Orbital Symmetry Control of Chemical Reactions Author(S): Roald Hoffmann and R

Orbital Symmetry Control of Chemical Reactions Author(s): Roald Hoffmann and R. B. Woodward Source: Science, New Series, Vol. 167, No. 3919, (Feb. 6, 1970), pp. 825-831 Published by: American Association for the Advancement of Science Stable URL: http://www.jstor.org/stable/1728401 Accessed: 15/07/2008 11:54

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http://www.jstor.org 6 February 1970, Volume 167, Number 3919 SCIENCOE

nents may undergo some extremely complicated motions in order to provide low-energy electronic paths.

Orbital Symmetry Control of General Theoretical Development Chemical Reactions The question of concertedness arises whenever more than one bond is broken or formed in the course of a chemical The tendency to maintain bonding governs the complex reaction. For each of the three cases motions of molecules in the course of reaction. illustratedbelow a concerted pathway is contrasted with one proceeding through diradical intermediates. Roald Hoffmann and R. B. Woodward

Molecules are complicated three-di- and of thinking of its transformations mensional assemblages of nuclei and exclusively in terms of the mechanical electrons, in which the atomic sub- billiard-ball experiences of the exterior structure is to a great degree preserved. world. That is, in spite of what was It is three-dimensionalawareness of the known about molecules rotating and structure of molecules which most dis- vibrating and about the spatial delocal- tinguishes modern chemists from their ization of electrons, all these motions predecessors of 50 years ago. The being controlledby quantum mechanics, phenomenal advances in x-ray crystal- chemists returned to the mental equiv- Re lography, electron diffraction, micro- alent of a ball-and-stick model in wave and magnetic resonance spectro- analyzing chemical transformations. scopy and other methods of structure Thus in the construction of potential the determination, general availability energy surfaces for chemical reactions RA R of molecular models, the willingness of one easily fell into the habit of assum- publishersand editors to set in type two- ing least motion of nuclei along the hIR2. dimensional representations of three- reaction path. Presumably the electrons dimensional structures-all of these would readjust to the bulk nuclear factors have created a revolution in our motions. The nonconcerted reaction leads from image of what molecules really look In the last few years, with the aid reactants R to products P through an like and what we can conceive of them of some qualitative 'but extremely pow- intermediate molecule or set of mole- doing or not doing in the course of a erful quantum mechanical arguments, cules, usually comparatively unstable, chemical- reaction. The perfection of it has become clear that the primary with a net diradical structure which we the to think ability in three dimensions factor which determines the reaction will call D. We can follow the energy has, however, had one deleterious con- path of any chemical reaction is the levels of all components through this sequence. necessity of maintaining maximum nonconcerted reaction. The reactants As the molecule as a three-dimen- bonding throughout the reaction (1). R as well as the products P are normal sional graph became more easily visu- We have in effect a least-motion prin- ground-state singlet molecules, with a alized in the minds of researchers,there ciple for electrons and not for nuclei. sizable energy gap separating a band came the inevitable side effect of at- Some remarkably specific chemical re- of doubly occupied molecular orbitals to the tributing model too much rigidity actions have been explained, and some from a band of antibonding unoccupied striking verifiable predictions have been orbitals. The diradical intermediate D Dr- Hoffmann is professor of chemistry at made and confirmed. It is now clear is characterized by one less bonding Cornell University, Ithaca, New York; Dr. Wood- that in ward is professor of chemistry at Harvard Uni- the course of a chemical reac- orbital and one less antibonding orbital versity, Cambridge, Massachusetts. tion the nuclei of the reaction compo- than R or P. Instead, D possesses two 6 FEBRUARY 1970 825 ---The significantfeature of the concerted must be formed. Application of the reaction is then that in the course of procedures of group theory (4) yields reaction, and in particular at its ener- such combinations automatically, and getic high point, the transition state, all in most cases the simple process of levels derived from bonding levels of forming all possible independent sums reactants remain bonding and all anti- and differencesof the component orbi- 3 / bonding levels remain antibonding. tals will suffice. Thus the isolated C To distinguish