-1.STREITWIESER, JR.,AND I. SCHWAGER
2316
f.e.m.0. method predicts a still smaller difference in energy (0.01 e.v.> between these states. It is interesting that the s.p.0. treatment agrees with thc usual s.c.f. m.o. method (including configuration interaction) as regards the assignment of the transitions; the results given by thc latter method are, however, greatly in error. VI. Summary The main conclusions of this paper can be summarized as follows. (1) The s.p.0. treatment can be regarded as a modification of the usual s.c.f. method in which allowance is made for vertical correlation by adjustment of integrals. It could be regarded in this sense as a semi-empirical extension of the s.c.f. treatment along the lines pioneered by Pariser and Parr,' but with the integrals modified in a logical and self-consistent manner. The approach provides a further justification for the use of the s.p.0. method and further support for our contention2 that the neglect of non-orthogonality between s.p.0. functions and the core may not in practice have any serious consequences. (2) The results in this and the two preceding papers2 suggest that the s.p.0. method is a very promising one for calculating the properties of ronjugated systems. (3) The only one-configuration treatment that can compare with the s.p.0. method is the Poples approximation. In the case of hydrocarbons the two methods would be expected to give very similar results, for the following reason. Using a Coeppert-nIayerSklar potential and neglecting penetration integrals, eq. 19 becomes8
F,,
=
W i p
t l/'*q,(ii,ii)
+
3#i
(a, - l)(ii,jj)
(25)
The corresponding s.p.0. equation (21) becomes
F,, =
w?l,+
-
+
'g,(ii,ii)
(q, - l ) ( i i , j j ) (26) 3#a
VOl. 66
Pople assumes, following Pariser and Parr,' that all the repulsion integrals have reduced values, corresponding in our system to "upper-lower" integrals. Since Qi = 1 for all atoms in an alternant hydrocarbon, if differential overlap is neglected,8 the Poplc and s.p.0. expressions for the diagonal elements in the F-matrix are identical for such compounds. The expressions for the off -diagonal elements differ, being given by
However, since bond orders do not vary much in aromatic compounds, and since the elements F,, are small for non-bonded atoms! the values for the two methods can be brought into near coincidence by using different values for p. The value appropriate to the s.p.0. treatment should of course be numerically smaller-as in fact it is. However this correspondence between the Pople and s.p.0. treatments applies only to alternant hydrocarbons; in the case of non-alternant hydrocarbons, or of compounds containing heteroatoms, the charge densities pi are no longer unity and the expressions for the diagonal elements of the Fmatrix differ. Preliminary results suggest that the s.p.0. method is significantly superior for heteroaromatic systems. Acknowledgment.--We are very grateful to Dr. L. C. Snyder of Bell Telephone Laboratories for helpful discussions and for his Molecular Orbital Program, to Bell Telephone Laboratories for computational facilities, and to the National Science Foundation for support. N. L. S. thanks the Consejo Nacional de Investigaciones Cientificas de Argentina for a Fellowship, for part of the period covered by this work.
A MOLECXLAR ORBITAL STLTDYOF THE POLSROGRAPHIC REDUCTIOS IS DIJIETHYLFORhfAMIDE OF UNSUBSTITUTED An'n METHYLSTTRSTITUTED AROMATIC HYDROCARBOXS' B Y A. STREITWIESER, JR.,* .4ND I. SCHWAGER Department of Clwriistry, Unii eruity of California, Berkeley, Cal. Received June 20, 1968
The half-wave potentials of a number of aromatic compounds have been determined and are found to fit the same type
of correlation with the energies of the lowest vacant molwmlar orbitals in the HMO approximation established in other solvents. The deviation of biphenylene from this correlation can he accounted for in terms of "long bonds" but this esplanation fails when applied to 2,3-benxobiphenylene. Azulene and acepleiadylene do not obey the simple theory. The effect of methyl substituents is accounted for successfully in ternis of a combination of conjugative (hyperconjugation) and
inductive influences.
