Molecular Orbital Theory of Orientation in Aromatic, Heteroaromatic, and Other Conjugated Molecules Kenichi Fukui, Teijiro Yonezawa, Chikayoshi Nagata, and Haruo Shingu
Citation: The Journal of Chemical Physics 22, 1433 (1954); doi: 10.1063/1.1740412 View online: http://dx.doi.org/10.1063/1.1740412 View Table of Contents: http://aip.scitation.org/toc/jcp/22/8 Published by the American Institute of Physics
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provided comparisons are made only between closely methods. Commercial samples were purified by re related compounds. This observation suggests that the crystallization or distillation. Unless otherwise indi central atom is strongly involved in the transition cated, the spectra were determined in solution in concerned. Although the data presented here are commercial 95 percent ethanol which was transparent insufficient to make a decision on this point, it is not above 210 m,u. A Beckman DU spectrophotometer and unlikely that the end absorption corresponds to a 1 em quartz cells were used throughout. The concentra 7 dissociation process, as Milazzo has proposed. tions of the solutions were so chosen as to obtain EXPERIMENTAL optical densities between 0.3 and 0.7 at the absorption All compounds were either obtained from commercial maxima, and no optical density data below 0.15 were sources or prepared in this laboratory by known used.
THE JOURNAL OF CHEMICAL PHYSICS VOLUME 22, NUMBER 8 AUGUST, 1954
Molecular Orbital Theory of Orientation in Aromatic, Heteroaromatic, and Other Conjugated Molecules
KENICHI FUKUI, TEIJIRO YONEZAWA, CHIKAYOSHI NAGATA, AND HARUO SHINGU Faculty of Engineering, Kyoto University, Kyoto, Japan (Received March 31, 1953)
As to the LCAO MO treatment of the orientation problem in chemical reactions of 7r-electron systems, the frontier electron concept which has been previously introduced by the authors for explaining the reactiv ities in aromatic hydrocarbons is subjected to an extension in the sense that the frontier orbitals are specified according to the type of reaction. Thus, fltndamental postulates relating to the reactivities of 7r-electron systems are set up, which are believed to include general principles involved in the mechanism of both sub stitution and addition of electrophilic, nucleophilic, or radical type. On the basis of these postulates it is possible to predict the position of attack in conjugated molecules in all the three types of substitution as well as addition in a consistent manner. There is a nearly perfect agreement between the theoretical con clusions and experimental results hitherto reported.
1. INTRODUCTION tion method," is related to the calculation of the differ NE of the recent successes achieved by quantum ence in unsaturation energy of the hypothetical transi O mechanics in the field of physical organic chem tion complexes. istry is the development of the theory in explaining the Prominence of the latter method should be admitted orienting effect of substituents in aromatic molecules. in that it is capable of explaining the reactivity in all the The quantitative treatments of this problem so far three types, i.e., electrophilic, nucleophilic, and radical reported may be roughly classified into two groups. type, of substitution from a unified standpoint, whereas The one,l which may be called the "static method," is by means of the former method it is difficult to account based on the hypothesis that the position of higher (or for the point of attack in the radical substitution, and lower) calculated density of total 7r electrons is more in this respect the "free valency method"5 serves as easily attacked by electrophilic (or nucleophilic) re filling up that defect of the static method. agents. The other,2 which may be called the "localiza- In this paper it is shown that another unifying method can also be established on the basis of the ''frontier 1 E. Hiickel, Z. Physik 72, 312 (1931); Z. physik. Chern. B35, 163 (1937); Z. Elektrochem. 43, 827 (1937); G. W. Wheland and electron" concept which has been previously introduced L. Pauling, J. Am. Chern. Soc. 57, 2086 (1935); T. Ri, Rev. Phys. by some of the present authors in the case of electro Chern. Japan 17, 1, 16 (1943) (in Japanese); M. J. S. Dewar, philic substitution in condensed aromatic hydro Trans. Faraday Soc. 42, 764 (1946); H. C. Longuet-Higgins and a C. A. Coulson, Trans. Faraday Soc. 43, 87 (1947); C. A. Coulson carbons. On treating the orientation problem in sub and H. C. Longuet-Higgins, Proc. Roy. Soc. (London) A191, 39; stituted atomatic and other related molecules, it is A192, 16 (1947); A. Pullman, Rev. sci. 86, 219 (1948); A. Pullman and J. Metzger, Bull. soc. chim. France 1948, 1021 (1948); H. C. found that the concept should naturally be extended in Longuet-Higgins and C. A. Coulson, J. Chern. Soc. (London) the sense that the frontier orbitals are specified according 1949, 971 (1949); C. Sandorfy, Bull. soc. chim. France 1949,615 to the type of reaction. Thus, we are led to set up the (1949); H. C. Longuet-Higgins, J. Chern. Phys. 18, 283 (1950); Orgel, Cottrel, Dick, and Sutton, Trans. Faraday Soc. 47, 113 fundamental postulates, in the light of which the position (1951); J.-I. F. Alonso, Compt. rend. 233, 403 (1951); L. SzabO, of attack by electrophilic, nucleophilic, and radical Compt. rend. 233, 625 (1951). reagents can be predicted not only for substitution but 2 G. W. Wheland, J. Am. Chern. Soc. 64, 900 (1942); H. C. Longuet-Higgins, J. Chern. Phys. 18,283 (1950); M. J. S. Dewar, also for addition in an excellent agreement with ex J. Chern. Soc. (London) 1949, 463 (1949); C. A. Coulson, Re periment. search 4,307 (1951); M. J. S. Dewar, J. Am. Chern. Soc. 74, 3355, 3357 (1952). 3 Fukui, Yonezawa, and Shingu, J. Chern. Phys. 20, 722 (1952). 1434 FUKUI, YONEZAWA, NAGATA, AND SHINGU