the two situations we bonding orbitals of the cyclobutane a, have utilized a variety of qualitativebut and Or2 Fig. 1. The high-symmetryapp )roach of powerful molecular orbital arguments: two ethylene molecules. Thre(e mirror simple scrutiny of the bonding prop- I planes of symmetryare shown. erties of the decisive highest occupied molecular orbital, the construction of -4- correlation diagrams, and the examina- approximatelynonbonding orbitals (see tion of interaction diagrams for the 2). transition state (1). The same results cr, As the reaction progresses from R could be achieved with detailed calcu- through D to P, the individual energy lations of the potential surfaces for levels move approximately as follows: these reactions. However, the simple while not being either symmetric or qualitative arguments are based on the antisymmetricwith respect to reflection most fundamental properties of mole- in plane 2,. may be combined into the ontibonding cules, such as bonding, overlap, symme- symmetry-adapted ol + C2 and , -(.- try, and nodal properties. If correctly formulated, such arguments, although 1 i E i qualitative, are much stronger than any approximatenumerical calculation and bonding in fact provide a gauge by which any future theoretical treatment must be R D P measured. o- +-c2; SS a1- 2o; AS It is obvious that in the absence of circumstances which stabilizestabil The o* orbitals of and the special The 2 + 2 Cycloaddition cyclobutane the diradical intermediateor d4estabilize 7. and 7r*orbitals of the ethylene molecule are combined the reactants or products, or b oth, this Let us first examine the dimerization analogously (5). The level correlation of Fig. will be a high-energyprocess. 'the high of to or the re- diagram r ethylene cyclobutane, 2 then be constructed connect- activation energy is created by the de- verse reaction: may by stabilization of a bonding orbiital of P ing to each other levels of the same carrying two electrons to a 1relatively symmetry. The most obvious and strik- Hx /H' high-energy nonbonding positi on in D. = C H H ing feature of this diagram is the cor- H It will normally be the highest ioccupied H/ \H H~C-C' relation of a bonding reactant level + with an level and molecular orbital of P, its weakest H H.-" I I antibonding product bond, which will become noribonding the correlation of an antibonding re- H^^~HH in the nonconcerted process. H/ i actant level with a bonding product In our work we realized that the level. This correlation results in two distinguishing characteristic off a con- The least-motion approach is highly high-energy nonbonding orbitals in the certed, low-activation energy process symmetric (Fig. 1). This approach is transition state for the reaction, a is that in the course of the realction the characterizedby D21h symmetry, and it situation plainly analogous to our gen- levels move not as illustratecI above, is a simple matter to construct a level eral considerations for a nonconcerted but rather in such a way as to avoid correlation diagram (3) relating the process. the high-energy diradical situation. If orbitals of the reactants, two ethylene The matter may be further illumi- there is a direct pathway leadiing from molecules, to the product, cyclobutane. nated by inspection of the correspond- R to P in which all new b(onds are Of the several symmetryelements maining state diagram (6) for the reaction formed in a tightly time-corre-lated, if tained in the approachgeometry, it will (Fig. 3). The ground-state electron not synchronous, manner, then the suffice to classify levels with respect to configurationof two ethylene molecules energy levels will be transformed as their being symmetric (S) or antisym- correlates with a very high-energy, follows: metric (A) under reflection in the mir- doubly excited state of a cyclobutane ror planes 1 and 2. The semilocalized r molecule; conversely, the ground state - - -- levels of the individual mole- of correlateswith a doubly --- I C- I--- ethylene cyclobutane - ----^- cules or the a bonds of the excited state of two ethylene molecules. -- -- cyclobutane - ?L molecule are not proper molecular Electron interaction will prevent the orbitals of the complex. In order that resulting crossing (7) and force a cor- the orbitals satisfy the property of be- relation of ground state with ground But the actual -- ing symmetric or antisymmetric with state. in physical situa- - I- 1 L respect to every symmetry operation' tion, the reaction still must pay the --?---- -i, --r ------LI under which the molecule is invariant, price in activation energy for the in- proper symmetry-adaptedcombinations tended but avoided crossing. An order- 826 SCIENCE, VOL. 167 of-magnitude estimate of the symmetry- imposed energy barrier to the concerted face-to-face combination of two ethylene molecules may be made by consid-

