyl radicals approaching each other from infinity in both the boat and chair orientations (NB16/33, Figure 33). (A) At the top, Hoffmann drew the transformation of two allyl radicals approaching each other via the boat orientation to bicyclo[2.2.0]hexane (14, eq. 1‐bicyclo). Below the reaction is its correlation diagram. (B) The correlation diagram is the transformation of two allyl radicals approaching each other via the chair orientation to cyclohexane 1,4‐diyl (15, eq. 1‐dirad). Hoffmann drew the structure of 15 just to the right of its correlation diagram. That he used a ruler to draw the correlation lines in (A) and (B) is a sign of the importance that Hoffmann attached to these correlation diagrams.

Figure 35

Page 50 from Hoffmann's Laboratory Notebook 16. (A) This correlation diagram represents half of the Cope reaction, namely from two allyl radicals at infinite distance approaching each other in the boat orientation to 1,5‐hexadiene (1). (B) This correlation diagram represents the other portion of the Cope reaction, namely from two allyl radicals at infinite distance approaching each other in the chair orientation to 1,5‐hexadiene. These two correlation diagrams are identical. It is noteworthy that Hoffmann drew both of them, as he surely could anticipate the second when developing the first. See Scheme 3.

Scheme 3

Hoffmann applied eHT to the formation of 1,5‐hexadiene from two allyl radicals coming together from infinity to distances in which the two allyl radicals interact and the Cope product is formed. See Figure 35.

Figure 36

This graphic illustrates Hoffmann's eHT calculations that begin with the two allyl radicals at infinite distance apart (Figure 33). As the two allyl radicals get within bonding distance, they intersect on a complex, multidimensional PES of the Cope reaction. Combining Scheme 1, Scheme 2, and Scheme 3 will result in Scheme 4, discussed below.

Figure 37

(A) The correlation diagram for the Cope reaction of 1,5‐hexadiene (eq. 1‐bicyclo, Scheme 3), obtained by stitching together the boat correlation diagram in Figure 35A with its mirror image. An equivalent correlation diagram would have been obtained by stitching together the chair correlation diagram (Figure 35B) with its mirror image. (B) Page 51 from Hoffmann's Laboratory Notebook 16. (Top left) Hoffmann drew what he thought was the correlation diagram for the Cope reaction (eq. 1). However, the ordering of the MOs in the region of the TS is incorrect, as shown in (A) and (C). There are two MO energy level crossings in the correct correlation diagram. At the bottom right in (B), Hoffmann drew the various reactions involved in the extended Cope reaction (drawn in Scheme 3). (C) The correlation diagram of the Cope reaction through the boat transition state reproduced from Hoffmann and Woodward's 1965 communication on SOIs (W−H 5). The symmetry element is the mirror plane in the boat‐like TS. Reprinted with permission from R. Hoffmann, R. B. Woodward, J. Am. Chem. Soc. 1965, 87, 4389–4390. Copyright 1965 American Chemical Society.

Figure 38

Illustrations that, in the interaction of two MOs, the out‐of‐phase MO is always of higher energy, i. e., more destabilized, than the in‐phase MO is stabilized, relative to the interacting species. (A) Two hydrogen radicals forming dihydrogen. (B and C) The MO energy levels for two interacting allyl radicals in the boat orientation. Whether they approach each other in the boat, as shown, or chair orientation, the symmetries of the boat and the chair orientations are the same in each MO, and the out‐of‐phase combination is of higher energy than the in‐phase combination.

Scheme 4

The extended Cope reaction shown here expands Scheme 1 to include the vertical transits eq. 1‐bicyclo and eq. 1‐dirad into the horizon transit, that being the standard Cope reaction. Implied in this scheme is a second source of 13 b‐TS and 13 c‐TS, that being from two interacting allyl radicals coming together from infinity (Figure 36). Note that TSs 13 b‐TS and 13 c‐TS are shown to interconvert, a characteristic not explicated by Doering and Roth in their publications[ ³⁰ , ³¹ ] nor stated in Woodward and Hoffmann's publication on this model of the Cope reaction. Still, the interconversion 13 b‐TS $\stackrel{\rightharpoonup }{\leftharpoondown }$ 13 c‐TS is implied in Figure 2 in Woodward and Hoffmann's fifth JACS communication of 1965 on SOIs and the Cope reaction, as illustrated in this scheme. Somewhat parenthetical and for completeness, 15 could also be formed via 13 b‐TS. This additional route to 15 is not discussed by Woodward and Hoffmann[ ⁵ , ³⁶ , ³⁷ ] (nor in Hoffmann's laboratory notebooks), and thus will not be discussed further – without any loss to the integrity of Hoffmann's mechanistic explorations and explanation.) In the vertical transit, the distance 1—1‘ = 3—3‘, and both decrease to 14 and 15. In the horizontal transit, left to right, 1—1‘ < 3—3‘ changing to 1—1‘ > 3—3‘. As discussed above, Hoffmann first studied the vertical transit (Figure 34), the the horizontal transit (Figure 35), and ultimately used both as in this scheme (and in Figure 39B).

