Pedersen therefore proposed that the term “gel filtration” should be replaced by the term “exclusion chromatography” for the high molecular-weight range. Other authors disliked the name “filtration” fcr this chromatographic process and suggested the terms “restricted diRusion chromatography” [ 1581 or “gel permeation chromatography” [30]. However, 7iselius supports the hitherto usual term “gel filtration” [1801, and points out the fundamental difference between this and other chromatographic separations, namely, that the concentration in the stationary phase can, at the most, be only as great as that in the mobile phase. [180] A. Tiselius, J . Porath, and P.-A. Albertsson, Science (Washington) 141, 13 (1963). German version: Angew. Chem. 76, 635 (1964) Translated by Express Translation Service, London Some of the difficulties in nomenclature can be avoided by agreeing to the division attempted in this summary (from practical considerations, among others) into “gel filtration” and “gel chrornatogrnphy”. Whatever name is given to the process, its use guarantees clean and easy separation of substances with different molecular sizes, as shown by the profusion of the applications quoted. I should like to thank Doz. Dr. B. G‘elotte, A. B. Pharmacia, Uppsala (Sweden),for information and stimulating discussions. Received, October 22nd, 1963 [A 384/177 IEI Electron Affinity of Organic Molecules BY PROF. DR. G. BRIEGLEB INSTITUT FUR PHYSIKALISCHE CHEMIE DER UNIVERSITAT WURZBURG (GERMANY) Dedicated to Dr. W . Foerst on the occasion of his 65th birthday Theformation of organic radical ions by direct electron exchange between a donor molecule D and an acceptor molecule A is becoming increasingly imporfant,particularly with regard to reaction mechanisms involving intermediate radical ions. All redox processes also involve electron exchange. Finally, the knowledge of electron affinities and ionization energies of organic molecules is necessary for a quantitative theoretical interpretation of intermolecular resonance and of the semiconductor properties of crystalline organic compounds and molecular compounds. The electron-donating properties of organic molecules can be estimated from their ionization energies which for some organic molecules are directly measurable. However, direct experimental determination of the electron affinities of organic molecules, which govern their electron-accepting properties, was not possible until only a few years ago. This paper deals with the methods and means OF determining the electron affinities of organic molecules; the discussion will be restricted to neutral molecules and will exclude consideration of radicals as electron donors and acceptors. The electrondonor and electron-acceptor properties of aromatic hydrocarbons will be treated separately in Chapter IT. All the electron donors discussed this article are listed in Table 1 . Ej = -EA = EA- - ‘A + eo- The ionization energy I of an electron-donor molecule D is equal to the energy Ei of the highest occupied orbital of D in the ground state or to the difference in energy (E,-ED+ + e o - ) between the cation D+ + en- and the uncharged molecule D. Angew. Chem. internat. Edit.1 Vol. 3 (1964) 1 No. 9 = ED - E D’ + eo- The difference in energy between the lowest vibrational level of the ground state of the neutral molecule and the corresponding level of the ion is termed the a d i a b a t i c ionization energy, or the a d i a b a t i c electron affinity, respectively. The energy difrerence between the energy level of the ground state and that part of the potential curve of the ionized state to which - applying the Franck-Condon principle - transition is most likely to occur, is denoted as v e r t i c a l ionization energy and v e r t i c a l electron affinity, respectively. I. Organic Electron Acceptors (excluding Aromatic Hydrocarbons) The electron affinity EA of an electron-acceptor molecule A is the energy E j of the lowest unoccupied orbital of A in the ground state and is equal to the difference in energy (EA--EA + eo- ) between the anion A- and the unch,irged molecule A + eo-. (1) Ei = -I (2) 1. Electron Affinities Derived from the Electron Absorption Coefficient Lovelock [ 1 ] determined the electron absorption caefficient y, (3) ~~ -- Ie-I = [e-10 ex&% [A]) -- [ l ] J. E. Lovelock and R . S . Lipsky, J. Amer. chern. SOC.82, 431 (1960); J. E. Lovelock, Nature (London) 187, 49 (1960); 188,401 (1960); 189, 729 (1961). 617 Table 1. Electron donors discussed In the present paper. The numbering adopted here is also used in the text, in Figures I , 2, 3, 7, 8, and 9. and in Tables 3, 5 , 6 , 7, and 8. Numbers 66, 85, and 87 have keen omitted for technical reasons. No.1 Name Formula Nainz 0 1 ]Benzene Hexaphene 5 6 Benzo[c]pentaphene 7 Dibenzo[c,m]pentaphene Naphtha[2,3-clpentaphene 8 Benzo[a]perylene 9 D~henzo[a,j]peryIene I 0 10 Triphenylene Formula s Name 0.1 Formula & I 9 Acenaplxhylene 8 8 s n 1 Benzo(c]tetraphene 2 Toluene 3 m-Xylene 4 Mesitylene OCH3 3c, L>CH, IH,C <>CH, H3C CHI I Dihenzo[a,n]perylene D~henzo[h,pqr]perylene @? Trihenzo[h,k,pqr]perylene 88 2 - 3 4 Di henzo [h,klper ylene '8 20-Methylcholanthrene H3C@ I U 15 trans-Stilhene s 15 Benzo[tuv]bisanthene OCH=CHC ,9 9,10-Dimethylhenz[a]anthracene n 16 Benzo[j]terrylene 10 Aniline I I N,N-Dimethylaniline $2 18 Benzo[e]pyrene I-Naphthylamine Cfi, QNHz ON(CH,), CP $3 2-Naphthylaminc 19 Benzo[a]pyrene 19 Benzo[a]phenanthrene 20 Dibenz[a,j]anthracene 21 Picene 1 52 Dihenzo[e,l]pyrene 22 Pentaphene 23 Perylene 54 Dihenzo[a,i]pyrene 2 4 Benzo[ghi]perylene 55 Naphtho[2,3-e]pyrene 25 Coronene 68 26 Biphenyl @ 32 Benzo[c]fluorene &H? 56 Naphtho[2,3-a]pyrene 1 57 Dinaphtho[2,3-a:2,3,-h]pyrene % 93 9-Benzylidenefluorene 94 Benzo[ghi]Auoranthene 95 Benzo[h]fluoranthene K I 3 1 Trihenz[a,c,J]anthracene 33 Benzo[c]chrysene 34 Benzo[a]tetraphene w 6 3 Dibenzia,j]anthanthrene 64 Dihenz[a,k]anthanthrene Angew. Chem. internat. Edit. 1 Vol. 3 (1964) 1 No. 9 for the capture of thermal electrons e- by a few organic molecules A. This represents the only possibility for experimental determination of the relative order of electron affinities. Under experimental conditions for which [ec] [A], the absolute electron absorption becomes identical with the equilibrium coefficient constant K A 121: > x gAgA'ge- K - - - e (4) A- EA/RT -~[A-I - 1-41 [e-I The electron affinity EA can be calculated from Equation (4) by setting gA-/gA = 2, and hence gA-/gA .ge- = l. Lovelock reported several electron absorption coefficients x' K'A referred to chlorobenzene as standard (Table 6. Column 2). Wentworth and Becker [3] determined the absolute equilibrium constant for electron capture by anthracene. Using this value and Equation (4), they obtained a value of 0.42 eV for the electron affinity of anthracene. For a given acceptor A, and for Klanthracene = 12 [za], we have: 5 RT In K, (5) = EAA = RT In K , + 0.42 - RT In 12 The electron affinities of a few organic acceptors, calculated for = KIA using Equation ( 5 ) are listed in Table 5 , Column 3. x' 2. Electron Affinities derived from the Electron-Transfer Energy and from the Ionization Energy of the Electron Donor On the basis of Mulliken's theory [4] of intermolecular interaction between electron-acceptor and electron-donor molecules, it is possible to derive an expression for the energy FjcT of electron transfer from D to A in terms of the ionization energy I of the electron donor and the electron affinity EA of the acceptor [5,6]: (6) FjcT ~ = I - (EA-E) + E is predominantly t h e energy of t h e C o u l o mb attraction b e tween D+ a n d A- after t h e transfer of o n e electron f r o m D t o A . E also comprises t h e polarization energy [6, 71 a n d a n energycontribution AH from t h e intermolecular b o n d D.... A in t h e ground state. C2 can be calculated theoretically [61. Theoretically, Equation (6) is based o n t h e adiabatic ionization energy. However, i t is not yet certain whether t h e various methods for determining t h e ionization energy of organic molecules (e.g., t h e electron impact a n d photoionization methods) yield the adiabatic or t h e vertical ionization energy. It has been established that E and C2 can be assumed to be nearly constant, for electron-donor/electron-acceptor complexes (EDA complexes) of the same bond type [IO], so that for complexes involving one and the same acceptor, Equation (6) reduces to Equation (7). C1 can b e determined experimentally [ I l l by plotting 7cr against I for t h e EDA complexes o f a given acceptor with various donors, when Equation (7) is normalized t o a standar d , e.g. naphthalene. T h e electron affinities listed in Column 4 of Table 6, were calculated f r o m C1 according t o Equations ( 6 ) a n d (7) using t h e value E = Ecou~= -4.3 eV for the x,r-complexes. It was assumed here t h at t h e average intermolecular distance for t h e z,x-complexes is nearly constant. This assumption is supported by t h e fact t h at t h e validity of Equations (6) a n d (7) has been demonstrated f o r a large number of E D A complexes [I 11. T h e charge o n D+ a n d A- is shifted towards t h e center of t h e complex molecule. Because of t h e approximations used, electron affinities derived f r o m C1 (Table 6, Column 4) have a n uncertainty o f ab o u t *0.2 eV. In Table 2, the electron affinities calculated by Person [9] and by Jorfwer and S?kolov [I21 for the l~:.l~gens Table 2. Electron affinities [eV] for halogens and iodine chloride. CI, Eqs. (6) and cz I-(EA-E) EAvertical [ * ] I EA from Eq. ( 2 5 ) [**I 112.161 I ~ [2] [e-] : Stationary electron concentration at equilibrium; [e-10: electron concentration before approach of acceptor A to e!ectron gas; g: number of realizable quantum states ("quantum weight"). For e-, g = 2 ( s = + 1 1 2 ) ; see,for example. 7 . L . H i l l : Introduction to Statistical Thermodynamics, Addison-Wesley Publ. Co., Reading, Mass. (U.S.A.) 1960. Equation (3) can be written, to a good approximation, as follows: [e-l= [e-10 - [A-l= leIo(1 - x[Al). Then, for the case where [e-3 [A] or [A-] << [ e - ] ~we obtain: > [2a] If K c ~ BIS~ the electron-capture equilibrium constant for chlorobenLene, then, for an acceptor A, we have: KA/KCIBz K'A and Kanthracene/KCIBz = l 2 and hence: (4') KA = ( K ' ~ i 1 2 )' Kanthracene, The change in free energy for electron capture by A is by definition -EA = -RT InKA, and, hence, using Equation (4'), we obtain Equation (5). [3] E. W. Wrntworrh and R . S . Becker, J. Amer. chem. SOC.84, 4263 (1962). [4] R. S. Mnlliken, J. Amer. chem. SOC.72, 600 (1950); 74, 811 (1952); J. chem. Physics 19, 514 (1951); J. physic. Chem. 56, 801 ( 1952). [5] S. H. Hustings, J. L. Franklin, J . C. Schiller, and F. A. Matsen, J . Amer. chem. SOC.75, 2900 (1953); G. Briegleb and J. Czekalla, 2. Elektrochem., Ber. Bunsenges. physik. Chem. 59, 184 (1955); 6 3 , 6 (1959); Angew. Chem. 72, 401 (1960); R . Foster, Nature (London) 181, 337 (1958). 161 For further details, see G. Briegleb: Electronen-DonatorAcceptor Komplexe. Springer, Berlin-Gottingen-Heidelberg, 1961. Angew. Chern. internat. Edit. Vol. 3 (1964) No. 9 1.7 = 0.5 1.56 I I 1 . 2 1 0.5 1.48 1 1 1.3 + 0.4 1.3 I I 1.7 1 0.6 1.43 [*I Calculated theoretically from the potential curves for Hall and Hal-2 by applying the Morse function and making use of the interatomic equilibrium distance, dissociation energy, and fundamental vibrational frequency. [**I Relative t o the iodine atom with EA = 3.23 eV [I51 _ ~ -~ _ [7] The valence bond energy Eval contributes to a slight extent to the polarization energy Epol and vice versa. In general, Epol should be equal to about 0.1 Ecoul..Only for iodine-amine complexes does the contribution of Eval apparently become larger [8,8a], as a result of the relatively small intermolecular distance (about 2.3 .&). According to Person [9], for iodine-amine complexes Eval w 0.25 ECoul,: In the case of n, a-complexes, for example, those between iodine and amines, the constants C1 and C Zin Equation (6) are markedly different compared t o those for n,n- or n,a-complexes. H . Yada, J . Tanaka, and S . Nagnkura, Bull. chem. SOC.Japan 33, 1660 (1960) proved this for iodineamine complexes. See also [8 a]. [8] See [ h ] ,pp. 7, 18. 76, 79, 81, 132, and 173. [gal R. S. Mulliken, Annual Rev. physic. Chem. 13, 107 (1962) [9] W . B. Person, J . chem. Physics 38, 109 (1963). (101 x,o-; n,n-;n,a-; a,a-complexes; for further information see 161, pp. 5 et seq. [l 11 C. Briegleb and J. Czekalla, [5]; see also [6], pp. 74 el seq. [12] J. Jormer and U. Sokolov, Nature (London) 190, 1 (1961). 619 Table 3. Values of a and b [eVl from Equation (9) for electron-donorielectron-acceptorcomp!exes 2,6-Di. Tetracyanoethylene Chloranil 0.87 [*I 0.90 0.72 ['*I Brornanil chlorop-benzoquinone Ch'orop-benzoquinone 0.85 0.85 ___ 1 0.93 1'1 0.97 [**I p-Benzoquinone I ' g 3 5 Trinitrobenzene 0.85 0.97 0.85 ~~~ 4.86 [*] 3.48 [**I [191 [*I ["I I18al 4.5 1 4.94 ["I 5.27 [**I 4.36 4.19 1 3.89 4.5 _________ [18b,191 [18bl [18b] I181 [181 1181 I 3.9 i 2,4,6Trinitrotoluene m-Dinitrobenzene 0.85 0.85 1,. I 0.94 087 ~ _ _ _ _ _ _ _ 3 68 3.47 4.2 3.6 I __________ l18cI I181 [181 1181 [IScI [8aI €or polycyclic aromatic hydrocarbons Average values for substituted benzenes. To be precise, methoxybenzenes (a = 0.74; b halogenobenzenes (a = 0.60; b = 2.34) [18al woold have to be distinguished. and iodine chloride are given for comparison with those of organic acceptors. The order of these affinities seems reasonable. X-ray studies [I31 of the complexes of iodine and the other halogens with n-donors, particularly benzene, have indicated that a configuration in which the axis of the halogen molecule is vertical to the benzene plane is more probable than the alternative configuration with parallel axes. According to Equations (6) and (7) E, and Ell differ by about 1 eV [14]. At sufficiently large ionization energies (I > 7.5 eV), the third term in Equation (6) can be neglected: Hence, for EDA complexes between one and the same acceptor and various donors, the following approximation is often used 1171, As comparison with Equation (6) shows, the term b in Equation (9) contains the electron affinity of the acceptor and the Coulomb energy E ; thus, when E is nearly constant, b can be taken as a measure of the electron affinity and is therefore often referred to as the a p p a r e n t electron affinity. For EDA complexes of the same bond type [lo] the term a can be assumed to be constant, i. e., largely independent of the acceptor. This, however, is not always true, particularly for interactions with weaker donors [18] (cf. Table 3, where the values of a and b obtained from Equation (9) are listed for a few acceptors). The values of a and b for complexes of the very strong electron-acceptors tetracyanoethylene and bromanil with polycyclic aromatic hydrocarbons [13] 0. Hassel, Molecular Physics 1 , 241 (1958); 0. Hassel and K . 0. Stromnte, Acta chem. scand. 12, 1146 (1958). I141 The value EA = 0 . S eV for 12 quoted by Briexleb and Czekalla 151 refers to the parallel model, which was originally adopted because of symmetry considerations [4] arising from the quantum-mechanical group theory. [IS] 0 . H . Pritchard, Chem. Reviews 5 2 , 529 (1953). (161 It is improbable that the values of E for EDA complexes of atomic iodine, molecular halogens, and TC1 are identical. However, the order of the electron affinities calculated by Jortner and Sokolov [12] agrees -. within the limits of error - with the electron affinities calculated by Person [9] for the vertical model. 1171 H . McConnel, J. S . Ham, aad J . F. Platt, J . chem. Physics 21, 66 (1953). [18] R . Faster, Tetrahedron 10, 96 (1960). 