ering the energy required to raise two H H- rAS bonding electrons in the occupied bonding level to the nonbonding level -perhaps 5 electron volts or about 115 kilocalorie/mole. No symmetry- imposed barrier intervenes in the excited-state complex of two ethylene molecules. The dimerization of two ethylene molecules in the least-motion transition state is clearly a ground state forbidden and excited state allowed r SS process. There exists, however, a reaction SSa pathway by which two ethylene molecules may form cyclobutane while pre- 2. serving the bonding character of all oc- Fig. Level correlation diagram for the high-symmetry dimerization of ethylene. Only those levels which are affected the that the cupied energy levels. It occurs through significantly by reaction, is, ethylene vr and 7r* levels, and the newly formed ro and cr* levels of the are a nonleast-motion in which ad- cyclobutane, process included. The dashed horizontal line is an approximate nonbonding energy. Planes 1 dition to one ethylene is on the same and 2 of Fig. 1 are used for classifying the symmetry properties of the levels. side or suprafacial, whereas on the other ethylene the addition occurs on opposite sides, which we term an antarafacial pathway is encumbered by the much same difficulties, however, into positive process. The choice between cis, syn, less favorable steric environment of the advantages by providing molecules in or suprafacial and trans, anti or an- inner hydrogens of the 2a component, which the offending hydrogens are re- tarafacial modes of addition to a double and by the double bond torsion which moved or in which the requisite torsion bond has long been a legitimate primary must accompany bond formation. These is built in. It is only for such species concern of physical organic chemists obvious difficulties prevent the ethylene that the 28 + 2a reaction has so far studying additions of species such as dimerization or its reversion from being been experimentally observed. Each of hydrogen halides to olefins (8). The two facile processes. One can transform the the four cases shown below is com- addition modes

Configuration State State Configuration .supr (level occupation) symmetry symmetry (level occupation) supra ontora

are operationally distinguishable when SS (SS)2(SA)2 the substrate is either a cyclic olefin or (SS)2AS)2 SS an ethylene sufficiently labeled to exhibit geometrical isomerism. A priori we may ask the mode of addition for each component in the reaction. We use a notation in which >:-- AA (SS).(AS)AAA) the modes suprafacial or an- (SS)(SA)2(AA) AA _ _ _ _ _ SA (SS (AS)(SA)t dynamic )1I (SS)t(SA)'(As AS \-- SA (SS2(AS) tarafacial are the use of (SS) (SA)1 (AA)t designated by (AA)t AS _L~ AbA (SS)2(AS) (SA)t subscript letters s or a shown after the (SS)2(SAt (AS)t AA number of electrons involved in each cycloaddition component. Thus the ethylene dimerization which we have shown to be thermally forbidden is 2, - 28, and the allowed process now being described is 2, + 2a. The two pathways are operationally distinguish- (SS)2(SA)2 SS able through their products if the reactants are labeled to exhibit geometrical SS (SS)AAS)2 isomerism (see Fig. 4). The electronic Fig. 3. State correlation diagram for the dimerization of ethylene. The allowedness of the + symmetry 2s 2a cycloaddi- of the states is obtained by multiplying the symmetry labels for each electron, according tion may be revealed by the correlation to the rules (3, 4) diagram for the process, if we use the S X S--S S--A X A twofold rotation axis which is preserved. SXA- A-- A x S with the least-motion By comparison Only singlet excited states are shown, and at this level of sophistication they should 2, + 2s transition state, the 2s + 2, be regarded as degenerate at either extreme of the diagram. 