Types of Attacking Reagent 1. In case of the reaction with an electrophilic re 1. Electrophilic 2. Nucleophilic 3. Radical agent, that position is more susceptible to attack which ,', -.-li!-::~ -. '" has the higher density of the two electrons occupying the ," • • ", -0--0- • 0--::: highest molecular orbital in the ground state. -0---0- --0----0- --0---0- 2. In case of the reaction with a nucleophilic reagent, (a) that position is more susceptible to attack which would -0---0- -0-:--0-- -0--0- have the higher density of the two electrons assumed to -0---0- -0--0- ----0--0- occupy the lowest unoccupied orbital of the ground state. -0-----0- -0--0- -0---0- 3. In case of the reaction with a radical reagent, that position is more susceptible to attack which would have the higher density of the two electrons, one occupying the highest orbital and the other occupying the lowest unoccu ,. ;!: -0---*-::: pied orbital of the ground state. As a consequence of these postulates we can classify • 0--;:'-0--0- -0---0-- the frontier electrons and orbitals for various types of --0--0- (b) -0--0- -0--0- reactants and reagents, which is illustrated in Fig. 1, --0--0--- --0--0- including the cases of even and odd 1r-electron systems. -0---0-- -0---0- In the latter case where the 1r-electron system is a 0: electron in the ground _tat• • : frontier electron radical, the above postulates should be somewhat modi *: trontier orbital fied as shown in Fig. 1 (b). Also in the case of an excited FIG. 1. Frontier electrons and frontier orbitals. (a) Even ,,"-electron state of the 1r-electron system, e.g., in the case of a system. (b) Odd 1r-electron system. diradical state, the principle involved in the postulates may be correspondingly applicable. 2. FUNDAMENTAL POSTULATES As a general characteristic of chemical activation it 3. ELECTROPHILIC SUBSTITUTION may be assumed that in the vicinity to the transition Substitution in Heterocyclic Compounds state the electrons in the reagent as well as those in the reactant molecule will be delocalized and a transfer of For the quantum-mechanical treatment of reactivity electrons will occur between the reagent and the re in heterocyclic compounds several parameters repre actant. From the standpoint of the frontier electron senting the influence of heteroatom as to the Coulomb concept we suppose that the frontiers are most sus and exchange integrals have been introduced by several ceptible to the electron transfer and that this transfer authorsl,2 from some empirical or theoretical arguments. of electrons, which may serve to lower the energy of the
activated complex, will form the essential part of the .149 .534 .235 .322 .057 electronic interaction in question. Two electrons should 364 N 1 2.013 be characterized in this connection as frontiers in that 5 3 .454 3.157 they are most closely related to the formation of a 4 4 0.214 .177 3q~ covalent u bond between the 1r-electron system and the reagent, and these two are provided either from the PYRIDINE QUINOLINE ISOQUINOLINE highest occupied orbital in the 1r-electron system to the reagent in an electrophilic reaction, or from the reagent to the lowest empty orbital in the 1r-electron system in 3r a nucleophilic reaction, and in a radical reaction one 4 3 .276 .058 co·5.005 3 .5'15 ~'724 6. I 2.21'1 electron is provided from the reagent and the other from ~N~' 217 N the 1r-electron system. H.ooo .233 H .278 From this point of view, in order to make reference to ACRIDINE PYRROLE INDOLE the reactivity in terms of the electron distribution in an isolated 1r-electron system, it is convenient to define a new concept of frontier orbital in relation to the isolated 1r-electron system as characterized by partial occupation by the frontier electron in case of the electron transfer at the transition state, according to the type of reaction. On the basis of these considerations, the following CARBAlOLE ISOINDOLE INOOLIZINE fundamental postulates are set up, which enable us to FIG. 2. Frontier electron density for electrophilic substitution predict the reactivity of 1r-electron system in a most in heterocyclic compounds. As to pyridine, the calculation is made general and consistent manner: with the help of Eq. (1). THEORY OF ORIENTATION IN CONJUGATED MOLECULES 1435
TABLE I. Coulomb and exchange integrals for heteromolecules containing nitrogen atom.
Pyridine type Pyrrole type Type of nitrogen atom Coulomba.b •• Exchanged Coulomb Exchange Integrals al a, p" p" '" a, a, p" p" Wheland-Pauling" Longuet -Higgins-Coulson (1947)e a+2i3 a+li3 a i3 i3 a+2i3 a+li3 a i3 i3 Pullman" Orgel et al.e a+t:l a+tcri3 a i3 i3 a+2i3 a+!i3 a i3 13 Dewar" a a a 0.5513 t:l Present authors a+i3 a a i3 i3 a+i3 a a i3 i3
flo Subscript 1: nitrogen atom. b Subscript 2: carbon atom adjacent to nitrogen. c Subscript r: other carbon atoms. d Subscript rs: any pair of mutually adjacent atoms except 12 (exchange integrals between nonadjacent atoms and all overlap integrals neglected entirely). e See reference 1.