620 = 3.64), methylbenzenes (a = 0.68): b = 3.01), and differ from those obtained for their complexes with substituted benzenes [18a, 191. Judging from the strengths of their EDA complexes with aromatic hydrocarbons, the following order of electron affinities can be derived from the b values listed in Table 3: bromanil > tetracyanoethylene > chloranil = 1,3,5trinitrobenzene > 2,6-dichloro - p - benzoquinone > chloro-p-benzoquinone > p-benzoquinone > 2,4,6trinitrotoluene > m-dinitrobenzene. This order is not ic7 agreement with the relative order of electron affinities resultiog from Equations (9,(7), (14), (23), and (25); see Table 6. Obviously, the constant b in Equation (9) is less suitable to determine a relative sequence of electron affinities. From Equations (8) and (2) we obtain As we shall see in the following, there are numerous possibilities for expressing I or -Ei by means of other quantities. 3. Electron-Transfer Energy as a Function of the Ionization Energy of the Donor For polycyclic aromatic hydrocarbons as donors, it follows from Hiickel's simple A M 0 theory that : (11) E.=-l=a o + f".P In Equation (1 l), a0 is t h e Coulomb integral, the resonance integral for t w o neighboring atoms (k, l), an d fH is t h e Hiickel coefficient which expresses the contribution of p to t h e total energy Ei. T h e electron overlap integral is assumed to b e zero, an d t h e electron repulsion is neglected. T h e decrease in electron repulsion on transition f r o m D t o D+ may be taken i n t o account (by a decrease in t h e Coulomb attraction) in or0 [20]. In a simplification recently proposed by -____ [ l sa] E. M . Voigt, Ph. D. Thesis, University of British Columbia, 1963. [18b] M . Kinoshita, Bull. chem. SOC.Japan 35, 1609 (1962). [18c] See [6]; pp. 79 et seq. 1191 H . Kurodn, M . KrrbaJ%zshi,M . Kinoshita, and S . TakenJoro, J. chem. Physics 36, 457 (1962). 1201 G. W . JVhehelnnd and D . E. Mann, J. chem. Physics 17, 264 (1949) assume that the increase in a, expressed in units of 8, is proportional to the positive charge (I-q)p on the carbon atom (q is the relative negative charge on the carbon). Angew. Chem. internat. Edit./ Vol. 3 (1964) No. 9 Ehrenson [22], OL can b e expressed in units of a n d p a r e negative; la1 < la"(): p a s follows (cr,cro, a (12) = ao-(l-l/n)c@ where co is a n empirical proportionality factor a n d n is t h e number of conjugated =-electrons in t h e aromatic hydrocarbon. Substituting cc for CIO in Equation (11) and using Equation (12), we obtain: -Ei (13) = I = - (f -NO H - n- 1 ~~ n w)p = -a0 - xp When cc = -9.878 eV, F = -2.11 eV, and w = 1.4 [21], Equation (1 3) gives satisfactory values for the ionization energy of aromatic hydrocarbons [22]. Substituting Equation (13) into Equation (lo), one obtains : (14) GCT = (14a) k -EA-ao = (-EA-ao + E)-@ = The charge-transfer band maxima GCT for EDA coniplexes between the acceptors given in Table 4 and the donors listed in Column 5a of Table 6 and the corresponding x values are related by the linear function represented by Equation (14). The values of p and k calculated from this linear QCT vs. x relationship, and the electron affinities derived from the k values obtained from Equation (14a) by setting E = -4.3 eV and cco = -9.88 eV are listed in Table 4 for the electron acceptors tetracyaneethylene, chloranil, 2,4,7-trinitro-9-fluorenone, 1,3,5-trinitrobenzene, and iodine [23]. Table 4. Electron affinities of a few typical organic electron acceptors and of iodine, calculated from the values of k obtained according to Equations (14) and (14a) [*I. 1 1 k-xp Tetracyanoethylene 1 I I -p [eVl 2.2 +E This expression is based on the observation that the values of EA and E for EDA complexes of analogous donors (e.g. polycyclic aromatic hydrocarbons) with one and the same acceptor are nearly constant. According to Equation (14), CcT should be linearly proportional to K. Figure 1 shows for the example of the EDA complexes of tetracyanoethylene with aromatic hydrocarbons that this requirement is satisfactorily fulfilled, considering the variability of E and CcT and the uncertainty in I as obtained from Equation (13). (The values of x and f, in Figure 1 are listed in Columns 5 and 6 of Table 4.) Chloranil ~ 2'437Trinitro9-fluorenone 1 ;:; I ;:: 2.3 k [eVl 3.67 EA [eVl 1.9 1 1 Trinitrobenzene I 2.6 1 1.9 & ; ['I For 12, E = -4.3 eV or E = - 3 . 5 eV, depending parallel or vertical model is considered. ~ 011 4.55 1.0 (11) whether the Within the limits of error (!c 0.2 eV), the electron affinity values calculated using Equation (14) are in good agreement with those calculated from C1 in Equation (7); compare Columns 4 and 5 of Table 6. The values of listed in Table 4 refer to the aromatic hydrocarbons summarized in Column 5a of Table 6 and correspond to the values quoted by Streitwieser [21] and Hoijtink [31]. 9 4. Ionization Energy and Intermolecular Electron- Transfer Energy as a Function of the Electron Excitation Energy C , of Aromatic Hydrocarbons as Donors Setting for a given molecule, in general: (15a) Ei = cc+ f . p (15b) Ej = OL and + T.8, we obtain For the energy difference between the highest occupied and the lowest unoccupied orbital : 1/ 073 I -100 EBZ I I - 60 -80 x I I -20 -LO loZ-- Fig. 1. Linear dependence of the electron transfer energy CCT on the value of K obtained from Equation (14) for tetracyanoethylene-hydrocarbon complexes (the numbers refer to the hydrocarbons listed in Table 1). [23] Instead of Equation (lo), Dewar and Lepley [241 use C ~ = T I-EA = E.-Ei (10) In other words, the energy term E is omitted. Moreover, Dewar and Lep1e.v use Hiirkel's simple equation [Equation ( I l)] for I and obtain, in place of Equation (14), a linear relationship between CCT and f H : (14') ~ C = T k'-fH P (14a') k' = - E A - q ~ [21] A. Streitwieser and P . M . Nair, Tetrahedron 5 , 149 (1959); A. Strritwieser, J. Amer. chem. SOC.82, 4123 (1960). - Hoijtink's calculations [3 I], based on the one-electron half-wave reduction potential of aromatic hydrocarbons (p. 626 and p. 629), in combination with Hiirkel's equation [Equation (15b)l and Whelnnd's f'-values [20], gave an average value of p= -2.26 eV. See also P. Balk, S. De Brui.vn, and G . J. Hoijtink, Recueil Trav. chim. Pays-Bas 76, 860 (1957). [22] S . E. Ehrenson, J. physic. Chem. 66, 706 (1961). Angew. Chem. internat. Edit. 1 Vol. 3 (1964) 1 NO. 9 [*I I 2.35 ~ Iodine However, the simple. uncorrected Huckel equation [Equation (1 l)] gives less satisfactory values for the ionization energy than Equation (13) 1211. In addition, the values of k' calculated by Dewar and Lepley from Equation (14') differ by a factor of E from those obtained using Equation (14). As a result, the EA values derived from k' are 3.5-4.5 eV too high. [24] M . J. S . Dewar and A. R. Lepley, J. Amer. chem. SOC.83, 4560 (1961); M . J . S . Dewar and H . Rodgers, ibid. 84, 39.7 (1962); A. R. Lepley, ibid. 84, 3577 (1962). 