6 FEBRUARY 1970 827 pletely stereospecific.In each case other The conrotatory motions provide posi- The result may be understood in quali- stereochemical outcomes were a priori tive overlap, and thus bonding and at- tative terms when it is realized that as possible and would in fact have been traction. The disrotatorymotions force the bond between C-2 and C-3 is brok- consistent with nonconcerted processes. a plus lobe of one terminus on the en by disrotatoryoutward rotation (see minus lobe of the other. This is a de- III), the electron density stabilizing, repulsive interaction which R creates the nonbonding situation characteristic of a nonconcerted process. Note the essential mechanical / R R quantum nature of the argument in its reliance on the relative of the wave func- , nr R phase I tion. of that which was more The same stereochemical bond, originally CH3 H question or less in the of the -- plane cyclopropane - that arises in the CH H3 1 ' t < Ref.10. butadiene-cyclobutene shifts above the It is then -^ interconversion be asked of other ring, plane. may available for backside of H valence isomerizations. The is displacement analysis the other the CH leaving group-in words, cH,H .. H H just as simple, and our predictionshave CH " .cH reaction is a normal nucleophilic sub- :- been confirmed in case studied. ,,? CH$ H35 every stitution of the X H displacement group by the electrons of the backbone (r A hvireference Ref.11 bond of the cyclopropane ring. dis con 15 Several corollaries of these conclusions follow. If R is some bulky group (CHR,6 0-0 as in compounds I or II, then we d+l . d,I should expect for steric reasons a faster con dis 16 solvolysisfor compoundII. On the other H lc. 12 H^^ Ref. 0--f hand, when cis positions are linked by (7+7) 26 /(CR)e a short methylene chain we should dd -- 1t+X _ meso dis con 17 expect the opening of a compound ((CR)6 such as structure IV with the leaving group anti to the ring to be severely The first reaction in the above scheme con dis 18 disfavored, since the resulting rotation is the well-known electrocyclic inter- would lead to a trans-transallyl cation conversion of a butadiene and a cyclo- in a small ring. We should expect a butene. The ring closure could have con dis 19 facile opening only for a syn leaving been imagined to proceed in either a -=e group, as in structure V. conrotatory or disrotatory sense (1) A most interesting subsidiary question in connection with the electrocyclic Disrotafory A of a cation to an opening cyclopropyl x allyl cation was first posed to us by 1 C. H. De Puy: If we assume that the x f f 3xs departure of a leaving group from a These have been found Conrototory A ring, and the bond-break- predictions cyclopropane to be reliable For ing electrocyclic reaction to give an allyl (17). example, whereas VI solvo- cation, are concerted, could there be a compound undergoes D"-- A ^-^J at its VII difference between the two a priori lysis readily 125?C, epimer possible disrotatory modes, defined in Cl H or in some nonconcerted combination relation to the position of the leaving H CI of both. In a specific case an average group? Extended Hiickel calculations molecule carries out at least 106, and (20) provided the initial answer, which probably several orders of magnitude may be summarized by saying that the • more, faultlessly conrotatory motions substituents on the same side of the before a disrotatory mistake is made three-membered rings as the leaving is recovered unchanged after prolonged (13). group rotate toward one another, treatment with acid at 210?C [see ref- The original simple argument we whereas those on the other side rotate erences in (17, 21)]. In the electrocyclic used for deciding that the conrotatory apart. reactions of cyclopropyl cations, one motion is preferred remains pertinent thus finds straightforwardexamples of (1). Consider the effect of the two mo- the subservience of steric control to R-... tions on the highest occupied molecular primary electronic effects. orbital of butadiene (14). I Disrototory Conrototory Sigmatropic Shifts R R ..- _ Jr 4- ir Consider another concerted i possible I process, a degenerate 1,3 shift of a