These parameters are tabulated in Table I together with tively, to be 3 in consideration of the complete agree those which are adopted by the present authors.* ment between calculation and experiment which has The calculated densities of frontier electrons in pyri been obtained3 in aromatic hydrocarbons without con dine, quinoline, isoquinoline, acridine, pyrrole, indole, sidering the contribution of the next orbital. carbazole, isoindole, and indolizine are indicated in In regard to LCAO MO treatment, mono-substituted Fig. 2, and the reaction products of halogenation, nitra benzenes are classified into several types of isoaromatic§ tion, and sulfonation are tabulated in Table II. The hydrocarbon, that is, benzene type, benzyl anion type, agreement between calculated and experimental results styrene type, and 2-phenylpropenyl anion type (Fig. 3), is almost satisfactory. and other types. Nuclear Substitution in Benzene Derivatives Benzene Type In this paragraph the object of calculation is restricted To this type belong, for example, t-butyl benzene and to mono-substituted benzenes.t The twofold degeneracy benzene sulfonic acid in which the effect of substituent of frontier orbitals in nonsubstituted benzene is re is only inductive. This effect can be represented after 2 moved by the influence of the substituent. If the per Sandorfyl and Dewar (1949) by two parameters a and E turbation is small, two separate orbitals, the corre in Eq. (2). r 1 sponding energies of which are in close proximity, are ar = a+ e - a{3, (2) produced as the result of the removal of degeneracy. In TABLE II. Products of electrophilic substitution in such a case, the contribution of the density of electrons heterocyclic compounds. in the lower orbital must be taken into account in the calculation of the frontier electron density. Predicted Structure of reaction products In order to evaluate the degree of contribution of the Compounds position Halogenation Nitration Sulfonation Pyridine 3.5 3-Cla 3-NO,' 3-S0,Hp lower orbital the following Eq. (1) is assumed as giving 3-Bra the frontier electron density for the electrophilic reaction Quinoline 8. (5) S_Ib S-NO,. 8-No,i S-SO,H. 8-S0.HQ Isoquinoline 5 S-NO,. 8-NO,k at the rth atom in the molecule f/E ) : Acridine I-NOt. 3-NO,l 1.3-di-NO,m 2 2 DdA 1 C/l) 1 + 1 Cr (2) 1 e- Pyrrole 2.5 2-Cl' fr(E)=2· ,(1) 2.S-di-Cld DdA Indole 3 2.3-di-Cl' 3-NO," 1+e- 3_1' Carbazole 1.(3) 3-Clg I-NO,. 3-NO,o where <1;\ is the energy difference between the two 3-Brh orbitals in units of {3 and C r (1), Cr (2) are the coefficients a H. J. Den Hertog and J. P. Wibaut. Rec. trav. chim. 51. 382. 940 (1932) . of LCAO MO at the rth atom corresponding to the b W. La Coste. Ber. deut. chern. Ges. 18. 781 (1885). , G. Mazzara and A. Borgo. Gaz. chim. ita!. 35 II. 20 (1905). highest and the next orbital respectively, and D is a d G. Mazzara and A. Borgo. Gaz. chim. ita!. 35 I. 477 (1905). constant which determines the degree of contribution of , G. Mazzara and A. Borgo. Gaz. chim. ita!. 35 II. 536 (1905). f H. Pauly and K. Gunderman. Ber. deut. chern. Ges. 41. 4006 (1908). the lower MO to the frontier electron density. Through g Mazzara. Lamberti. and Zanardi. Gaz. chim. ital. 26 II. 238 (1896). h W. Vaubel. Z. angew. Chern. 14. 784 (1901). out the present papert the value of D is taken, tenta- , P. Schorigin and A. Toptschiew. Ber. deut. chern. Ges. 69.1874 (1936). i W. Koenigs. Ber. deut. chern. Ges. 12. 449 (1879). * As it is intended in the present paper to examine the general k Ad. Claus and K. Hoffmann. J. prakt. Chern. (2) 47. 253 (1893). I C. Graebe and H. Caro. Ann. Chern. 158. 275 (1871). validity of the frontier electron theory using the smallest number m K. Lehmsteat. Ber. deut. chern. Ges. 65. 834 (1924). of uncertain parameters, the effect of the heteroatom on the Cou h F. Angelico and G. Velardi. Gaz. chim. ita!. 34 II. 60 (1904). o H. Lindemann. Ber. deut. chern. Ges. 57. 557 (1924). lomb integral of the adjacent carbon atom is neglected, as is pO. Fischer. Ber. deut. chern. Ges. 15. 62 (1882). shown in Table I. q A. Kaufmann and H. Hiissig. Ber. deut. chern. Ges. 41.1735 (1908). t For di- or polysubstituted aromatic systems the present method can be also useful, but especially in benzene derivatives Eq. (1) is necessary, if any orbital lies in close proximity to the it becomes important to consider the steric circumstances. frontier orbitals. t Also in nucleophilic or radical reaction, the equation similar to § See H. C. Longuet-Higgins, J. Chern. Phys. 18, 283 (1950). 1436 FUKUI, YONEZAWA, NAGATA, AND SHINGU
(a) ( b) (C) Cd) to the electronic state, it seems reasonable that toluene may be put into the class of benzyl anion type, where b is taken to be a large positive value and a a small negative value.§§ Styrene Type Molecules which have the following substituents belong to this type: BENZENE TYPE BEN ZYLANION TYPE STYRENE TYPE 2·PHENYL· POOPENYL ANION lJ'PE 6Jr~ElECTRONS IN ) (81t-ElECTRONS IN) (8n-ELECTRONS ,,,,\ ('On:-ElECTRONS IN) R ( fjlt-ATOMJC ORBITAlS 7Jt-ATOMJC ORBITALS 81r-ATOMICORBI"UlLS) 91£-ATOMIC ORBITALS + I FIG. 3. Characteristic types of 7r-electron system in -CH=CH2, -C=N, -N=N, -C=O, etc. mono-substituted benzenes. In this type another similar parameter c in addition to in which aT is the Coulomb integral at the rth carbon a and b in Eq. (3), is considered concerning the side atom (in Fig. 3). The parameter a is negative for the chain atom C8 • The calculated results are shown in substituent which repells the (]" electrons in the X - C Fig. 6. If a~O and b, c«1, the substituent is ortho-para (]" bond, and positive for the substituent which attracts directing, and when a~O and c> 1, it is meta-directing. the (]" electrons. The parameter E, which represents the In Fig. 6(a) the frontier electron density at C8 atom diminishing factor of the inductive effect, is taken here in styrene is seen to be very large in conformity with the to be zero. II In Fig. 4, the frontier electron densities at high reactivity of w position of that compound. ortho-, meta-, and para-positions are given for various values of a ranging from -1 to + 1. Qualitatively the 2-Phenyl-propenyl Anion Type results are as satisfactory as that obtained by other Nitrobenzene, benzoate anion, benzoic esters, etc., methods.l,2~ belong to this type, and parameters a, b, d, and d' are Benzyl A nion Type adopted relating to the CJ, C7, C8, and C9 atom, re spectively. Calculated result for nitrobenzene is shown Halogenobenzenes, phenol, aniline, etc., belong to in Fig. 6(c). this type. Two parameters a and b** in Eq. (3) are adopted here as being characteristic of each substituent. Other Types al=a+aj3, Diphenyl, stilbene, azobenzene, etc., belong to none (3) of the above four types. These conjugated systems may a7=a+bj3. be treated separately without classification. Calculated In Fig. 5, the calculated frontier electron densities frontier electron densities for some of these molecules are plotted for various values of a and b. In halogeno are shown in Fig. 6(d), (e), and (f). benzenes, phenol, and aniline, the values of a are as sumed to be positive and small, so that, as is shown in Substitution in Substituted Condensed Aromatics Fig. 5 (b), the substituents are ortho-para directing. It is, in principle, possible to apply here the same The reactivity of toluene has been hitherto under method as used in the case of substituted benzenes,111I stood by considering the hyperconjugationtt or, other wise, the purely inductive effect.tt In consideration of the possible contribution of the structure
" For some appropriate values of E which are not equal to zero the calculation is also carried out, but the results remain unchanged as to whether ortho-para directing or meta-directing effect is con cluded. ~ We reserve here the detailed discussions on the problem of o:p ratio, as it seems hopeless to expect any valuable result, hav ing neither sufficient knowledge for determining the exact values of a and E nor a quantitative method of taking into account the 0.1 influence of steric factors. ** According to Sandorfy (reference 1), Dewar (reference 2), and Jaffe Chern. Phys. 20, 279 (1952)J, the relation between U. -I -0.5 o 0.5 a and b is represented by a= Eb, but it may not always be necessary to adhere to this relation when, as in this case, phenolate ion and Q- other anions are also included in the benzyl anion type. FIG. 4. Frontier electron density vs a in benzene type molecules. tt For example, Wheland (reference 2) considered §§ As an example, if b=5 and a= -0.1, following frontier elec O-A-B tron densities are obtained: ortho=0.3442, para = 0.3697, and type. meta = 0.2820. H E.g., see Wheland and Pauling (reference 1) and Longuet 1111 For example, in 1-vinyl naphthalene, the positions wand 4 Higgins (reference 2). are predicted to be most susceptible to attack, and in 2-vinyl THE 0 R Y 0 FOR lEN TAT ION INC 0 N JUG ATE D MOL E C U L E S 1437 but this requires rather tedious calculations. Here we C.683 N .193 .343 make use of a simplification similar to that adopted by I I o 0 (.259 "- N /000 Longuet-Higgins as to the treatment of substituted C .005 condensed aromatics.4 Namely, the electronic effect of .170. .212 a substituent is represented by only one parameter, .318 either a or b which are given by ac=a+a{1, and .o.Q8 .335 .m ax=a+b!3 eX: substituent; C: adjacent carbon). For d.259 0.246 0.181 the electron-repelling,-r,-r substituents, we take a
The perturbation method is applied in the cases (1) .,0.\77.175 .Oqq and (2). .183 .154 N-N-Q
0.4 (f> Alo.BE N lENE t PARA (01. ~ 01 + P ) >- I- ORTHO ~ 03 FIG. 6. Frontier electron density in some styrene type and I!l 2-phenyl-propenyl anion type molecules, and in some complex benzene derivatives. Experimental results: ~ t 0.2 (a) ~ w Compound Reaction Products ... styrene nitration W-N0211. ;:::'" 0.1 benzonitrile nitration 3-NO,b diphenyl nitration· 2-NO,. 4-NO" ~ stilbene u. azobenzene nitration p-NO,. p,p'-di-NO,"
0 2 467 q 10 b- 8 E. Simon. Ann. Chern. 31. 269 (1839). b M. Sch6pff. Ber. deut. chem. Ges. 18. 1063 (1885). " Schultz. Schmidt. and Strasser. Ann. Chern. 207. 352 (1881). d A. Werner and E. Stiasny. Ber. deut. chern. Ges. 32. 3268 (1899). 0.4 --_~RA As to 1- and 2-substituted naphthalenes the results of -----=--=::-::,."" ORTHO calculation are shown in Fig. 7. As can be seen in the :: 0.3 ----~~------OBTHo ~ PA,;---- figure the frontier electron distributions in the case z Ib I»1 coincides exactly with that in the case Ia I~1 2 (b) if a is taken to be -l/b. The coincidence can be easily proved mathematically for any aromatic hydrocarbon. r~ ~ __~ME~T~A ______1 Thus the two effects, mesomeric and inductive, may be ~ 0.1 z discussed quite indiscriminately if they are small and in ~ ... the same direction . o 0.1 0.2 0..3 0.4 0.5 0.6 0.7 as 0.9 1.0 In Table III experimental results as to the orientation 0.- in substituted naphthalenes are compared with the pre FIG. 5. Frontier electron density in benzyl anion types. (a) dictions obtained from Fig. 7. The agreement is good, Frontier electron density vs b when a=O. (b) Frontier electron density vs a (>0) when b= 1 (full line curves) and b=2 (dotted when, as for electron-repelling substituents, b is taken curves). to be zero for amino and hydroxyl and to be large for naphthalene, the positions 1 and w. These predicted positions are halogen and methyl and when, as for electron-attracting identical for electrophilic, nucleophilic, and radical reactions. substituents, a as well as b is assumed to be small. The 4 H. C. Longuet-Higgins (see reference 2); A. and B. Pullman, Rev. sci. 84, 145 (1946). Longuet-Higgins attempted to explain results of similar treatments of other substituted con the orientation in 2-naphthylamine by calculating the densities of densed aromatics are tabulated in Table IV, showing total 11' electrons, taking OIN=OI. He considered that the effect of amino group was approximately the same as that of - CH2 group a good agreement of the theory with experiment. in the corresponding isoaromatic system. ~~ Here, the substituents which in benzene derivatives are ortko 4. NUCLEOPHILIC SUBSTITUTION para-directing are referred to as electron-repelling substituents, and those which are meta-directing, as electron-attracting sub The nucleophilic substitution treated here is restricted stituents. *** The case b=O is omitted for the convenience of calculation. to the direct replacement of a hydrogen atom with 1438 FUKUI, YONEZAWA, NAGATA, AND SHINGU
TABLE III. Products of electrophilic substitution in substituted naphthalenes.