62 1 1.95 (1) From Equations (15a), (15b), and (16). we obtain: E. = a (17) f + -. f‘-f Go The data listed in Column 6 of Table 5, show that f/(f’-f) is in rough approximation constant for several aromatic hydrocarbons for which f and f‘ have been calculated theoretically [26]. Hence, from Equation (12), the ionization energy will be, in general: b) by basing the calculation o n the 0,O-frequency Voo, provided the latter can be identified [25]. Matsen [26] selected for CO the frequency of the longest wavelength absorption maximum (Table 8, Column 6), as recommended by Clar [27], and obtained (19) 1 2 3 No. I [261 Eq. (I5a) -f‘ 1261 “I Eq. (15b) 5 f E‘-f 6 1.000 0.618 0.414 0.167 0.642 0.887 1.333 3.731 3.462 1.37 1.45 1.45 4 3.369 3.232 3.713 1.42 6 0.275 0.208 0.526 1.40 0.220 0.605 1.117 0.696 7 10 11 0.406 D.584 0.444 3.510 j.825 3.570 1.44 1.42 1.43 0.452 0.684 0.499 0.870 0.648 0.538 14 16 0.460 0.423 3.598 3.587 1.44 1.42 0.520 0.473 0.802 0.864 19 0.497 0.438 3.662 3.561 1.42 1.44 0.49 1 0.846 3.574 3.49 3.38 1.44 1.45 1.46 0.501 0.836 0.347 0.983 0.439 0.539 0.704 0.898 0.502 0.580 0.445 0.497 0.371 0.868 0.833 0.959 51 0.398 0.442 0.943 0.899 65 66 67 0.477 0.662 0.592 0.783 0.660 0.730 68 69 71 57 0.635 0.637 0.405 0.400 0.649 0.647 0.932 0.947 89 90 91 0.405 0.618 0.520 0.945 0.695 0.793 92 93 94 0.505 0.650 0.630 0.808 0.680 0.702 95 96 0.600 0.500 0.730 0.830 97 98 0.410 0.230 0.937 1.136 21 22 23 24 25 26 47 48 49 50 0.446 0.394 0.320 0.475 0.599 3.632 3.855 1.46 1.41 0.401 0.406 3.501 3.501 1.44 1.50 + 0.857 CO [eV] (Fig. 2, 11) I = 5.156 + 0.775 GO [eV] (Fig. 2, 111) Considering the ionization energies (which have been determined with some certainty for only relatively few aromatic hydrocarbons), cf. Table 8, Column 4, and using the 10frequencies (Table 8, Column 6), we obtain: Eq. (1 3) 0.800 0.535 0.375 20 4.39 --K fH 1 2 3 5 = Becker and Wentworth [28] based their calculation on the 0,O-frequency and obtained: (20) Table 5. Corrected and uncorrected Huckel coefficients and values of -K for some aromatic hydrocarbons I (21‘ 3 I = 5.11 + 0.701 Go [eV] (Fig. 2, 1) 35 Fig. 2. Experimentally determined ionization energies Iexp (Table 8, Column 4) of some aromatic hydrocarbons as a function of their first excitation energy GO (Table 8, Column 6); the numbers refer t o the hydrocarbons listed in Table I . Differing ionization energy values were obtained for Nos. 2, 3, 4, and 6 by various authors using different methods. I: Equation (21); 11: Equation (19); 111: Equation (20). The ionization energies calculated from Equation (21) are listed in Column 5 of Table 8. Substitution of Equation (18) into Equation (10) gives (since I = -Ei): JCT = YGO + C-EA + E (22) Considering EDA complexes of the same bond type [lo] between an acceptor and analogous donors (e.g., angularly condensed, unsubstituted aromatics), so that E = -4.3 eV [29] may be considered as nearly constant, we obtain : JCT = YO” + C’ (23) where C’ = C-EA [*I The numbers refer to the hydrocarbons listed in Table I Equation (18) can be fitted t o experimental data only with limited accuracy, because ionization energies are known to within a n accuracy of 0.1 -0.2 eV for only a few aromatic hydrocarbons. Moreover, often th e first excitation energy of aromatic hydrocarbons cannot be determined with great accuracy. This energy is determined a) by taking t h e maxim u m of the longest wavelength absorption b an d as Qo, an d 622 15 1 +E -~ [25] The 0,O-frequency is the excitation energy required to raise an electron from its zero vibrational energy level in the ground state to the zero vibrational level in the excited state. [26! See, among others, F. A . Muneiz, J. chem. Physics 24, 602 (1956); G. W. Wheland, J. Amer. chem. SOC.63,2025 (1941). [27] E. Clurr Aromatische Kohlenwasserstoffe, Springer, Berlin 1941. [28] R. S . Becker and W. E. Wentworth, J. Amer. chem. SOC.85, 4263 (1963). Angew. Chem. internat. Edit. Vol. 3 (1964) 1 No. 9 Substitution of Equations (18) and (21) into (23) reduces the latter to: Gcr (23’) = 0.701 ’70 + 0.81-EA [eV] ~ 9 1 The calculation of electron affinities from Equation (23’) is limited by the inaccuracy in the values of I obtained from Equation (18) or (21). The uncertainties in the values of Iexp and GO or q00 are strongly reflected in those of the electron affinities (variations of 0.2 to 0.3 eV). The electron affinities of acceptors in EDA complexes with aromatic hydrocarbons of known excitation frequency GO can be calculated using Equation (23’) provided the values of FCT for the EDA complexes are known. The electron affinities of a given acceptor in EDA complexes with various donors (Table 6, Column 6a) were calculated using Equation (23’) and the average values are listed in Column 6 of Table 6. Figure 3 shows a plot of the electron-transfer energies FcT I.”. the first excitation energies GO of a series of aromatic hydrocarbons for EDA complexes of 1,3,5trinitrobenzene, chloranil, and tetracyanoethylene. The values given in parentheses in Equations (24a)-(24c) correspond to the experimental straight lines shown in Figure 3. The deviations of the values given in parentheses from those expected from Equation (23’) fall within a range of inaccuracy of about 0.2 eV. The averaged electron affinities calculated by different methods, viz. according to Equations (9, (7), (14), (23’), and (25), are collected together in Table 6, Column 8. For EDA complexes of a given acceptor (EA = const.) with analogous donors (E = const.), it follows from Equation (22) that: GcT-SO (23”) (23”a) C” = C-EA = (y-1) Go + C” + E = 0.81-EA and from (21) that: (23”’) G0-GcT = 0.299 90-0.81 + EA [eV] Thus, although we have complexes of one and the same acceptor, i.e. EA = constant, (+JCT) is not constant, as is to be anticipated if Hiickel’s simple relationships [Equations (15a) and (15b); f = f’] were valid; instead, (Go-Gcr) decreases as the wavelength of the first excitation energy of the donor increases. The empirical approximate constancy of F0-FcT [6, p. 741 is valid only for aromatic hydrocarbons of nearly equal 5,) within the limit of accuracy (about 0.2 eV) of Equation (23”’). 5 . Electron Affinities Relative to Chloranil If we assume that for EDA complexes of the same bond type [lo] and configuration [6,13], e . g . n,Tt-complexes E may be considered to be nearly constant - a n assumption that is approximately correct then from Equation (8) we obtain the following expression for two acceptors, relative to one and the same donor: I - (25) ( ~ C T ) I - ( ~ C T ) k= EAk-EA; Hence, after normalization to a given standard acceptor, Equation (25) can be used to calculate the electron affinities of other acceptors of the same type [30]. In Column 7 of Table 6, a list is given of electron affinities relative to chloranil (EA = 1.37 eV) calculated using Equation (25) . 25 rn 35 3 L 45 $[eVl- Fig. 3. Relationship between the electron transfer energy ’ ~ C T and the for a few EDA complexes of the accepfirst donor excitation energy tors tetracyanoethylene (I), chloranil (II), and trinitrobenzene (111). The numbers refer to the hydrocarbons (donors) listed in Table 1 . (24a) Tetracyanoethylene: (EA = 1.8 eV) qcT = 0.701 GO-0.99 (0.72) [eVj (24b) Chloranil: (EA = 1.37 eV) JcT = 0.701 Fo-0.56 (0.37) [eV] I , 3,S-Tr initro benzene : (EA = 0.7 eV) G,, = 0.701 GO-0.10 (0.3) [eV] (24c) - -~~ [29] For halogens and XY-type interhalogen compounds, we must set E = -3.5 eV, in accordance with the vertical model (p. 619). Equation (23’) then becomes ?CT = 0.701 50 + 1.61-EA Angew. Chem. internat. Edit. 1 Vol. 3 (1964) No. 9 The agreement between electron affinities calculated from Equation (25) and those obtained from Equations (5),(7),(14), and (23’) in Columiis 3,4,5, and 6 of Table 6, respectively, is satisfactory. The accuracy of the absolute electron affinity values is certainly not better than about 0.2 eV. Considering this error, their relative order should be correct. [30] M . Butley and L. E. Lyons, Nature (London) 196,573 (1962) use iodine a s acceptor standard. With iodine (EA = 1.8 eV) and Equation (25), they calculate the values of EA for x-acceptors (quinones, trinitrobenzene, tetracyanoethylene, etc). However, since it is known that EDA complexes of iodine (which is a aacceptor) have an entirely different configuration than the corresponding complexes of x-acceptors (trinitrobenzene, chloranil, etc.) [6], it is certain that the values of E [Equation (8)] for the iodine complexes are different from those for the x-acceptors (cf. the values of E given o n p. 621 for the parallel and vertical model of iodine complexes with aromatic hydrocarbons). The values of E for EDA complexes of iodine with aromatic hydrocarbons are aboutO.S-1.0 eVIess than the values for n-acceptors. Correspondingly, the electron affinities (relative to iodine) of rr-acceptors calculated by Butley and Lyons should be too high by the same amount. 