Laitinen and Wawzonek found bhat phenylsubstituted olefins and acetylenes and aromatic polynuclear hydrocarbons are reduced a t hhe dropping mercury elect'rode in aqueous dioxane and
give reproducible half-wave potentials. The first reduction wave of these compounds corresponds to the approximately reversible addition of one or two electrons to the c o m p ~ u n d . ~ - 'Hence, ~ the half-
(1) This research was supported in p a r t by a n .4ir Force Grant, AFAFOSR-62-175. (2) Alfred P. Slosn Fellow, 1958-1962.
(3) H. A. Laitinen and S. Wawronek, J . Am. Chem. % e . , 64, 176.; (1942). (4) S. Wawzonek and H. A. Laitinen, ibid., 64, 2365 (1942).
Dec., 1062
HALF-WAVE POTENTIALS OF AROMATIC HYDROCARBONS
wave potential for this reduction corresponds to an electron affinity of the hydrocarbon. Such halfwave potentials have been found to give excellent, correlations with the lowest lying molecular orbital in simple MO theory.ll These correlations provide an important means of comparing theoretical predictions with quantitative experimental results. 2-Methoxyethanol also has been used as a solvent for polarographic studies of polycyclic aromatic hydrocarbons12 and more recently Given13 has shown the advantages of dimethylformamide for such studies. We have extended the measurements of Given in dime thylformamide and have established the same type of correlation of half-wave potentials with the energies of the lowest vacant MO’s shown previously in other solvents. This correlation then has been used to examine departures from the simple polycyclic aromatic hydrocarbons. Several non-alternant hydrocarbons have been included and we have studied the effect of the “long bonds” in biphenylene systems. Finally, we have looked at the effects of methyl substituents and the explanation of the effects in terms of molecular orbital theory. Experimental Instnunentation.-Current-potential curves were recorded with a Sargent Model XV polarograph. All potentials were meaaured with reference to an internal mercury pool anode in 0.1 N tetra-n-butylammonium iodide in dimethylformamide (which was -0.55 v. us. 5.c.e.). The Hg 0.2”. A commercial pool cell waa therniostated at 25.0 conductance bridge obtained from Electromeasurements Inc., Portland, Oregon (Model 250-DA) wag used to measure solution resistance. An average value for resistance in the supporting solution was 700 f 50 ohms. Materials.-Dimethylformamide was purified by distillation in a sixteen-plate Oldershaw column. The fraction used distilled in the range 152-1.53”. Polarograph grade tetra-n-butylammonium iodide was supplied by Southwestern Analytical Chemicals, Austin, Texas. The majority of the aromatic hydrocarbons were obtained from various commercial sources, and purified when necessary by chromatography on neutral alumina, gas chromatography on a carbowax column, or by repeated crystallization from suitable solvents. The authors wish t o express their gratitude to Dr. W. C. Langworthy, who supplied samples of several methyl-substituted aromatic hydrocarbons, and to Dr. F. R. Jensen, who supplied a sample of 2,3-benzbiphenylene. Acepleiadylene was the kind gift of Dr. Y. Boekelheide; biphenylene was prepared by Dr. R. M. Williams. Experimental Procedure.-Solutions of the hydrocarbons (about 0.001 M ) were prepared with previously deoxygenated dimethylformamide and were further degassed for 10 min. Cylinder nitrogen, used for degassing, w m purified according to Fie~er.1~ Experimental System.-Dimethylformamide, as reported previously,13proved to be an excellent solvent for the polarographic investigation of aromatic compounds. Its ease of (5) 8. WaweonekandJ. W.Fan, J . A m . Chem. Soc., 68, 2541(1946). (6) G. J. Hoijtink rtnd J. van Schooten, Rec. trav. chim., 71, 1089 (1952). (7) G.J . Hoijtink and J. van Schooten, ibid., 72, 691 (1953). (8) G. J. Hoijtink, J. van Schooten, E. de Boer, and W. I. Aalbersberg, ibid.. 78, 355 (1954). (9) G.J . Hoijtink, R e c . trav. chim., 7 8 , 895 (1954). (10) A. C. .4ten, C. Biithker, and G. J . Hoijtink, Trana. Faraday Soc., 6 6 , 324 (11959); K. Schwahe and E. Schmidt, 2. physik. Chem. (Leipzig), Sonderheft, 278 (1958); K. Schwabe, ibid., 289 (1958); H. J. Gardner, Nature, 188, 320 (1959). (11) For a summary see A. Streitwieser, Jr., “Molecular Orbital Theory for Organic Chemists,” John Wiley and Sons, Inc., New York, N.Y., 1961. (12) I . Bergman, Tvans. Faraday Soc., 60, 829 (1954). (13) P.H.Given, J. Chem. SOC.,2684 (1958). (14) L. F. Fieser, J . A m . Chem. SOC.,46, 2639 (1924).