(a) Electron-repelling substituents Predicted Structure of the reaction products Compounds position Chlorination Bromination Nitration Sulfonation I-F-naphthalene 4 4-Brh 4-S0aHh l-Cl-naphthalene 4 4-CI" 4-Bri 4-N02' 4-S0aH, 5-S0aHcC I-Br-naphthalene 4 4-Clh 4-Bri 4-S0aHdd 5-Brk 1· I-naphthalene 4 4-Clc 4-Br' 1-0H-naphthalene 2,4 2-Cld 2-N02t 2-S0aHce 4-Clc 2,4-di-N02u 4-S0,Hff 2,4-di-Cle 2,4-di-SOaHec I-NH2-naphthalene 2,4 4-Clf 2,4-di-BrlD (4-N02, 5-N02, 8-N02v) 4-S0,Hgg 2,4-di-SOaHgg l-CH a-naphthalene 4 4-Brn 4-N02w 4-S0aHhh 2-F-naphthalene 1,8 I-N02h 2-CI-naphthalene 1,8 8-S0aH, 6-S0aHii 2-Br-naphthalene 1,8 l-N02,3-N02x 8-S0aHii 2-I-naphthalene 1,8 l-Bre 8-S0aHii 2-0H-naphthalene 1 1-Clg l-Br" l-N02Y l-SOaHkk 8-Br" l,6-di-N02' 6-S0aH" l,6-di-Br" 2-NH2-naphthalene l,6-di-Brr (8-N02, 5-N02"") (5-S0aH,8-S0aHmm) 2-CHa-naphthalene 1,8 l-N02bb 6-S0aHhh
(b) Electron-attracting substituents Predicted Structure of the reaction products Compounds position Halogenation Nitration Sulfonation I-COOH-naphthalene 8,5 5_Clnn 5-N02""" 5-S0aHggg 8_Clnn 8-N02""" 6-S03Hggg 5-8-di-Cloo 7-S0aHggg 5-Br"" l-N02-naphthalene 8,5 5-Clqq S-N02hbb 5-S0aHhhh 8-ClqQ 8-N02bbb 5,8-di-Clrr 5_Br88 l-SO,H-naphthalene 8,5 5_Brtt 4_N02cCC 5-S0aHiii 5-N02cCC 8-N02cCC l-CHO-naphthalene 8,5 5_BrUu l-CN-naphthalene 8,5 5_Clvv 5_N02ddd 5_BrWW 2-COOH-naphthalene 5,4 5,8-di-Clxx 5-N02eee 5-S0aHiii 5-BrYY 8-N02cce 8-S0aHkkk 2-N02-naphthalene 5,4 5-S0aHIll 8-S0aHIll 2-S03H-naphthalene 5,4 5-CI" 5-N02fff 5-S0aHiii 8-Clzz 8-N02fff (6 and 7-S0aHmnun)
• H. E. Armstrong. Chern. News 66, 189 (1892). "M. Conrad and W. Fischer, Ann. Chern. 273, 105 (1893). b I. Guareschi and P. Biginelli, Chern. Zentr. 1877, 518 (1877). If K. Holdermann, Ber. deut. chern. Ges. 39, 1225 (1906). c C. Willgerodt and P. SchlOser, Ber. deut. chern. Ges. 33, 693 (1900). gg W. H. Hunter and M. M. Sprung, J. Am. Chern. Soc. 53, 1432 (1931). dR. Lesser and G. Gad, Ber. deut. chern. Ges. 56. 972 (1923). bb L. F. Fieser and M. Fieser, Organic Chemistry (D. C. Heath and • P. T. Cleve, Ber. deut. chern. Ges. 21. 894 (1886). Company, Boston, 1950), second edition, p. 793. f P. Seidler, Ber. deut. chern. Ges. 11, 1201 (1878). ii H. E. Armstrong and W. P. Wynne, Chern. News 55, 91 (1887). g Ioffe, Kuznetzov, and Litovskii, J. Gen. Chern. (U.S.S.R.) 5, 1685 ii H. E. Armstrong and W. P. Wynne, Chern. News 60,58 (1889). (1935). kk H. E. Armstrong, Ber. deut. chern. Ges. 15, 202, 207 (1882). b Schieman, Gueffroy, and Wikeimilller, Ann. Chern. 487. 270 (1931). II L. Schaeffer, Ann. Chern. 152, 296 (1869). i I. Guareschi and P. Biginelli, Gaz. chim. ita!. 16, 152 (1886). mm H. Erdmann, Ann. Chern. 275, 280 (1893). i C. Glaser, Ann. Chern. 135, 42 (1865). DD A. G. Ekstrand, J. prakt. Chern. 38, 148 (1888). k Yu. S. Zalkind and S. B. Faerrnann. J. Russ. Phys.-Chem. Soc. 62,1021 00 A. G. Ekstrand, J. prakt. Chern. 38, 151, 153 (1888). (1930). pp O. Gausmann, Ber. deut. chern, Ges. 9, 1520 (1875). I H. Hirtz, Ber. deut. chern. Ges. 29, 1409 (1896). qq A. G. F. Anilinf, Germ. Pat. 99,758; Chern. Zentr. 1899 I, 463 (1899). m R. Condon and J. Kenyon. J. Chern. Soc. (London) 1935, 1591. "Bayer & Co. Germ. Pat. 293, 318; Chern. Zentr. 1916 II, 359. n L. F. Fieser and M. Fieser, Organic Chemistry (D. C. Heath and .. I. Guareschi, Ann. Chern. 222, 291 (1884). Company, Boston, 1950), second edition, p. 792. tt L. Darmstaedter and H. Wichelhaus, Ann. Chern. 152, 303 (1869). o H. Hirtz, Ber. deut. chern. Ges. 29, 1409 (1896). uu P. Rup;gli and R. Preus, Helv. Chim. Acta 24, 1345 (1941). p Verma, Mozumdar, and Rajah, J. Indian. Chern. Soc. 10, 591 (1933). vv A. G. Ekstrand, J, prakt. Chern. 38,147 (1888). q K. Fries and K. Schimmelschmidt, Ber. deut. chern. Ges. 58, 2840 ww O. Hausmann, Ber. deut. chern. Ges. 9, 1516 (1876). (1925). xx A. G. Ekstrand, Ber. deut. chern. Ges. 17, 1605 (1884). 'L. Michaellis, Ber. deut. chern. Ges. 26,2196 (1893). YY H. Goldstein and R. Matthey, Helv. Chim. Acta 21,62 (1938). 'A. Atterberg, Ber. deut. chern. Ges. 9, 927 (1876). "Chr. Rudolf, Germ. Pat. 101,348; Chern. Zentr. 1899 I, 960 (1899). t H. H. Hodgson and E. W. Smith, J. Chern. Soc. (London) 1935, 671 • .. A. G. Ekstrand, J. prakt. Chern. 38, 156,241 (1888). (1935). hhb P. Friedlander, Ber. deut. chern. Ges. 32, 3,531 (1899). U J. Schmidt, Ber. deut. chern. Ges. 33, 3245 (1900). '" H. Erdmann and C. Silvern, Ann. Chern. 275, 231 (1893). v R. Meloda and J. Streatfeld, J. Chern. Soc. (London) 63, 1055 (1893). ddd Fr. Graeff, Ber. deut. chern. Ges. 16, 2246 (1833). w R. Lesser, Ann_ Chern. 402, 11 (1914). ... A. G. Ekstrand, J. prakt. Chern. 42, 273 (1890). x Yu. Zalkind and F. Filinov, J. Gen. Chern. (U.S.S.R.) 4, 979 (1943). fff H. E. Armstrong and W. P. Wynne, Chern. News 59, 94 (1889). Y A. Pictet de Krijanowski, Chern. Zentr. 