623 -- - 0 P ? 0 '9 m o 22 ? P ? ? - 0 0 0 L lli 0 0 - 2nc m y1 b n 8 c g -v W U .- c P L 0 rd u -0 m L lli x 0 n F z W w W 5 c-" 624 u - 4 0 Z m o - N W b b b Angew. Chem. internat. Edit. / Vol. 3 (1964) / No. 9 Dibromopyromellitic dianhydride 5-Hydroxy-1,4-naphthoyuinone Pyromellitic dianhydride Diacetyl Ethyl pyruvate Diethyl maleate Diethyl fumarate Dimethyl oxalate Tetrachlorophthalic anhydride Maleic anhydride Acctamide Acetylacetone Ethyl acetoacetate Ethyl acrylate Phthalic anhydride Carbon tetrachloride Hexachlorobenzene Chloroform 57 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 0.59 0.40 0.39 0.54 3.16 0.00 0.78 2.57 3.00 0.95 0.42 0.34 0.32 0.25 0.65 0.58 0.57 1.08 -0.15 -1.00 3.84 3.00 2.90 0.08 0.60 0.60 0.60 0.59 0.59 3.30 3.23 3.23 3.18 3.10 - -- 0.40 0.58 0.54 2.59 [**I According to P. R. Hammotrd, J. chern. SOC.(London) 1964, 471, the following electron affinities are obtained for monosubstituted pbenzoquinones from the FCTvalues of the EDA-complexes with hexamethylbenzene using Equation (25): NOrbenzoquinone: 1.45; CN-benzoquinone: 1.04; F-benzoquinone: 0.91 ; CI-benzoquinone: 0.97; I-benzoquinone: 0.95; CH,-benzoquinone: 0.75. These values correspond t o those given in Table 6. ['I For key numbers t o donors, see Table 1. 58 Nitrobenzene 1,2-Dinitrobenzene 2.4.6-Trinitrotoluene 2,4,6-Trinitro-m-xylene 2,4-Dinitrotoluene Dinitrophenol Chlorobenzene Broniobenzene Iodohenzene Hexachloro benzene Azobenzene 1,4-Dicyanobenzene 1,3,5-Tricyanobenzene 1,2,4,5-Tetracyanobenrene 43 44 45 46 47 48 49 50 51 52 53 54 55 56 0.6 50, 51, 65-69,71. 3.71 3.65 0. I 0.84 0.86 1.09 [i] 10, 11. 14, 16, 21, 23, 25, 47, 49-51, No. 2, 3, 6, 7, 10, 14, 16, 21. 23, 25, 47-49, 71. [h] No. 2, 3, 5-7, 71. Is] No. 2, 3, 6, 7, 10, 11, 14, 16, 21, 23, 25, 47, 49, 51, 71. [r] No. 2, 3, 6, 26, 47. [q] No. 1-4. 6, 7, 10, 14, 16, 21, 23, 25, 47, 49, 72-75, 77, 79--54, 99. 6, 7, 10, 14, 16, 21, 23, 25, 47, 49, 68. [p] No. 2-4, No. 2, 3, 6, 23, 47, 49. 101 No. 1-3, 15, 23, 47, 49, 72-74, 77, 80-82, 84, 99. [€I No. 2-4, 6, 7, 10, 14, 16, 21, 23, 25, 47, 49. [g] [n] No. 1-4, 6, 7, 10, 14, 16, 21, 23, 25, 26, 47, 49, 72-86, 99. [el No. 2, 3, 6, 10, 25, 47. [k] No. 2, 3, 6, 7, 10, 14, 16, 21, 23, 25, 26, 47, 49, 72-77. [I] No. 73-75, 77. f1.31 t8.60 f0.8J t0.32 t0.52 t0.55 [m] No. 2, 3, 6, 10, 25, 26. 47, 85. 65.68, 69.71, 89-98. 0.15 0.57 0.41 0.3, 0.3 0.25 0.58 0.6 0.6 0.6 0.6 0.6 0.85 1.16 0.9 0.1 0.4 t O 0.5 .'- 0 0.6 0.4 0.1 0.6 0.4 0.4 0.57 0.6 0.4 [dl No. 2, 3, 6, 7, 10, 14, 16, 21, 23, 25, 47, 49. 21, 23, 25,47-51, 41.77 [rl 47 47.77 86 47.77 86 86 86 47 86 86 86 86 [cl No. 1-3, 6. 7, 10, 11, 14, 16, 20, 21, 23, 47, 49, 51, 69. [bl No. 2, 3, 5-7,10,11,14,16, [a] No.l,2,6,7,10,11,14,16, 20, 21,23,25,26,47-49, 0 0.56 0.57 0.6 0.9 0.8s 1.16 0.1 0.4 + 0 0.57 0.6 0.4 0. I -0 - 6. Electron Affinities from Polarographic Half-Wave Reduction Potentials The first step of reversible polarographic reduction of an electron acceptor or of reversible oxidation of an electron donor proceeds as follows: = -3.66 eV, obtained as an average value from the ~ ~6, Column ~ ~ lo), we obtain: values of A F (Table EA (28) = -ERed ‘/2 + 1.41 Figure 4 shows a plot of EA against E;Zd [34]; the agreement with Equation (28) is satisfactory. The straight line in Figure 4 corresponds to Equation (28‘). (28’) EA = -1.04 EtZd + 1.39 [eV] MuccuZ[31] was the first to show tinat, for angularly condensed aromatic hydrocarbons, there is a relationship between the polarographic one-electron half-wave reduction potential, ECZd, and the energy of the highest unoccupied orbital, Ei. The reduction potential, measured against a saturated calomel electrode, is given by the expression : Fig. 4. Linear relationship between the electron affinity and the typical half-wave reduction potential according to Equation (28’); for acceptors in zcetonitrile and dimethylformamide as the numerical values and numbering of the acceptors, see Table 6. solvent. The half-wave potentials are largely independent of the solvent. Usine EA’ and EA (Table 6, T h e average value of AFsoiv (-3.66 eV) for t h e acceptors in Column 6) in Equation (27), it is possible to calculate Table 6 is of t h e correct magnitude, a s indicated by comparithe difference in solvation energy of the anion and of son with the solvation energies t h e anions o f aromatic hydrothe neutral acceptor molecule A F (Table ~ ~6, Column ~ ~ carbons (Table 8, Columns 8 an d 9). T h e values of AFsolv for lo). SinceA-FsoIv AFsolV,the major part of A F ~ t h e~acceptors ~ ~(Table 6) are relatively constant; this is probably d u e t o t h e fact that t h e negative charge of the A- ion is represented by the solvation energy of the anion. AFsolv m A-FsolV is nearly constant [35]. For h-Fsolv is located in certain parts of t h e molecule (e.g. -C=O, -C=N, Peuvdr [34] measured ECZd for a number of > .- [31] A. Mnccoll, Nature (London) 163, 178 (1949); L . E. Lyons, ibid. 166, 193 (1950). In addition: A. Pullman, E . Pullman, and G. Berthier, Bull. SOC.chim. France 591 (1950); G . J. Hoijtink, Recueil Trav. chim. Pays-Bas 74, 1525 (1955); G. J . Hoijrink, E. de Boer, P . H . van der Meij, and W . P . Weijlnnd, ibid. 75,487 (1956); P . Balk, S . de Bruyn, and G. J. Hoijtink, ibid. 76, 860 (1957); P. H . Given, Nature (London) 181, 1001 (1958); P . H . Given and M . E. Peover: Advances in Polarography. Pergamon Press, London 1960, p. 948; M . Eatley and L. E. Lyons, Nature (London) 196,573 (1962); M . E. Peover, J . chem. SOC.(London) 1962, 4540. [32] E . A . Matsen, J. chem. Physics 24, 602 (1956); R . M . Hedges and F. A . Matsen, ibid. 28, 950 (1958); G. J . Hoijtink and J. van Seliootan, Recueil Trav. chim. Pays-Bas 71, 1089 (1952); A. Lainlinen and S. Warzonek, J. Amer. chem. SOC.64, 1765 (1942). [33] The electrochemical process: Asolv + C l ~ o +~ vHqiq + AFolv 7 (HgCl)solv:(E~~d) -NO2 groups), whereas in the anions of polycyclic hydrocarbons, the negative charge is dispersed over larger portions of t h e molecule. Therefore, in these cases A-Fsolv is not constant. Since Equation (28) is fulfilled satisfactorily, Equation (28’) can be used to estimate the electron affinities of acceptors for which only Et:d has been measured. Electron affinities calculated in this manner from Equation (28’) are listed for a few acceptors in Column 1 1 of Table 6. According to Equations (27) and (8), there must be some relationship between CCT and EZ :d [35] when CcT is based on EDA complexes of different acceptors with one and the same donor: can be separated into the following steps Agas + e- + ~ s o l v+ Agas Hqiq + + Cl&lV (29) : (-EA) A& gas + ~ + (HgCI),,IV o :~( ~ ~ l vA Fs o ~ v - A ~ s o ~ v ) v s o= + e- (in Hg) : ( A F H ~ ~ c I= , e- (in Hg) + Hgliq + e- E H ~ ~= c0.53 ~ ~eV) : (4.54 eV) According to Equation (26a), negative values of ECZd should be used for strong acceptors, and positive values for weak acceptors (the sign is sometimes given in the opposite sense). AFsolv is negative, EA is positive by convention. It is assumed that electron addition a t a dropping mercury electrode according to Equation (26a) is sufficiently fast and reversible so that overvoltage phenomena and secondary reactions can be neglected. Moreover, no proton addition should take place (solvents devoid of proton activity, such as acetonitrile, dimethylformamide, or dioxane, must be used). 1341 M . E. Peover, Nature (London) 191,702 (1961); Trans. Faraday SOC.58, 656, 2370 (1962). [35] M . E. Peover, Trans. Faraday SOC.58, 1656 (1962). 