828 SCIENCE, VOL. 167 2s+2s 2s +2a supra L retention A B D N I x Z Y /;ig --4 supra C E X , inversion . x A C A B D

E A B B / antara y y I retention r X -c X Z

antara A B X\x' x Y Y inversion C D Fig. 4 (left). Approach geometrics for 2s - 28 and 2, + 2a cycloadditions. The ethylenes are labeled originally with cis <^0 \x substituents X and Y. The middle illustration shows an approximate view of the reactants as they would appear if viewed along the arrow direction shown in the top part. The bottom sections show the stereochemical consequences of the cycloaddition. Fig. 5 (right). Four possible st4ereochemical outcomes of a 1,3 sigmatropic shift. Carbon atom C can migrate to the top (suprafacial) or bottom (antarafacial) of C-1 and in the process may undergo retention or inversion. The four possibilities give rise to distinct products. group R in a propylene. The topologi- of all orbitals for the stereochemical al- tion states where nuclear least-motion cal questions which may be operation- ternatives predicts that the allowed is most likely to be misleading. ally asked of this process are whether processes are a suprafacial shift with 1) The square transition state for the the shift is suprafacial (to the top of inversion and an antarafacial shift hydrogen exchange reaction, C-l) or antarafacial (to the bottom of with retention (1). The steric con- H C-I) and whether it occurs with reten- straints on these transition states are H H tion or inversion at the migrating group formidable, and yet a clear example of HH---H--H H H R. The four possibilities are illustrated the first process has been realized in in 5. the work of Berson (24). Fig. long accepted as the only reasonable The least-motion transition state is transition state for this very simple the one in which the clearly migra- reaction, should lie at a very high tion is with retention. Let suprafacial energy (26). This has been recently us examine whether this is H- process supported by the most accurate cal- allowed. Since elements are H / H symmetry culations on this potential energy sur- absent in reactants or we products, face (27). Similarly the vicinal 1,2 elimi- cannot construct an informative corre- nation of a hydrogen molecule is not a lation for the reaction. We diagram can, symmetry-allowed process, whereas however, utilize the symmetry of the QAc transition state to construct an inter- H H 8 D H /H \/ action diagram (22). In the transition -CHC C H state we may describe the as a I -*- k + I system C H three-center bond (23) involving the Other Reaction Paths /\ v\H terminal carbons and the or orbital of Controlled by Orbital Symmetry V the and the radical H migrating group, AC/C\H '~C~c" 1 2p orbital left behind. The interaction We have so far explored several ---- I H of these two systems is shown in alternate theoretical for /C^C/ Fig. approaches I 6. evaluating for any chemical reaction A The nonbonding orbital of the three- the extent of bonding in the transition center bond does not possess the cor- state. Still other theoretical analyses are the corresponding 1,4 elimination rect symmetry to interact with the re- feasible (25). In the vast majority of should be. Some experimental evidence maining p orbital. There arises a non- cases simple arguments suffice, and de- exists to support these conclusions (28). bonding situation in the transition state tailed computations are not required. It might be remarked here that characteristic of a forbidden reaction. We will now mention briefly some fur- our preference for a detailed analysis Construction of similar interaction dia- ther examples of the type of conclusion of reasonably complicated (in terms of grams or the detailed following through we are able to draw, focusing on transi- atoms) reactions, such as 1,3 migrations 6 FEBRUARY 1970 829 or 2 + 2 cycloadditions, is not an irra- culations favor an approach with the tion of the orbitals or the construction tional choice nor one devoid of con- two reactants in perpendicular planes, of a correlation diagram reveal im- clusions of value to those studying with a lone pair of one molecule im- mediately that this "linear" departure much smaller systems. A balanced pinging initially on an unoccupied non- or attack is a forbidden reaction. The evaluation of the tools available to the bonding or low-lying antibonding 7r symmetry-allowed pathway is a "non- chemical kineticist indicates that, with orbital of the other (31), as shown be- linear" departure (see also Fig. 7) in the current ease of isotopic labeling and low for the methylene case. which the plane containing the depart- some courage in synthesis, more infor- ing group shifts from being perpendic- mation can be experimentally obtained ular to the ethylene plane to being concerning the potential surfaces for parallel. The reaction coordinate is best the reactions of medium-sized mole- described then not as a pure stretching cules (5 to 20 atoms) than for their motion but as a combination of stretch- smaller counterparts. ing with bending or wagging (38). The 2) Methylenes dimerize with very establishment of a nonleast-motion little activation energy (29), and nitroso transition state which leaves no stereo- compounds do so only slightly less chemical traces poses to the experi- reluctantly (30). Eventually bending occurs, leading to mentalist a most fascinating challenge. the planar product. H H H H 3) Three-membered rings are known \ / \ C: :C C to readily expel small stable or unstable Summary / \ H H H H fragments. One should not conclude from our R R R R \ / work that least-motion transition states N: :N - N=N // \\ are unattainable. They should in fact 0 0 0o X(YZ...)- + X(YZ...) be observed more often than the nonleast-motion ones. Thus orbital-sym- The simplest approach of two planar metry control favors the 4, + 2, cyclo- molecules to form a planar product The expelled be carbon addition, which is the normal Diels- would appear to be one with both fragments may monoxide (32), (33), sulfur Alder reaction; it makes allowed the molecules in the same plane, as implied nitrogen dioxide (34), nitrous oxide (35), and the 1,5 suprafacial shift with retention, by the above structures. A correlation like. The reverse of one and it provides for a linear departure diagram readily shows that this path- microscopic such process is observed in the well- of carbon monoxide, accompanied by way is a high-energy one. Detailed cal- known addition of singlet methylene disrotation, from a cyclopentenone. The (36) or of sulfur atoms (37) to ethylene. symmetry-allowed nonleast-motion path- These processes are often stereospecific, ways are almost by definition discrimi- and many are suspected of being con- nated against by steric factors-they certed. The least-motion process is il- will thus often not manage to be com- 3-center bond lustrated in Fig. 7. Detailed examina- petitive with nonconcerted processes.

X p

'4 IT . . . 1 .**Y...... ----~1 ~

AS ...m- . .. S...