1903, II, 1109 (1903). ggg M. Stumpf, Ann. Chern. 188, 10 (1877). • J. Schmidt, Ber. deut. chern. Ges. 33, 3246 (1900). bbh H. Erdmann, Ann. Chern. 247, 311 (1888). •• P. Friedlander and St. Szymanski, Ber. deut. chern. Ges. 25, 2076 iii A. E. Armstrong and W. P. Wynne, Chern. News 55, 136 (1887) . (1892). iii M. Stumpf. Ann. Chern. 188, 10 (1877). bb H. E. Fierz-David and E. Mannhart, Helv. Chim. Acta 20, 1024(1937). kkk M. Stumpf, Ann. Chern. 188, 12 (1877). "H. E. Armstrong and W. P. Wynne, Chern. News 61,285 (1890). III H. Kappeler, Ber. deut. chern. Ges. 45, 633 (1912). dd H. E, Armstrong and S. Williamson, Chern, News 54, 256 (1886), mmm H. E, Armstrong, Ber, deut. chern. Ges, 15, 204 (1882). THEORY OF ORIENTATION IN CONJUGATED MOLECULES 1439
x I .000 I .'100 .362-.202.1"1 i .362+.046Ial .362 - . 202 Yb .362 t .046 J1, .000 .000 ·.. ·-(~::r"··'02·, .I~ .."'" .138+.202 ~ .100 .400 .138-.0\\)~ .000 .138-.048Ial .138 -.090)1, .138-.048~ .000 .000 .362-.l341a1 .362 +. 200lal .362- 134l1. .362 +. 200)1, .100 .400
(aJ .362 + .0521£11 .362+.210Ial)( .IIB .412 1.062 .13B-.038lal~~I;;+.07BI"1 .000 .13B+.05Olal~ .138-.1761£11 liB .362-.Qq2IaJ .362-.0801£11 .362-.092)1, .362- 080 M, .000 .000
-I«Q ::< .000 : .362+.202Q :.362-.046£1 .362+.202HbI .362-.046)('1 .138-024a~.138-.202£1 13B-.024)(" .138-.202J.(bI .13B+.09OaVV .138 + .048£1 138 +.090)(bl .138 +.048J.rbl .362+.134£1 .362-.200£1 .362+.134J.t'b1 .362 - .200 ).(" (bJ .362-.052£1 .362-.210a. ,X .138+.038a~~;~-.018a .138+.038)(bI .13B-.050a~ .138 + .176Q .138-.050)(w .362+.092£1 .362+.080£1 .362>.092){bl .362 +. 080)('1 I» a:> 0 b «-I FIG. 7. The frontier electron densities in 1- and 2-substituted naphthalenes. (a) Electron-repelling substituent. (b) Electron-attracting substituent. nucleophilic reagents such as OH- and NH2-.ttt The S. RADICAL SUBSTITUTION results of the calculation as to the five known cases, are The calculated frontier electron densitiesttt as to the shown in Fig. 8 together with the experimental results. reactivity in radical substitution in several aromatic and ttt A typical example of the nucleophilic substitution in con jugated systems may be the hydrolysis of aryl halides, which, which one of all the possible mono-halogeno-derivatives is most however, cannot be the object of the present treatment, because liable to hydrolysis. in such a reaction the point of attack is originally fixed. Of course itt In this calculation the contributions of two unpaired elec it is possible, by means of the frontier electron method, to predict trons in different two orbitals are assumed to be in equal weight. TABLE IV. Products of electrophilic substitution in substituted condensed aromatic hydrocarbons. (a) Electron-repelling substituents Predicted Structure of the reaction products Compounds position Halogenation Nitrosation or nitration Sulfonation 9-CI-anthracene to to-CIa 9-Br-anthracene to 10-Brh 9-0H-an thracene to 10-Brc 1-0H-anthracene 2,4 2-NO,4-NQm 2-0H-anthracene 1 I-NOm 9-CI-phenanthrene to lO-CId 9-Br-phenanthrene to to-N02ll (2-S03HP) 9-0H-phenanthrene to 1O,3-di-Bre 2-CI-chrvsene 8 8-CIf 2-Br-chrysene 8 3-Br-pyrene 5,8 5,8-di-Br" 3-NH2-pyrene 5,8 S-Clh 5-S0aH, 8-S0aHq 12-CI-naphthacene 5 S-CIi 6-Cli 12-Br-naphthacene 5 5-Brl, 6-Bri 3-CI-peryIene to 9-CIk 3-Br-peryIene 9,10 9-Br, lO-Brl (TABLE IV. Continued on next page with footnotes.J 1440 FUKUI, YONEZAWA, NAGATA, AND SHINGU TABLE IV-Continued. (b) Electron-attracting substituents Predicted Structure of the reaction products Compounds position Halogenation Nitration Sulfonation 9-N02-anthracene 10 10-NO.· 9-COOH-anthracene 10 lO-Br,lO-Clr 2-NO l-chrysene 8 8-NO.t 2-CN-chrysene 8 8-N02t 2-COOH-chrysene 8 8-N02' 3-S0aH-pyrene 5 3-N02-perylene 4,(9) (1O-N02u) 3-S0aH-perylene 4,(9) (9-S0aH, 10-S0aHw) 12-substituted naphthacene 11 13-substituted pentacene 6 • Ed. Lippmann and I. Pollack, Ber. deut. chern. Ges. 34, 2768 (1901). 1 Zinke, Kinner, and Wolfbauer, Ber. deut. chern. Ges. 58, 328 (1925). b C. Graebe and C. Liebermann, Ber. deut. chern. Ges. 1, 186 (1868). m R. AnschUtz, Chernie der Kohlenstoffverbindungen (1935), p. 702. "Fr. Goldmann, Ber. deut. chern. Ges. 20, 2437 (1887). n R. K. Callow and J. M. Gulland, J. Chern. Soc. (London) 1929,2424. d H. Sandqvist and A. Hagelin, Ber. deut. chern. Ges. 51, 1521 (1919). • I. G. Farbenind. A.-G. Fr. Pat., 794. 534 (February 19, 1936). • J. Schimel and O. Spoun, Ber. deut. chern. Ges. 43, 1802 (1910). pL. E. May and E. Mosettig, J. Org. Chern. 11, IS (1946). f Soc. Pour. L'ind. Chim. a Bale, Swiss Pat. 204,239 (July 17, 1939). q M. Corell, U.S.P. 2,046.249 (June 30. 1936). g E. Clar, Ber. deut. chern. Ges. 69, 1671 (1936). 