626 ECZd = GCT-(I + E-AFsoIv-5.07) If the ionization energies of pyrene, hexamethylbenzene, and tetramethyl-p-phenylenediamineare taken as 7.8, 8.0, and 6.7 eV, respectively, and E = -4.3 eV is used for the Coulomb energy of the EDA complexes of the acceptors listed in Table 6 (for complexes with tetramethyl-p-phenylenediamine E = -3.9 eV), the following linear relationships result for the different acceptors, when A F in ~Equation ~ ~ (29) ~ is assumed to be -3.66 eV : (30) Pyrene: Eczd = GcT-2.09 (2.13) [eV] Hexamethylbenzene: EcZd = C,,-2.29 Tetramethyl-p-phenylenediamine:Er)Zd (2.40) [eV] = CcT-1.35 (1.365) [eVl Angew. Chem. internat. Edit. Vol. 3 (1964) I No. 9 The numerical values refer to straight lines plotted in Figure 5 which best fit the experimental Ef)zd and ~ C T . values. Because of the uncertainty in E and the variability of A F ~ deviations ~ ~ ~ , are not of great import an ce . tron-transfer energy GCT and the electron affinity EA of the acceptor. Applying the ionization energies and values of E given above for pyrene, hexamethylbenzene, and tetramethyl-p-phenylenediamine, Equation (8) gives the following linear relationships : (33) 7' t Pyrene: GCT Hexamethylbenzene: qCT = -EA = -EA + 3.51 (3.42) [eV] + 3.7 (3.75) [eV] Tetramethyl-p-phenylenediamine : JCT = -EA + 2.8 (2.78) [eV] 3 --7=25 The straight lines in Figure 6 refer to the numerical /=la values given in parentheses. In view of the relatively large inaccuracy in the EA values, the agreement between Equations (33) and (8) is satisfactory. Fig. 5. Correlation between the half-wave reduction potential of the acceptor Et:d [34,35] and the electron transfer encrgy ?CT f o r donor acczptor complexes, according t o Equations (29) and (30). Donors: tetramethyl-p-phenylenediamine (I), hexamethylbenzene (II), and pyrene (111). The numbers on the experimental points refer t o acceptor numbers given in Table 6. 7. Electron Affinities from Polarographic HaIf-Wave Oxidation Potentials According to Equation (26bj, polarographic oxidation of aromatic unsubstituted and substituted hydrocarbons may be described in terms of a relationship corresponding to Equation (28) in which the first polarographic half-wave oxidation potential is a function of the ionization energy of the hydrocarbon. Pysh and Yung [36] found empirically: (31) 1 = 1.473 EG: + 5.82 From Equations (31) and (8), using E obtain: (32) EA = -GcT = --4.3 eV, we + 1.473 E: + 1.52 The values of :E : [36] and VCT for E D A complexes between the donors listed in Column 12a and the acceptors listed in Column 1 of Table 6 have been determined experimentally. Thus, for the donors in Column 12a, the electron affinities can be caiculated and averaged using Equation (32) [see Column 121. However, the electron affinities obtained from Equation (32) are somewhat low compared to those obtained and averaged using Equations (23') and (25) [see Table 6 , Column 81. 8. Correlation between Electron Affinity and ElectronTransfer Energy It follows from Equation (8) that, for complexes of one and the same donor with various acceptors, an approximately linear relationship must exist between the elec[ 3 6 ] E . S . Pysk and N . C. Yung, J. Amer. chem. SOC.8.5, 2124 (1963). Angew. Chem. inrernat. Edit. 1 Vol. 3 (1964) 1 No. 9 Fig. 6. Electron-transfer energy SCT of E D A complexes as a function of the electron affinities F A of various acceptors, according t o Equation (33). Donors: tetramethyl-p-phenylenediamine(I), pyrene (II), and hexamethylbenzene (111). For the values and acceptor numbering, see Table 6. 9. Electron Affinity and Chemical Constitution The relatively great inaccuracy in the electron-affinity values precludes discussion of the more refined effects induced by the structure of the compounds involved. The strongest acceptors are 2,3-dichloro-5,6-dicyano-pbenzoquinone, tetracyanoethylene, 2,6-dinitrobenzoquinone, tetracyano-p-benzoquinone, 2,3-dicyanobenzoquinone, and bis(dicyanomethy1ene)quinones. The electron affinities of unsubstituted quinones lie in the following order: 9,lO-anthraquinone < I ,4-naphthoquinone * 9,lO-phenanthrenequinoneM 1,2-naphthoquinone w pbenzoquinone < o-benzoquinone < 1 &diphenoq u i none. Alkyl substituents tend to reduce the electron affinity, the effect becoming more pronounced as their number increzses. Electrophilic (halogeno, CN, NOz) groups 627 tend to augment the electron affinity of a compound, this effect increasing with the number of such substituents. C N and NO2 tend to increase the electron affinity to a larger extent than do halogens. C1, Br, and 1 do not differ appreciably in this respect. The nitroaromatics are relatively good acceptors : 2,4,7-trinitrofluorenone > 1,3,5-trinitrobenzene KY 1,4-dinitrobenzene > nitrobenzene > 1,3-dinitrobenzene > 1,2dinitrobenzene. With the exception of 1,2-dinitrobenzene, the electron affinity increases with increasing number of nitro groups. Unexpectedly, the electron affinity of 1,3-dinitrobenzene is less than that of nitrobenzene. (Since the electron affinity of these two nitro compounds has been determined only once, and by two different methods, this difference may be due to the difference in the methods used.) The fact that the electron affinity of 1,2-dinitrobenzene (in contrast to that of I ,3- and 1,4-dinitrobenzene) is practically zero is consistent with steric inhibition of the mesomeric stabilization of the 1,2-dinitrobenzene anion, i. e., both nitro groups cannot become coplanar with the benzene ring. Substitution by methyl generally decreases the electron affinity: 1,3,5-trinitrobenzene > 1,3,5-trinitrotoluene > 1,3,5-trinitro-rr;-xylene; also, 1,3-dinitrobenzene > 2,4-dinitrotoluene. The polycyanobenzenes are definitely poorer acceptors than the corresponding nitrobenzenes. The electron affinity of polycyanobenzenes increases with increasing number of cyano groups. Simply substituted halogenobenzenes are relatively good acceptors. An increase in the number of halogen s u b stituents on the benzene ring does not seem to exert as strong an influence as does substitution by N02. This is exemplified by hexachlorobenzene. Molecules with two adjacent electrophilic carbonyl groups, e.g. diacetyl, ethyl pyruvate, and dimethyl oxaloacetate, are relatively good electron acceptors (comparable to trinitrobenzene). The electron affinity of these compounds and that of the electrophilic -CO-C-C-COgroup, e.g., in diethyl maleate and diethyl fumarate, are nearly equal. Compounds with F-dicarbonyl groups have lower electron affinities (acetylacetone, ethyl acetoacetate). Phthalic anhydride is practically devoid of electronacceptor properties. It acquires such properties by electrophilic substitution (tetrachlorophthalic anhydride). The relatively high electron affinity of C C 4 is noteworthy. This is consistent with the fact that, in the presence of CC14, donors such as hexamethylbenzene show a characteristic absorption band indicative of electron-donor/electron-acceptorinteraction [36a]. Carbon tetrachloride and chloroform are o-acceptors which, despite their high electron affinity, have an EDA interaction energy that seems to be lower than that of Ti-acceptors with comparable electron affinities [36d]. ~ [36a] D . P. Stevenson and G . M . Coppinger, J. Amer. chem. SOC. 84, 149 (1962); M . Templetfon, J. chem: Physics 37, i61 (1962); F. Dorr and G . Buttgereit, Ber. Bunsenges. physik. Chem. 67, 867 (1963); R. Anderson and J . M . Pramnitr, J . chem. Physics 39, 1225 (1963). 