S 3-center p bond Fig. 6. The top of the figure shows the three-center bond and the remaining p orbital. The propylene system is viewed 180? from the position in Fig. 5. At bottom the orbitals are classified with respect to their symmetry properties on Fig. 7. Linear (top) and nonlinear (bottom) modes of departure of a small molecule reflection in the vertical mirror plane. XYZ from a cyclic species. The ring formed by the carbon atoms and X lines in The allyl orbitals alternate in symmetry the xz plane, and X departs approximately along the z-axis. In the linear process (14), and the lone p orbital lies in the Y and Z remain in the yz plane as they depart. In the nonlinear process they move mirror plane and thus must be symmetric. up (or down) until they ultimately assume position in a plane parallel to the xy plane. 830 SCIENCE, VOL. 167 The point of our work is not that least- A. Kettle, J. M. Tedder [Valence Theory Electrons and Chemical Bonding (Benjamin, motion are to be (Wiley, New York, 1965)]. New York, 1965); C. J. Ballhausen and H. B. processes ignored. 7. The noncrossing rule, which is discussed in Gray, Molecular Orbital Theory (Benjamin, Rather, we urge a refocusing on the the texts of references 3 and 6, does have New York, 1964). Further examples of ap- limitations: G. Herzberg and H. C. Longuet- plications may be found in our work quoted primary quantum mechanical electronic Higgins, Discuss. Faraday Soc. 35, 77 (1963). in reference 2. nature of all chemical reactions. The 8. C. K. Ingold, Structure and Mechanism in 23. W. N. Lipscomb, Jr., Boron Hydrides (Ben- Organic Chemistry (Cornell Univ. Press, jamin, New York, 1963). preservation of the bonding character Ithaca, 1953), chap. XII; W. H. Saunders, 24. J. A. Berson and G. L. Nelson, J. Amer. of all electrons in a reaction is the Jr., Ionic Aliphatic Reactions (Prentice-Hall, Chem. Soc. 89, 5303 (1967); J. A. Berson, Englewood Cliffs, N.J., 1965). Accounts Chem. Res. 1, 152 (1968). primaryfeature of any chemical change. 9. E. Vogel, Ann. Chem. 615, 14 (1958); R. 25. K. Fukui, Tetrahedron Lett. 1965, 2009, 2427 This tendency to maintain bonding will Criegee and K. Noll, ibid. 627, 1 (1959); R. (1965); Bull. Chem. Soc. Jap. 39, 498 (1966); Criegee, D. Seebach, R. E. Winter, B. - and H. Fujimoto, Tetrahedron Lett. direct nuclear motions which may or Borretzen, H.-A. Brune, Chem. Ber. 98, 2339 1966, 251 (1966); Bull. Chem., Soc. Jap. 39, may not be least-motion ones. (1965); G. R. Branton, H. M. Frey, R. F. 2116 (1966); ibid. 40, 2018 (1967); L. Salem, Skinner, Trans. Faraday Soc. 62, 1546 J. Amer. Chem. Soc. 90, 543, 553 (1968); H. (1966); R. Criegee and H. G. Reinhardt, E. Zimmerman, J. Amer. Chem. Soc. 88, 1563, References and Notes Chem. Ber. 101, 102 (1968); R. Huisgen and 1566, 1566 (1966); M. J. S. Dewar, Tetrahe- H. Seidel, Tetrahedron Lett. 1964, 3381 dron Suppl. 8 (1966), p. 75; Chem. Soc. Lon- 1. R. B. Woodward and Roald Hoffmann, J. (1964); G. Quinkert, K. Opitz, W. W. don Spec. Publ. No. 21 (1967), p. 177; The Amer. Chem. Soc. 87, 395, 2511 (1965); Wiersdorff, M. Finke, ibid. 1965, 3009 (1965). Molecular Orbital Theory of Organic Chem- Angew. Chem. 81, 797 (1969); Roald Hoff- 10. G. L. Closs and P. E. Pfeiffer, J. Amer. istry (McGraw-Hill, New York, 1969); W. Th. mann and R. B. Woodward, J. Amer. Chem. Chem. Soc. 90, 2452 (1968); K. B. Wiberg A. M. van der Lugt and L. J. Oosterhoff, Soc. 87, 2046 (1965); Accoulnts Chem. Res. 1, and G. Szeimies, Tetrahedron Lett. 1968, 1235 Chem. Commun. 1968, 1235 (1968); H. C. 17 (1968); R. B. Woodward, Chem. Soc. Lon- (1968). Longuet-Higgins and E. W. Abrahamson, J. don Spec. Publ. No. 21 (1967), p. 217. 