Figure 39

(A) Seeman prepared this graphic by stitching together (on the left) the mirror image of the boat correlation diagram of 13 b →14 (eq. 1‐bicyclo) (mirror image of Figure 34A) with (on the right) the chair correlation diagram of 13 c →15 (eq. 1‐dirad) (Figure 34B). (B) Figure 2 from W−H 5. Woodward and Hoffmann's composite correlation diagram for the vertical transit of the Cope scheme in Scheme 4. From left to right, 15 ← 13 c 13 b →14. Reprinted with permission from R. Hoffmann, R. B. Woodward, J. Am. Chem. Soc. 1965, 87, 2046–2048. Copyright 1965 American Chemical Society. (C) A blow‐up of the central portion of (B). The red and blue coloring was added by Seeman for emphasis. Note than in these correlation diagrams, in the chair mechanism, no filled MO crosses an untilled MO – as is found in the boat mechanism. These are indicators of W‐H allowed and W‐H forbidden reactions, respectively.

Figure 40

Page 80 of Hoffmann's Laboratory Notebook 16, ca. February 21, 1965. On this page, Hoffmann recorded the eHT calculations of two allyl radicals approaching each other in non‐parallel planes to better model the real Cope reaction compared to the eHT calculations in Figure 33. This non‐parallel approach is denoted by the distances “a” and “b” (written only once) that head the six columns in the two tables. For a graph of these results, see Figure 41.

Figure 41

Page 81 of Hoffmann's Laboratory Notebook 16, ca. February 21, 1965. On this page, Hoffmann plotted the results of his eHT calculations of two allyl radicals approaching each other in non‐parallel planes (from Figure 40). The boat orientation is on the left, and the chair orientation is on the right. The vertical line at 3.0 Å represents the distance of minimal interaction between the two allyl radicals, i. e., at infinite distance apart. The lines represent the energies of the six π‐MOs. This double correlation diagram is analogous to the double correlation diagrams in Figure 39.

Figure 42

Hoffmann's handwritten letter to Woodward dated June 28, 1965, updating him on his status at his new arrived position at Cornell University and hoping to motivate Woodward to respond to a draft manuscript he had recently provided him.

Figure 43

(A) First page of Hoffmann's and Woodward's draft that would later become their fourth and fifth JACS communications. Hoffmann provided the typewritten document, and Woodward added the handwritten modifications. The references at the bottom of this page have “0000” typed for the page numbers of the second and third JACS W−H communications and “0000” typed for the page numbers of Longuet‐Higgins and Abrahamson's 1965 JACS communication. Actual pages numbers were added by Woodward. At this stage of development, the draft embodies what would soon become the fourth and fiftth W‐H communication of 1965. (B) First paragraph of Hoffmann and Woodward's fourth JACS communication of 1965. Note that the text is nearly identical to the first paragraph of Hoffmann's draft with Woodward's modifications except for the last few words.

Figure 44

(A and B) Page 3 from Hoffmann's and Woodward's first draft of what became the fourth and fifth W−H communications in 1965. (A) Structures IIa and IIb illustrate SOIs in the Diels‐Alder reaction and served as the basis for chemical pictography that appeared in W−H 4 (compare with 4 and 5 in Figure 13C). (B) The equations represent the LUMOs for maleic anhydride and p‐benzoquinone reproduced from Hoffmann's eHT calculations in his laboratory notebook (Figure 21A) and in W−H 4 (Figure 21B).

Figure 45

Woodward's handwritten chemical pictographs of SOIs in the Diels‐Alder reaction. At the top is his correlation diagram with some qualitative perturbation theory included for the [4+2] cycloaddition of 1,3‐butadiene with one of the double bonds acting as a dienophile in another 1,3‐butadiene. Below that are several interaction diagrams for the Diels‐Alder reaction of 1,3‐butadiene showing SOI's for (top) the HOMO of the dienophile I and the LUMO of the diene II as in the eventually published structure 5 in Figure 9; and (below) the LUMO of the dienophile I and the HOMO of the diene II, as in the also published 4 in Figure 8 (also reproduced in Figure 13C). Some of the p‐orbitals – those at the bottom left in structure II are misshapen. Woodward's p‐orbitals are always rather elegantly drawn. Hoffmann commented, “They look like they might have been drawn by me. I'm not sure. Could this page be the result of one of my trips to Cambridge?”