2317
purification, dissolving power, and the excellent character of the observed current-voltage curves demonstrate that i t compares very favorably with 2-methoxyethanol’z as a 1:seful aprotic solvent for polarography. The decomposition pot,ential of the supporting solution is approximately -2.40 v. US. Hg pool anode. No maxima were observed at the concentration range studied. The solut.ion resistance of 700 f 50 ohms caused, a t a I mJ4 concentration of aromatic hydrocarbon, an I R drop of 1 or 2 mv. The values reported have not been corrected for this small I R drop since it is less than the experimental uncertainty, and remains constant for similar concentrations of substrate. Many of the aromatic and methyl aromatic compounds also run us. 5.c.e. in an H-cell separated by an agar-saturated potassium chloride bridge, and were found to give good agreement with the results observed us. the int’ernal Hg pool reference electrode. The Hg pool electrode was preferred because both KCl and water diffused through the agar bridge into the sample compartment of the 8.c.e. cell, and were potential sources of difficulty. Potassium ion is itself reduced in dimethylformamide a t approximately -2.05 v., and the addition of a proton source such as water to dimethylformamide has been shown1a,l6 to cause small shifts in the half-wave potentials of aromatic hydrocarbons Experimental Results and Uncertainties.--For representative compounds such as naphthalene and anthracene, the diffusion current was found to be proportional to concentration over the range 0.5 to 5 mM, and the standard deviation of the half-wave potential over this range for ten different concentrations, and over a period of several days, was fO.010 v. However, the reproducibility was iO.005 v. for successive runs at similar concentrations. The values reported for the methyl-substituted and parent compounds are the average of three such consecutive runs made at similar concentrations.
Discussion The half-wave potentials for the benzenoid aromatic hydrocarbons (Table I) plotted against the energies of the lowest vacant MO’s give a good linear correlation (Fig. 1) as expressed by the equation16 -Ell2
=
(2.407
f
0.382)~~,+10.396
f
0.093 (1)
This correlation is a,mazinglp close to that, in 2met hoxyet hanol
-El/g = (2.414
f
0.092)m,+l 0.435
f
0.06;
(2)
It is noteworthy that the slopes and intercepts in the two solvents are so similar and show again the unexpected similarity of solvation energies of hydrocarbon anions in different solvents. Several hydrocarbons deviate markedly from the correlation line. In one of these cases, biphenylene, it has been reported recently, on the basis of Xray structure analysis, that the centFal bonds are virtually single bonds (1.52 f 0.03 A.)17and that the remaining six-membered ring bonds are almost normal benzene bonds. One of the assumptions made in the simple Huckel MO theory is the equality of bond integral terms for nearest neighbors. This assumption is equivalent t’o assuming an equality of all bond distances. The effect that a change in ,R of bond r-s has on the energy, q , (15) G. J. Hoijtink, Ricerca Sei., 80, Suppl. No.5,217 (1960). (16) The “unusual” compounds, biphenylene, 2,3-bensobiphenyl-
m e , aaulene, and acepleiadylene were omitted. (17) T. C. W. hlak and J. Trotter, J . Chem. Soc., 1 (1962).