628 11. Aromatic Hydrocarbons as Electron Acceptors 1. Quantum-Mechanical Calculation of Electron Affinity According to Pople and Brickstock [37], the energy of the highest occupied and that of the lowest unoccupied orbital of an aromatic hydrocarbon are: F [38] can be calculated by the semiempirical ASMOSC [42] method. The electron affinities calculated by Pople and Brickstock [37] and by Hedges and Matsen [39] from Equation (34b) are listed in Columns 3 and 4 of Table 7. sc' was normalized by Hedges and Matsen to the ionization energy of naphthalene (8.12 eV) to x' = -3.87 eV. These calculations [37,39] were carried out by Hoyland and Goodman [40] with even fewer assumptions; they also took into account the chanses in electron density following removal or capture of an electron, as well as the effect of theo-electron energy. The electron affinities calculated by these workers [40] are listed in Column 5 of Table 6. The w-approximation in the simplified treatment proposed by Ehrenson [22] gives an expression for the electron affinity corresponding to Equation (13): (34') -E.J = EA = -a o-(f,- ' 7 Q) p = -mo- %p + As already mentioned, the o-approximation [Equation (13)] gives satisfactory values for the ionization energies of aromatic hydrocarbons when sc = -9.878 eV, 9 = -2.1 1 eV, and w = 1.4. On the other hand, the electron affinities obtained from Equation (34) with w = 1.4 are much too high. To obtain good agreement with the electron affinities calculated from Equation (34') by Hedges and Matsen [39], Poples [37], and Hoyland and Goodmart [40], as well as with the experimental values of Wentworth and Becker [3], the very high value of [37] J . A . Pople, Trans. Faraday SOC. 49, 375 (1953); A. Brickstock and J . A . Pople, ibid. 50, 901 (1954); J. A. Pople, J . physic. Chem. 61, 6 (1957); C. J. Koothaan, Rev. mod. Physics 23, 61 (1951). N ywy=Coulomb interaction between one electron a t atom and one electron at atom V. Pwv= resonance integral for two adjacent atoms I* and v. N = number of occupied orbitals in the aromatic hydrocarbon. X i w and Xi, = Huckel coefficients of the ri-th and ,i-th atomic orbitals in the i-th molecular orbital. The %-values can be calculated with good approximation using the simple MO theory. [39] R. M. Hedges and F. A. Matsen, J. chem. Physics 28, 950 (1958). See also: A. Streitwieser and P. hf. Nuir, Tetrahedron 5, 149 (1959); A . Streitwieser, J. Amer. chem. SOC.82, 4123 (1960); W.F. Wolf, Abstracts J. Amer. chem. SOC.Meeting, New York 1960. [40) J . R. Hoyland and L. Goodman, J. chem. Physics 36, 12, 21 ( 1962). Angew. Chem. internat. Edit. / Vol. 3 (1964) No. 9 = 3.77 must be used in Equation (34’) [43,44]; similarly, a value of o = 3.73 must be used for phenanthrene, benzo[c]phenanthrene, and triphenylene [44]. No theoretical explanation is available for the fact that the calculations of I using Equation (13) and of EA using Equation (34’) require different values of w. In Column 6 of Table 7, a list is given of the electron affinities calculated by Ehrenson [22] according to the w-method, using a w = 3.5. Column 2 contains the electron affinities obtained for a few aromatic hydrocarbons by Wentworth and Becker [3] using the electron absorption coefficients determined experimentally by Lovelock [l]. 2. Semiempirical Methods for Determining Electron Affinities w Table 7. Electron affinities [eV] derived for aromatic hydrocarbons by various methods. a) Electron Affinity and the Longest- Wavelength Absorption Band of the Donor It follows from (34) that (EA (35) + 1)/2 = CL’ On the basis of the electron affinities determined experimentally for a few aromatic hydrocarbons (Table 7, Column 2) and the experimental values for the first ionization energies Iexp (Table 8, Column 4), one obtains in agreement with Becker and Wentworth [28] an average value of 8.14 eV for the sum (I + EA). From Equations (21) and ( 3 9 , we obtain for CY’= 4.07: 6 (36) Theor. [411 2 1 3 I 0.42 -= 1-1.63 1-1.40 1-1.40 I I I I 1 I 0.49 -0.14 0.64 -0.20 0.61 -1.590 I I -0.246 0.147 4 1.035 5 -6 0.20 7 I 0.46 10 0.14 -0.06 1 1 I 0.62 -0.28 -- 1 0.25 1 I 0.014 1 11 17 = 3.03-0.701 <” The electron affinities calculated from ijo (Table 8, Column 6) using Equation (36) are given in Column 2 of Table 8. The differences between the electron affinities calculated by the ASMOSC method (Table 6, Columns 3, 4, 5, and 6), those obtained from 30 (Table 8, Column 2) using Equation (36), and the few experimental EA values (Table 7, Column 2) may be considerable. The EA values obtained by averaging all EA values are given in Column 3 of Table 8. 0.446 1 1 0.75 -~ 19 -0.033 EA 0.33 201 -0.14 1iG 1 I I I 1I 1 I I 0.313 t e? 0.463 0.442 0.727 23 24 0.573 0.50 0.385 -0.78 -0.290 -0.37 27 - 28 I -0.41 29 -0.35 -- 47 0.39 0.68 -~ 48 -- 0.55 0.410 I 49 50 ’ -~ I- 51 65 0.417 0.92 I 0.676 0.683 0.590 0.052 [41] S. E. Ehrenson, J. physic. Chem. 66, 706, 712 (1961). [42] Antisymmetrized Molecular Orbital Self-consistent. [43] S. E. Ehrenson [41] uses w = 3.5. [44] D . R . Scott and R . S . Becker, J. physic. Chem. 66, 2713 (1962). Angew. Chem. internat. Edit. 1 Vol. 3 11964) 1 No. 9 Fig. 7. Averaged electron affinities of aromatic hydrocarbons (calculated by different methods) as a function of the first excitation energy Go. The straight line corresponds to Equation (37); for numerical data and key numbers to hydrocarbons, see Tables 8 and 7, respectively. Their absolute accuracy is never better than f 0.2 eV. Figure 7 shows a plot of these electron affinities against $0 for aromatic hydrocarbons. The linear relationship (37) - EA = 2.991-0.700 <o obtained in this manner is in good agreement with Equation (36), which was derived directly from experimental data, and with the expression of Becker and Wenrworth [28] : (38) EA = 2.92-0.762 Goo 629 It is noteworthy that the linear functions (21) and (36), which agree best with the experimental values for ionization energies and electron affinities, have the s a m e gradient. I ! which is in good agreement with Equation (42). The A F values ~ ~derived ~ from ~ Equation (44) are given in Table 8, Column 9. The decrease in solvation energy with increasing electron affinity of aromatic hydrocarbons is possibly associated with the distribution of the negative charge over the entire molecule. The solvation energy decreases, and the increase in electron repulsion energy o n transition from the neutral molecule to the anion also becomes less (Le., the electron affinity of the aromatics increases) as the range of dispersion of the negative charge over the aromatic anion increases. Also the interaction energy with the solvent molecules decreases with increasing radius of the aromatic anion. Fig. 8. Half-wave reduction potentials ERed [47Jof aromatic hydro- % carbons as a function of avera_eed electron affinities calculated by different methods. The solid straight line corresponds to Equation (39). For numerical data and key numbers to hydrocarbons, see Tables 8 and 1, respectively. b) Electron Affinity, Hal' Solvation Energy Wave Reduction Potential and Figure 8 shows a plot of ECId (Table 8, Colunm 7 [45]) obtained from Equation (27) vs. EA (Table 8, Column 3). The EtId and EA values fit Equation (39): (39) E t r d = 2.416-0.692 It follows from Equations (39) and (27) that there is a functional relationship between AFsolvand EA. If we set (40) AFsolv = -Tsolv + 6.EA then from Equations (27) and (40) we obtain: (41) -ERed '12 = EA (1-6) + qsOlv-5.07 [eV] and, by comparison with Equation (39): 6 = 0.308 and qsOlv= 2.654 Hence: (42) AFsolv = 0.308 EA-2.654 Equation (42) can be checked by using Equation (27) to calculate A F ~ (~Rt;,' ~ from Column 7, from Column 3 of Table 8). (43) AFsolv = EA-5.07 + ECrd = EA-EA' The values of AFsolv calculated using Equation (43) are listed in Column 8 of Table 8, and give rise to the following linear relationship : (44) AFsolv = 0.2714 m-2.624 [eV] [45] I. Bergman, Trans. Faraday SOC.50, 829 (1954); G. J. Hoijtink, Recueil Trav. chim. Pays-Bas 73, 355 (1954); 74, 1525 (19551, where references to previous publications are given. The Etzd-values of Eergman must be increased by 0.5 eV in order to obtain the EtId-values measured in 7 5 % dioxane against a saturated Hg2CIz-electrode. The E:zd-values measured in 75 % and 96 % dioxane show practically no differences. 