11. K. Kraft and G. Tetrahedron Amer. Chem. Soc. 87, 2045 (1965). The im- Koltzenburg, of 2. Whether the ground state of the diradical Lett. 1967, 4357, 4723 (1967). portance electronic control of concerted system is a singlet or a triplet hinges on a 12. W. R. R. D. T. M. reactions was anticipated in a remarkable Moore, Bach, Ozretich, F. 0. Rice and fascinating and delicate balance of electronic J. Amer. Chem. Soc. 91, 5918 paper by E. Teller, J. Chem. (1969). Phys. 489 factors. Further details may be found in the 13. G. A. Doorakian and H. H. 6, (1938). Freedman, 26. Roald J. following references: P. P. Gaspar and G. S. ibid. 90, 5310, 6896 (1968). Hoffmann, Chem. Phys. 49, 3739 in Carbene W. (1968). Hammond, Chemistry, Kirmse, 14. The molecular orbitals of polyenes have been Ed. Press, New Rein- 27. H. Conroy and G. Malli, ibid. 50, 5049 (Academic York, 1964); most extensively studied. They are well hard W. Hoffmann, Dehydrobenzene and (1969); C. W. Wilson, Jr., and W. A. modeled by the wave functions of a free Goddard ibid. 716 M. Rubin- Cycloalkynes (Academic Press, New York, electron in a box and exhibit an III, 51, (1969); H. accordingly stein and I. Shavitt, D. 1967); E. Simmons and A. G. Anastassiou, increase in the number of nodal ibid., p. 2014; Silver, in and surfaces R. M. M. com- Cyclobutadiene Related Compounds with Four ir Stevens, Karplus, personal New increasing energy. butadiene munication. (Academic Press, York, 1967); Roald molecular orbitals result from the delocaliza- G. D. 28. C. A. and J. Hoffmann, Zeiss, G. W. Van Dine, J. tion of four orbitals of the diene car- Wellington W. D. Walters, Amer. Chem. Soc. 90, 1485 Roald 2pz Amer. Chem. Soc. 4888 J. E. (1968); bon atoms. The highest occupied molecular 83, (1961); Hoffmann, A. Imamura, W. J. Hehre, ibid., orbital is second Baldwin, Tetrahedron Lett. 1966, 2953 (1966); in order of increasing R. J. Ellis and p. 1499; Roald Hoffmann, ibid., p. 1475; R. and thus H. M. Frey, J. Chem. Soc. Gleiter and energy possesses a single node. See 553 Roald Hoffmann, ibid., p. 5457; L. Salem Orbital 1966A, (1966); S. W. Benson and R. Tetrahedron 5899 [The Molecular Theory of Trans. Soc. 24, (1968); Angew. Chem. Conjugated Systems New Shaw, Faraday 63, 985 (1967); 81, 225 (Benjamin, York, J. Amer. Chen. Soc. 5351 (1969). 1966)] for further details. 89, (1967). 3. Correlation diagrams have played an impor- 29. Considerable quantities of are 15. E. Havinga, R. J. de M. P. ethylene usually tant role in theoretical chemistry. Perhaps the Kock, Rappold, formed in most synthetic procedures that Tetrahedron 11, 278 (1960); E. and best known application is the united atom- Havinga lead to the production of methylenes. These J. L. M. A. Schlattmann, ibid. 146 separated atoms. diatomic correlation diagram 16, sometimes do not result from a dimerization: (1961); G. M. Sanders and E. Havinga, Rec. G. B. and K. J. Amer. first drawn some 40 years ago by Hund and Trav. Chim. 665 Kistiakowsky Sauer, Mulliken: Z. 83, (1964); H. H. Inhoffen Chem. Soc. 78, 5699 ibid. 1066 F. Hund, Phys. 40, 742 (1927); and K. Fortschr. (1956); 80, ibid. 93 ibid. Irmscher, Chem. Org. (1958). 42, (1927); 51, 759 (1928); R. S. Naturstoffe 70 H. H. Rev. 186 Rev. 17, (1959); Inhoffen, 30. B. G. J. L. Chem. Mulliken, Phys. 32, (1928); Angew. Chem. 875 B. Gowenlock, Trotman, Batt, Mod. Phys. 1 J. Chem. 72, (1960); Lythgoe, Soc. London Spec. Publ. No. 10 4, (1932); Phys. 43, Proc. Chem. Soc. 141 (1957), p. 11 Science 13 Details 1959, (1959); W. G. 75; B. G. Gowenlock and W. S2, (1965); 157, (1967). Dauben and G. J. J. Liittke, Quart. the construction of correlation Fonken, Amer. Chem. Rev. 12, 321 concerning Soc. 81, 4060 P. Courtot (1958). be found in (1959); and R. 31. Roald diagrams may G. Herzberg [The Rumin, Tetrahedron Lett. Hoffmann, R. Gleiter, F. B. Mallory, Electronic Structure of Diatomic Molecules 1968, 1091 (1968); J. Amer. Chem. in E. Vogel, W. Grimme, E. Soc., press. (Van Nostrand, Princeton, N.J., ed. 2, Dinne, ibid. 32. N. J. P. A. H. Wil- 1950)] 1965, 391 (1965); E. N. G. Turro, Leermakers, R. and E. Heilbronner and H. Bock [Das HMO- Marvell, Caple, D. C. G. W. G. F. B. Schatz, ibid., p. 385; D. S. J. son, Neckers, Byers, Modell und Seine Anwendung (Verlag-Chemie, Glass, W. ibid. 2613 H. Watthey, S. Winstein, ibid., p. 377. Vesley, 87, (1965). Weinheim/Bergstrasse, 1968)]. 