A. STREITWIESER, JR.,AND I. SCHWAGER
231 8
Vol. 66
__I-
atomic orbital in the jth molecular orbital]. If we assume that B is proportional to overlap integral, Sg for each of the central bonds in biphenylene 2 001 is -0.20p0,ii and 6aWl = (2)(0.3685)2(-0.20) = -0.054p. Because there are two such bonds the corrected mm+l is -0.553, which yields a calculated -El/: = 1.73 v., in excellent agreement with the expenmental value, 1.73 v. Unfortunately, the success of this method does not appear to be general. A similar correction may t be made to 2,3-benzobiphenylene assuming that -E I/Z the bonds joining the benzene and naphthalene rings are also 1.52 A. in length. The corrected t mm+i corresponds to -El/, = 1.85, in poor agreel50k ment with the experimental value, 1.67 v. Actually I 2,3-benzobiphenylene agrees rather well with the correlation line without any corrections. The behavior of the non-alternant hydrocarbons merits comment. Fluoranthene behaves as a I *5L typical benzenoid hydrocarbon in fitting the cor-I relation. Azulene, however, has a lower reduction potential by 0.25 v. than that predicted by the of other hydrocarbons. The halfA I A * , l , , , l l , , , correlation I wave potential of acepleiadylene, -1.10 v., has 3 4 .5 6 7 not been reported before and is lower by almost -Mrn+i. 0.4 v. than the predicted value. These serious Fig. 1.-Half-wave potentials of aromatic hydrocarbons in deviations are not corrected by allowing for "long dimethylformamide us. energy coefficient of lowest vacant bonds." Instead, the enhanced oxidizing power of &IO in the HMO approximation. these hydrocarbons probably is associated with more serious limitations of simple MO theory. TABLEI The compounds are calculated to have greater HALF-WAVE REDUCTION POTENTIALS FOR AROMATIC stability than they actually possess; their resonance IN DIMETEIYLFORMAMIDE HYDROCARBONS energies are lower than expected on the basis of - E l / , ua. Hg calculated delocalization energies.l1 pool The effect of methyl groups on ionization poNo. in Dimethyltentials has been shown previously to be accounted Fig. 1 Hydrocarbon -mm+ 1' formamde for satisfactorily in terms of an inductive effect 1 Aaulene 0.400 1.10 a10ne.l~ A similar treatment has been suggested 2 Acepleiadplene .445 1.10 for the effect of methyl groups on polarographic 3 Perylene .347 1.17 half-wave potentials but the data available for 4 Fluoranthene .371 1.23 testing the method were rather meager.11320In this 5 l,%Benapyrene .365 1.31 method the r-carbon attached to the methyl 6 1,2,4,5-Dibenzpyrene .422 1.36 group is made more electropositive by the assign7 Anthracene ,414 1.41b ment of a negative h in the definition 8 1,2,3,4-Dibenaanthracene .499 1.53 " T-' r
"
!
"
'
O'!i
i
L A
9 Pyrene .445 1.53* 10 1,2,5,&Dibenaanthracene .474 1.55 11 4,5-Benapyrene .497 1.58 12 2,3-Benaobiphenylene .502 1.67 13 Biphenylene .445 1.73 14 Chrysene ,520 1.77 15 Triphenylene ,684 1.91 16 Phenanthrene .605 1.92b 17 Naphthalene ,618 1.9gb 18 Biphenyl ,705 2.05 Energy coefficient of lowest vacant MO in the HMO method (see ref. 11). b Givenlareports: naphthalene, 1.99; anthracene, 1.41; phenanthrene, 1.93; pyrene, 1,56.
of molecular orbital, $j, is given to a first approximation as1*
in which p J is the partial mobile bond order [ p - j = cj,cj,, in which cj, is the coefficient of the rth (18) C. A. Coulson and H. C. Longuet-Higgins, Proc. Roy. Soe. (London), A191, 39 (1947).