'G. Behla, Ber. deut. chern. Ges. 20, 704 (1887). h Corell, Vollman, and Becker, U.S.P. 2,185,661 (Jan. 2, 1939). • J. Meisenheimer, and E. Connerade, Ann. Chern. 330, 167 (1904). l I. J. Postovskii and R. G. Beyles, Compt. Rend. Acad. Sci. U.R.S.S. 39, t I. G. Farbenind. A.-G. Fr. Pat., 794,534 (Feb. 19. 1936), 102 (1943). U Zinke, Hirsch, and Brozek, Monatshefte Chern. 51, 205 (1929). i C. Marschalk and C. Stumm, Bull. soc. chim. France 1948, 418 (1948). v E. Tietze and O. Bayer, Ann. Chern. 540, 189 (1939). • Zinke, Funke, and Pongratz, Ber. deut. chern. Ges. 58, 330 (1925). w C. Marschalk, Chern. Zentr. 1927 I, 1833 (1927). heteroaromatic molecules are shown in Fig. 9 together N max and requires a most laborious calculation of bond with experimental results. The agreements of theory order in larger organic molecules.) with experiment are satisfactory, (Similar results are In alte:rnant hydrocarbons, 8 the electron distribution obtainable by means of the localization method2 and in the lowest unoccupied orbital is identically the same also by computing the free valency number.5 The latter method has been developed by Daudel, Vroelant, and Coulson et al. 5 and most recently examined experi .362 mentally by Kooyman and Farenhorst,6 and Roitt and ~138 Waters.7 It can, however, be pointed out that the free ~ valency method contains an ambiguity in evaluating NAPHTHALENE ANTHRACENE (q.BENZOYLOXY b) .493 188 .30B (I-PHENYL ") N 156 B 041 N 6 / 2 .358' 7 / 2 .358 5 4 3 .079.067 6 5 010 4 ~ C1.264 Q .321 .634 .260 .52B N NAPHTHALENE PYRIDINE QUINOLINE .11' 361 ( 1- NH,a) (CI" 6 C. Vroeland and R. Daudel, Bull. soc. chim. France 16, 217 • W. A. Waters, J. Chern. Soc. (London) 1939, 864 (1939). b See reference 7. (1949); Buu-Hoi, Daudel, and Vroelant, Bull. soc. chim. France 'Haworth, Heilbron, and Hey, J. Chern. Soc. (London) 1940,349 (1940). 16, 211 (1949); Daudel, Sandorfy, Vroelant, Yvan, and Chalvet, d D. H. Hey, J. Chern. Soc. (London) 1934, 1966. Bull. soc. chim. France 19, 66 (1950); Burkitt, Coulson, and Lon • M. Gomberg and W. E. Bachmann, J. Am. Chern. Soc. 46, 2389 (1924). guet-Higgins, Trans. Faraday Soc. 47, 553 (1951). f M. Gomberg and J. C. Pernert, J. Am. Chern. Soc. 48, 1372 (1926). g D. Detar and H. Scheifele, Jr., J. Am. Chern. Soc. 73,1442 (1951). 6 E. C. Kooyman and E. Farenhorst, Nature 169, 153 (1952). 7 I. M. Roitt and W. A. Waters, J. Chern. Soc. (London) 1952, 8 See C. A. Coulson and H. C. Longuet-Higgins, Proc. Roy. Soc. 2695 (1952). (London) A192, 16 (1947). THEORY OF ORIENTATION IN CONJUGATED MOLECULES 1441 Frontier electron E(l) N(l) R(l) .1.~J, . density for 1 234 5 6 c-c-c-c-c-c primary addition: ·543 .108 .,49 ·349 .108 .54, f.e.d. of hexatriene for elec trophilic, nucleophilic, and radical reagent Frontier electron a. E(1)_N(2) type addition b. E(1)_R(2) type addition densities for !l (2) R(2) felt- ! ") E (1) __------secondary addition: I J, ! H-C-C -c-c-c-c H-C-C-C-C-C-C I I H 2/, 0 2/3 0 2/3 H ...... ______7/12.J ~ 7/12 1/4 1/3 1/4 f.e.d. of pentadienyl cation f.e.d. of pentadieny1 cation for nucleophilic reagent for radical reagent c. N(1)-E(2) type addttion d. N(l) _R(2) type addition E(2) R(2) N (It---:--- N (1)-_-___...... , .. I.J, ~ ,l, J ~ ~ H-C-C -C-C-C-C H-C-C-C-C--C_C I I H 2/3 0 2/3 0 2/3 H 7/12 1/4 1/3 1/4 7/12 ~------~------...... ~ f.e.d. of pentadieny1 anion f.e.d. of pentadienyl anion for electrophilic reagent for radical reagent e. R(1)_E(2) type addition f. R(1)_N(2) type addition E (2) N (2) R(lL.. ~ , R (1)___ ------" I J. J. I 1 t H-C-C -C--C-C-C H-C-C-C-C-C-C I I . H 7/12 1/4 1/3 1/4 7/12 ...... --.,..-- ...... H 7(12 1/4 1/3 1/4 7/12 r.e.d. of pentadienyl radical f.e.d. of pentadienyl-----.....- radical for electrophilic reagent for nucleophilic reagent g. R(1)_R(2) type addition R(2) R(l)- - " H-C-C-C-C-C-.I.£. '" -C .t. I H 2/3 0 2/3 0 2/3 f.e.d.'------~------of pentadienyl radical for radical reagent FIG. 10. The frontier electron densities for addition to nexatriene (f.e.d. = frontier electron density). as in the highest occupied orbital,9 so that the pre· 6. ADDITION dicted points of attack are identical in any of electro· Addition reactions to a conjugated system may be philic, nucleophilic, and radical substitution. In most considered to proceed successively through the transi of hydrocarbons treated there predicted positions agree tion state similar to that of substitution. (Brownlo and very well with the points of the maximum free valency Dewarll assumed a simultaneous addition in their number, the values of which are found by Kooyman and treatment of the Diels-Alder diene synthesis. But, from Farenhorst6 to be parallel with the rates of radical the reaction-kinetical standpoint, successive mechanism substitution. 10 R. D. Brown, J. Chern. Soc. (London) 1950, 691, 2720, 3249 (1950) . e See our previous paper (reference 3). 