Figure 46

Page 6 of the double‐draft has some of Woodward's and some of Hoffmann's handwriting. The heading is in Woodward's handwriting, “2. The Cope rearrangement.” Woodward drew the chair‐like VIII and boat‐like IX transition states for 1,5‐hexadiene along with the correlation diagram for the identity reaction shown by VII. This correlation diagram is identical with that in Hoffmann and Woodward's fifth JACS communication reproduced in Figure 37C.

Figure 47

(A and B) Excerpts from Woodward's first handwritten draft of the fourth W−H 1965 communication that appeared in the JACS publication. (A) Woodward's new title and introductory paragraph. (B) Woodward's hand drawn chemical pictograph of the SOIs in the Diels‐Alder reaction (see Figure 45 for Woodward's earlier scribblings of these interaction diagrams). (C) Graphics from W−H 4 which reproduces the graphics at the bottom of (B). Hoffmann had previously put his name first in the double‐draft (Figure 43A).

Figure 48

Page 8 from Woodward's first draft of the fourth W−H 1965 communication of 1965. Note the heavily edited text. Note also that Woodward listed Hoffmann's name first, in the position of the senior author according to the norms of chemistry in the 1960s and as Hoffmann had so chosen in his first double‐draft (Figure 43]A.

Figure 49

(A) Excerpt from Woodward's draft of the fifth W−H 1965 communication. (B) Excerpt from Hoffmann and Woodward's fifth 1965 communication. (C) Page 4 from Hoffmann's seven page draft that was written and served as an early draft for the third W‐H JACS communication of 1965 on the mechanism of sigmatropic reactions. This page reveals that Hoffmann included a discussion of the chair versus boat Cope reaction puzzle that was not included in W‐H 3 but served as the theme in the fifth W‐H JACS communication of 1965. The blown‐up portion of this figure more clearly shows the electron occupancy of the first three MOs in the regions of the TSs.

Figure 50

Page 1 of Woodward's two‐page letter to Hoffmann dated August 4, 1965. in which Woodward informs Hoffmann that he split Hoffmann's draft manuscript into two and that he added citations and acknowledgments to Kenichi Fukui. Those proposed footnotes were published in W−H 5. Woodward's statement, “we may be ready to present detailed and extensive papers of some considerable scope,“ indicates his anticipation of more than one future major exposition. This page reveals that Hoffmann included a discussion of the chair versus boat Cope reaction puzzle that was not included in W‐H 3 but served as the theme in the fifth W‐H JACS communication of 1965. The blown‐up portion of this figure more clearly shows the electron occupancy of the first three MOs in the regions of the TSs.

Figure 51

Undated note from Hoffmann to Woodward, ca. February 8, 1965. The trimerization selection rule appears at the top of this note appears exactly as drawn herein on NB16/53, not reproduced herein. This is two pages after Hoffmann completed his four‐page study on the boat versus chair mechanism of the Cope reaction, i. e., on NB16/48‐51 (see Section 5.6 and Section 5.7).

Figure 52

Page 2 of Woodward's second draft of what became the fourth 1965 W−H communication on the exo‐endo Alder rule in the Diels‐Alder reaction. The first citation by Woodward and Hoffmann to Kenichi Fukui's FMO theory's contribution to orbital symmetry control[ ⁵⁸ , ¹⁸³ ] appears as an insert on the bottom of this page. This citation brought Fukui's FMO accomplishments to the attention of a broad community just becoming aware of the power of MO theory. The handwriting is that of Dodie Dyer, Woodward's secretary (as administrative assistants were then called), as directed to do so by Woodward.

Figure 53

Kenichi Fukui (left) and Roald Hoffmann, August 18, 1988. Photograph courtesy R. Hoffmann.

Figure 54

Hoffmann's cover note to his good friend Jean‐Marie Lehn together with copies of the two just submitted manuscripts.

Scheme 5

The orbital graphic is an excerpt from Seeman's eplanation of Berry's pre‐Woodward‐Hoffmann exposition of SOIs provided in Figure 32 shown in a comparison of the SOI in the HOMO‐1 in the boat TS and in the lack of a SOI in the HOMO‐1 in the chair TS. The POIs are shown in both graphics. The SOI appears in red font and the POIs in black font. Note that the destabilizing POIs are identical in both MO(Bt)‐2 and MO(Ch)‐2, and the SOI is present only in MO(Bt)‐2 and is destabilizing. TheC(2) ‐ ‐ ‐ C(2‘) orbital interaction in MO(Bt)‐2 is a SOI in the sense that these carbon atoms maintain their role as the center atom of an allylic system. This comparison explains the preference for the chair orientation of the Cope reaction in 1,5‐hexadiene which is based on the system having the least negative interactions.