630 Fig. 9. Solvation energy AFsolv of aromatic hydrocarbons as a function of the electron affinity according to Equation (44); for numerical data and the key numbers of the aromatic hydrocarbons, see Tables 8 and 1, respectively. Extrapolation of Equations (21) and (37) to GO + O is of questionable validity because these equations have been shown to be valid only within the rather narrow range from 90 = 2.5 to 4 eV. Extrapolation to GO + 0 would assume I and EA to be linear functions of CO [Equations (21) and (37)] even for very low values of 90;this, however, has never been proved. Though the difference (ILEA) = (1.4 90 2.12 [eV]) [Equations (21) and (37)] decreases with decrease in the excitation energy of aromatic hydrocarbons, Equations (21) and (37) give different values, viz. Iij,=o = 5.1 1 eV and EAj,=o = 2.99 eV. However, according to Huckel's theory, VO should tend to zero and I should tend to EA for infinitely large, conjugated aromatic ring systems, e.g. in graphite. The work function of graphite is 4.39 eV [46]. For hydrocarbons, we should expect IG,+O # EA since the electron repulsion energy of the hydrocarbon anion is greater than that of the hydrocarbon cation. Accordingly, I;,+o > EAij,,o. Finally, it should be borne in mind that Equations (21) and (37) refer to two-dimensional aromatic ring systems in the gaseous state. + 3. Electron Affinity and Chemical Constitution [ "1 a) The electron affinity increases with the number of rings fused together in a line, whereas the ionization energy decreases correspondingly (see Table 1, Nos. 1-5, 6-9, 10- 13, and 14-18). [46] A . Eraun and G. Eusch, Helv. physica Acta 20, 33 (1947). [*I The fact that aromatic hydrocarbons are electron donors as well as electron acceptors enables them to undergo intermolecular EDA-interaction. Wentworth and Chen proved this using the spectral shift of the absorption spectra or a few polycyclic hydrocarbons on addition of hexamethylbenzene in heptane solution: J. physic. Chem. 67, 2201 (1963). Angew. Chem. internat. Edit. Vol. 3 (1964) 1 No. 9 Table 8. Energy data for aromatic hydrocarbons. 1 2 3 Hydrocarbon no. [*I EA Eq. (36) EA Iexp -1.5 9.24 [47] -0.3 8.26 [481 8.12 I471 15 6 7 4.35 2.48 2.89 2.70 3.31 1.96 2.61 2.49 1.635 2.43 2.35 1.3612.51 1 2.30 I8 1 9 - I 1 2 4 -0.01 I 7.3 [471 3 0.71 0.5 4 1.18 1.0 5 1.52 1.2 7.43 7.00 1491 6.96 1501 6 0.05 0.1 8.06 8.03 8.10 8.03 7 0.61 0.56 7.6 I491 7.57 [47] 8 1.11 1.1 9 1.45 1.45 10 -0.02 I1 0.54 12 1.06 -0.05 0.5 1.41 1.4 14 0.31 0.3 16 0.55 0.56 - 17 1.04 0.9 18 1.36 1.36 19 0.27 0.15 - 20 0.55 0.6 2.63 6.62 2.15 7.6 4.24 7.53 3.45 I 7.03 I 6.69 8.0 [491 8.1 [SO] I 7.55 [47] I 7.6 2.74 - 2.03 1 1.69 2.17 4.36 2.47 3.55 - 2.04 I 6.72 2.48 2.28 2.25 8.17 I 7.08 1.1 - 13 I 2.65 I 2.53 2.81 1.705 2.30 2.30 1.43 2.23 3.88 2.47 7.95 [49] 15 21 0.38 0.4 22 0.61 0.6 23 1.03 0.85 24 0.78 0.6 25 [28] 1481 1491 [SO] 6.95 0.48 0.3 llrs 3.53 2.83 I 7.09 2.37 6.77 2.46 1.75 I 2.43 1.35 2.36 I T 3.93 2?45/2.67 3.53 2.07 I 2.42 I 7.58 - 7.8 [49] 7.15 [49] 7.07 [501 ( 7.6 I491 17.63 [50] +I 1 7.11 3.77 2.29 3.45 2.025 2.85 1.75 I 11 1 1 II 2.47 2.32 2.23 2.64 2.49 2.34 2.24 2.55 2.41 2.38 2.26 2.58 I 2.47 2.37 2.51 2.42 2.46 2.47 I 2.39 7.35 3.20 1.985 2.47 2.46 7.65 3.63 2.14 2.59 2.53 I 2.45 I 2.52 I 2.49 1 2.47 -0.5 - 26 I 1 30 0.43 0.4 3.71 2.15 31 0.52 0.5 3.59 2.07 32 0.56 0.56 - 3.53 2.09 I 2.07 I 2.42 33 0.31 0.3 3.87 2.23 2.53 34 0.80 0.8 - 35 1.05 1.os 1.72 1 2.30 I 2.34 36 0.66 0.66 2.41 2.45 37 0.66 0.66 - 38 0.78 0.8 39 1.29 1.3 40 1.43 1.4 41 1.29 1.3 b) A benzene ring fused on at the 1,2-positions i.e. onto the [ a ]side of a linear system, e.g. in Table 1, on passing, from No. 2 to No. 6 and from No. 3 to No. 7, from No. 4 to No. 8, and from No. 5 to No. 9, affects the electron affinity and ionization energy only slightly. A benzene ring fused o n at the 3,4-positions, i.e. the [c] side, (e.g. on going from No. 7 to No. 11, from 8 to 12, or from 9 to 13 in Table 1) [*I, at the 5,6-positions (from No. 6 to 14, from 7 to 16, from 8 to 17, Angew. Chem. internat. Edii. 1 Yoi.3 (1964) No. 9 1 7.82 - 7.33 -lI I1 T 7.35 6.84 6.84 1.965 I 2.32 1 1I 1.50 I 2.28 1 2.27 3.17 1109 2.82 3.37 2.37 1.995 3.37 3.20 2.39 2.54 2.41 2.45 2.41 2.47 2.27 2.47 [*I With the exception of triphenylene (No. 10, Table l), which has an extraordinarily small EA. 1471 H . Watanabe,J. chem. Physics 22, 1565 (1954); 26,542 (1957). 1481 M. E. Wacks and V . H . Dibeler, J. chem. Physics 31, 1557 (1959). [49] According to Equation (7); see G . Briegleb and J. Czekalla, Z . Elektrochem. Ber. Bunsenges. physik. Chem. 63, 6 (1959); Angew. Chem. 72,401 (1960). 63 1 Table 8 (continued). 1 1= 4 9 Iexp -Wolv Eq. (441 I Hydrocarbon no. [*I 42 43 Et(36) I 0.73 I 0.7 10.8710.9 7.27 ___-- 44 7.11 45 6.73 46 47 48 49 I-I0.5 0.42 1 0.40 -1-1 1 1 1 ::::1 1 7.72 [481 17.55 [49] 7.53 [SO] 3.08 2.86 2.31 1.415 2.39 2.27 2.35 -__ 2.24 2.24 6.46 1.93 1.175 2.22 --- 2.17 7.72 3.72 2.11 2.47 2.49 0.4 0.7 -- 7.37 0.77 50 7.27 51 7.41 ~ 1.945 52 7.75 2.185 1I t: I I 2.42 2.52 7.04 2.75 7.30 3.12 1.815 1.65 22; --- 53 54 ~ 7.60 3.55 ~ 2.005 7.03 7.38 59 1 I I I ::::I1 II 2.74 1.65 2.31 2.48 c _ _ - 61 -1.08 1.1 1.03 1.02 1.0 ~- 63 -1.15 65 1.15 1.55 64 I 7.10 1.0 62 1.55 I 2.33 2.40 1 2.32 58 ~ 7.06 7.11 11.78 2.86 ::::5 2.36 1.65 2.34 1.69 2.36 r / 2 6 8 / F 2.36 l 6.58 I 2.10 I 1.30 I 2.22 - 2.52 I 2.70 I 1.65 1 2.29 2.15 1.28 2.27 -6.62 57 2.43 2.48 7.00 56 1 I 2.52 55 60 2.43 2.35 I 2.21 I 2.32 1 2.42 I 2.34 1 2.33 I1 2.35 2.31 2.20 0.5 ['I For key t o hydrocarbon numbers, see Table 1. and from 9 to 12), at the 7,s-positions (from No. 6 to 19, from 7 to 20, and from 11 to 31) has essentially no effect on the electron affinity and ionization energy. Accordingly, the EA and I values for tribenz[a,c,g]anthracene (No. 31) and dibenzo[a,g]chrysene (No. 32) compared to dibenz[a,g]anthracene (No. 20) and benzo[a]chrysene (No. 30), respectively, are practically identical. c) Beginning with pyrene (Table 1, No. 47), a n additional benzene or naphthalene ring fused o n at the 1,2- and/or 6,7positions (i.e. the [u] or [f]sides) has no particular effect on the electron affinity and ionization energy. This is indicated by comparison of No. 47 with Nos. 48, 52, and 55. The electron affinity of pyrene increases, and its ionization energy decreases, as a result of fusion of benzene or naphthalene rings onto sides other than the [a],e.g. at the 3,4-, 8,9-, and 9,lOpositions([c], [h],and [i] sides). This can be seen by comparing the electron affinity of pyrene with those of Nos. 49, 53, 54, 56, 57, and 58. Fusion onto the [c, h] sides has a greater effect on the electron affinity than [c, i] fusion (Table 1 ; increase in [50] From E,: 632 Equation (31), [36]. EA in going from Nos. 53 and 57 to Nos. 54 and 58, respectively). d) Fusion of one or two benzene rings onto the [a] or [n, g] sides (Table I , Nos. 39 and 40, respectively) of perylene (Table 1 , No. 23) increases the electron affinity and decreases the ionization energy to the same degree as does double fusion onto the [b, h ] or [ u , j ] sides (No. 44 or No. 41). On passing from perylene (No. 23) to benzo[l]perylene (No. 24) and to coronene (No. 25), the electron energy decreases and the ionization increases correspondingly. e) The following compounds have the highest electron affinities, and, correspondingly, the lowest ionization energies: benzo[g]terylene (No. 46): EA = 1.4 eV; I = 6.46 eV; dibenz[b, Alanthanthrene (No. 64): €A = 1.55; I = 6.58 eV; dibenzo[a,g]perylene (No. 40): EA = 1.4; I = 6.7 eV; benzo[a]pentacene (No. 9): EA = 1.45; I = 6.69 eV; dibenzo[u, clpentacene (No. 13): €A = 1.4, I = 6.72 eV, and dibenzo[a, dlpentacene (No. 18); €A = 1.4 eV, I = 6.77 eV. Received, December 16tb, 1963 [A 365/17L IEI German version: Angew. Chem. 76, 326 (1964) Translated by scripta technica, New York Angew. Chem. internat. Edit. I Vol. 3 (1964) 1 No. 9

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