11 M. J. S. Dewar, J. Am. Chern. Soc. 74, 3357 (1952). 1442 FUKUI, YONEZAWA, NAGATA, AND SHINGU TABLE V. Comparison of predicted structures of addition as one atomic 1(" orbital at the terminal carbon has dis products with experimental results. appeared as a result of the primary addition, the point of attack is now controlled by the electron Conjugated molecules Predicted positions Experimental results frontier density of a conjugated system consisting of five carbon butadiene 1:2,1:4 1:2,1:4 hexatriene 1:2,1:4,1:6 1:2,1:6" atoms. From the results shown in Fig. 10, it can be styrene a:", a:", concluded that the structures of the addition products stilbene a:(i a:a' are predicted to be 1: 2, 1: 4, or 1: 6, taking all the pos anthracene 9:10 9:10 phenanthrene 9:10 9:10 sible cases of addition into consideration. Experimen tally, addition product of bromine to hexatriene is 2 II Farmer. Laroria, Switz, and Thorpe, reference 12. reported to be a mixture of 1: 2- and 1: 6-dibromide.I Similar calculations for all the possible modes of is naturally to be preferred.) Then we can apply here addition are carried out as to butadiene, stilbene, sty the frontier electron method analogously, using the rene, anthracene, and phenanthrene. The results are in same classification into three types, viz., electrophilic a complete agreement with experiment, as is shown in (E), nucleophilic (N), and radical (R). Table V·II II " In discussing the reactivity in polyene and some It is possibly of importance in obtaining a knowledge aromatic molecules, seven cases§§§ of successive addi of the true feature of activated complexes to consider tion are to be considered according to the type of re the theoretical foundation of the fundamental postu agent, which are indicated in Fig. 10. lates, which, however, is omitted in the present paper Taking hexatriene as an example, the pri laryattack and will be published elsewhere. is predicted to occur at the terminal carbon atom, in The authors are grateful to the Education Ministry any case of E(l), N(l), and R(l). In the secondary attack, of the Japanese Government for a grant-in-aid. §§§ Combining the three types of primary attack, viz., N(l), E(l), 12 Farmer, Laroria, Switz, and Thorpe, J. Chem. Soc. (London) and R(l>, with three types of secondary attack, viz., E(2), N(2), 1927, 2937 (1927). and R(2), we have nine varieties of mode of addition. But the two " " 11 The frontier electron method is also useful in the treat among these, E(1)-E(2) and N(1)-N(2) type additions, which are ment of cationoid, anionoid, and radical polymerization, which not likely to happen, are left out of consideration. will be published elsewhere. THE JOURNAL OF CHEMICAL PHYSICS VOLUME 22, NUMBER 8 AUGUST, 1954 Contributions of Vibrational Anharmonicity and Rotation-Vibration Interaction to Thermodynamic Functions R. E. PENNINGTON* AND K. A. KOBE Department of Chemical Engineering, University of Texas, Austin, Texas (Received March 23, 1954) Certain correction terms applying to the rigid-rotator harmonic-oscillator approximation for the thermo dynamic functions have been worked out in a general form. Tables of the functions which appear in these correction terms are presented. These results have been applied in the calculation of the thermodynamic properties of nitrous oxide. A comparison of the present procedure and that of Mayer and Mayer for di atomic molecules is given. I. INTRODUCTION The calculations for determining these corrections are ORE detailed knowledge of the spectra of poly rather lengthy. Therefore, approximations to a general atomic molecules is gradually becoming avail ized partition function and its derivatives have been M worked out, and tables of the functions which appear in able. With the determination of the anharmonicity and the correction terms have been compiled. These tables interaction constants of a molecule it becomes possible were used to calculate the thermodynamic functions of to improve the statistically calculated thermodynamic nitrous oxide at selected temperatures. functions by taking these effects into account. Several papersH have dealt with this problem in some detail. II. THE PARTITION FUNCTION For the present purposes, it is assumed that the en * Present address: Bureau of Mines Petroleum Experiment ergy levels of some molecule of interest may be repre Station, Bartlesville, Oklahoma. 4 1 A. R. Gordon, J. Chern. Phys. 3, 259 (1935). sented in the nomenclature of Herzberg in the following 2 L. S. Kassel, Chern. Rev. 18, 277 (1936). 3 Stockmayer, Kavanagh, and Mickley, J. Chern. Phys. 12, 4 G. Herzberg, Infrared and Raman Spectra of Polyatomic 408 (1944). Molecules (D. Van Nostrand Company, Inc., New York, 1945).