33. J. P. Freeman and W. H. Graham, ibid. 89, 16. R. Huisgen, A. H. Amer. 4. An excellent introduction to the utilization Dahmen, Huber, J. 1761 (1967); L. A. Carpino, personal com- of group theory in chemistry may be found Chem. Soc. 89, 7130 (1967); E. N. Marvell munication. and J. 3377. in F. A. Cotton [Chemical Applications of Seubert, ibid., p. 34. N. P. Neureiter and F. G. Bordwell, J. Amer. Group Theory (Interscience, New York, 17. P. S. Skell and S. R. Sandler, ibid. 80, 2024 Chem. Soc. 85, 1210 (1963); N. Tokura, T. 1963)]. (1958); E. E. Schweizer and W. E. Parham, Nagai, S. Matsumara, J. Org. Chem. 31, 5. One is free to deal with either localized or ibid. 82, 4085 (1960); R. Pettit, ibid., p. 1972; 349 (1966); L. A. Carpino and L. V. Mc- S. F. delocalized descriptions of chemical bonding Cristol, R. M. Segueira, C. H. De Puy, Adams III, J. Amer. Chem. Soc. 87, 5804 ibid. 4007 P. in discussing molecular properties which 87, (1965); v. R. Schleyer, G. (1965); N. P. Neureiter, ibid. 88, 558 (1966); are dependent on all occupied molecular W. Van Dine, U. Schollkopf, J. Paust, ibid. L. A. Accounts Chem. Res. 209 2868 Paquette, 1, orbitals-for example, bond lengths, bond 88, (1966); U. Schollkopf, Angew. Chem. (1968); F. G. J. M. 603 Bordwell, Williams, Jr., energies, and total dipole moments. Only 80, (1968). E. B. Hoyt, Jr., B. B. Jarvis, J. Amer. Chem. the delocalized picture is relevant when the 18. R. Huisgen, W. Scheer, H. Huber, I. Amer. Soc. 90, 429 (1968). Chem. Soc. properties depend on one or several of the 89, 1753 (1967). 35. R. D. Clark and G. K. Helmcamp, J. Org. occupied or unoccupied orbitals-for ex- 19. D. Kurland, thesis, Harvard University Chem. 29, 1316 (1964). ample, ionization potentials and spectra. This (1967); R. Lehr, thesis, Harvard University 36. See references in W. Kirmse [Carbene point has been discussed by M. J. S. Dewar (1968). Chemistry (Academic Press, New York, 1964)] [Hyperconjugation (Ronald Press, New York, 20. Roald Hoffmann, J. Chem. Phys. 39, 1397 and J. Hine [Divalent Carbon (Ronald Press, 1962); Chem. Eng. News (11 January 1965), (1963); ibid. 40, 2474, 2480, 2745 (1964); New York, 1964)]. P. 86]. Tetrahedron 22, 521, 539 (1966); and sub- 37. Reviewed by H. E. Gunning and 0. P. 6. Molecular orbital calculations yield one-elec- sequent papers. Strausz, in Advances in Photochemistry tron energy levels. These are then populated 21. Results similar to those in reference 17 were (Wiley, New York, 1966), vol. 4, p. 143. by electrons, subject to the Pauli principle, to communicated to us by W. Kirmse. 38. In the case of methylene addition, just such form configurations. The inclusion of electron 22. Interaction diagrams are a useful device by a transition state was suggested by P. S. spin and interaction finally results in states. which a system is broken down into non- Skell and A. Y. Gamer [J. Amer. Chem. The discrimination between these terms and a interacting components and then the interac- Soc. 78, 5430 (1956)]. general analysis of the molecular orbital meth- tion is initiated and its effects are qualitatively 39. Supported by the National Science Founda- od be found may in J. C. Slater [Quantum estimated by perturbation theory. This ap- tion (GP 5290, GP 8013), the Public Health Theory of Molecules and Solids: Electronic proach has been aptly utilized for ordering Service GM the Chevron Structure (GM 13468, 04229), of Molecules (McGraw-Hill, New energy levels in simple molecules and espe- Research Company, and the Sloan Founda- York, 1965), vol. 1] and J. N. Murrell, S. F. cially in inorganic complexes: H. B. Gray, tion.

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