+
(4) The effect that such a change in the coulomb integral has on the energy, em+1, of the lowest vacant MO is given by ar =
6em+l =
(YO
hrb
6ar = G+l,r2
hrpo
(5) As a test of this model we have determined the halfwave potentials of a number of methyl-substituted aromatic compounds (Table 11). Methyl groups invariably render the hydrocarbons somewhat harder to reduce, in agreement with the qualitative predictions of the simple model. The quantitative prediction that the energy change is proportional (eq. 5) is tested in Fig. 2 and is found to be unsuccessful. Inspection of this figure reveals that methyl groups at 0-naphthyl type positions (triangles in Fig. 2) give a good linear correlation among themselves but that a-methyl substituted compounds fall generally below this line. Cn+l,r2
(19) A. Streitwieser, Jr., J . Phya. Cham., 66, 368 (1962). (20) L. E. Lyona, Rsssorch, 4, 587 (1940).
HALF-WAVE POTENTIALS OF AROMATIC HYDROCARBOW,
Dec., 1962
2319
TABLE I1 EFFECT OB METHYLOR METHYLENE SUBSTITUENTSON HALF-WAVEPOTENTIALS
-E'/r
No. in Fig. 2, 3
16
(om.-')
(V.)
AS (V.1
L m + l.,'
-AEl/r
COW.
r
Naphthalene
35010 1.994 1 34220 2.022 0.098 0.126 0.180 2 35010 2.042 .000 .048 .069 3 2.046 ,103 34180 ,155 .249 4 2.023 ,187 .216 .360 33500 5 2.055 ,133 33940 ,194 .249 6 2.056 .094 ,156 .249 34250 2.090 .036 7 ,132 ,138 34720 2.070 8 .00'7 34950 .083 .138 Phenanthrene 1.920 34130 9 1.942 34070 ,029 .002 ,007 10 1.980 33670 .057 .11$ * 099 I1 1.969 .071 .120 ,172 33560 1.405 Anthracene 26740 1.450 12 26530 .026 .071 .048 13 25910 .IO3 1.417 .115 .194 Pyrene 1.526 29960 14 29210 1,549 .115 .135 .093 .026 29750 15 1.541 .041 .Ooo 16 ,026 29750 1.555 .055 ,087 F1uor:tnthcnc" 1.228 1.267 1.273 1.304 Biphenyl" 2.050 Tetrahydropyrene" 2.170 2.200 sym-Hexahydropyrene" 1.946 Dihyctropyrene' These compounds were not included in the correlations. Fluoranthene is a non-alternant hydrocarbon; the other compounds are not methyl-substituted. b Values were obtained from D. Peters, J. Chern. Soc., 646 (1957), and American Pet. Inst. Project 44; Natl. Bur. Standards.
,
ir75 1
0"
rlool-
W
Q
/ O8
I
0' 0"
oi3 Fig. 3.-Correlation of the effect of methyl groups on halfwave potentials corrected for conjugation effects using the inductive model. Fig. 2.-Attempted correlation of the effect of methyl groups on half-wave potentials using an inductive model only.
The inductive model of the methyl group alone is inadequate for the present purpose. The conjugative ability of the methyl group has been ig-
nored in this model. For the evaluation of this effcct me turn to absorption spectra. The p-band of aromatic hydrocarbons may be associated with transition of an electron from the highest occupied to the lowest vacant T-MO. The effect of a
HARRISON SHULL
2320
methyl substituent on Ohis band for alternant hydrocarbons is determined essentially entirely by the conjugation effect and not by inductive effects.21 This analysis suggests the use of the bathochromic shift given by a methyl substituent as a means to correct the shift in reduction potential for conjugation by the methyl group. Actually, the bathochromic shift results from changes in energies of both the highest occupied and lowest vacant orbit,als and only a part of the spect,ral shift should be associated with the change in one orbital alone. Nevertheless, the simple MO interpretation of spectra is highly approximate; hence, the entire bathochromic shifts accompanying methyl substitution as listed in Table I1 have been converted to volts and added to the observed AEI/2 values to give an estimat,e of the reduction potential in the absence of conjugation effects. The new values, AEi/t(:orr, should now be dependent only on the inductive effect as in eq. 5 . A plot of (21) C. A. Coulson, Pioc. Phys. Soc. (London), A65, 933 (1952); H. C. Longuet-Himins a n d R. G. Sowden, J . Chem. Soc., 1404 (1952). An illuminating graphic analysis is given by E. Heilbronner, Chapt. 5
of “Non-benzenoid Aromatic Hydrocarbons,” Interscience Publishers, Keu- York. S. Y.,1959; see also ref. 11.
THE
wrum
Vol. 66
A E I / against ~ ~ ~ ~Cm+l,r2 ~ in Fig. 3 shows a greatly improved correlation; the correlation coefficient is 0.94 despite the fact that both types of shifts are of comparatively small magnitude and contain rather substantial experimental errors. For po = -2.4 e.v. (the slope of Fig. l), the slope of Fig. 3 corresponds to hx = -0.21. This correlation provides evidence for the importance of both conjugative and inductive influences in the effect of methyl groups on reduction potentials. The inductive effect decreases the electron affinity and is generally more important than the conjugation effect which tends to increase the electron affinity; conjugation is clearly more important at a-naphthyl than a t p-naphthyl-type positions. Both effects are undoubtedly also important in ionization potentials but in this case the two effects operate in the same direction and probably to comparable extents. Hence, consideration of the inductive effect alone suffices to a reasonable approximation. I t is undoubtedly for this reason that the effective hx for the inductive model in ionization potentials, -0.54,19 is numerically greater than that for reduction potentials in Fig. 3, -0.21.
OF THE TWO-ELECTRON CHEMICAL BOND. 11. THE HETEROPOLAR CASE’ BY HARRISON SHULL
C‘heniistry Department, Indiana University, Blooininyton, Indiana Received June 80, 1962
B y using the artifice of dividing space into two parts by means of a plane perpendicular to the internuclear axis and passing through its mid-point, it is shown that there is possible a division of a two-configuration two-electron wave function into three orthogonal parts each of which has optimum properties associated with the plane intuitively corresponding to the names “ionic” and “atomic.” In this paper, the heteropolar case is considered, and it is shown that there arises a natural mathematical quantity, e, which is a function of three integrals over natural orbitals over half space. The quantity, e, seems to bear a considerable resemblance t o electronegativity difference. An example is given for the simple diatomic hydride two-electron system, HZ(z-1’ +,a t a fixed internuclear distance. Finally i t is pointed out that the treatment is a special case of the use of a much more general weight factor. Suitable choices of the latter may make i t possible to relate functionally the large number of different electronegativity scales.
I. Introduction approximate natural expansions.5 At an early In a previous paper* we have developed a treat- stage in the calculation, therefore, the use of the ment of the two-electron bond in the homopolar natural expansion frees one from the arbitrary case which seems to avoid some of the pitfalls of nature of the approach. A second pitfall that has been pointed out prethe typical textbook version. In particular, by st,art,ing from the natural orbital expan~ion,~viously2.6is the identification of chemical concepts we avoid completely the arbitrary features of previ- with non-orthogonal wave mechanical functions. ous treatments which depend upon a very particular Thus the rather generally used ‘(covalent” function choice of basis set. The natural expansion is of Wang for the hydrogen molecule and the “ionic” uniquely determined4from the exact wave function, terms introduced in the Weinbaum function had an which is obviously quite independent of the par- overlap of about 0.95. One might have said that ticular basis set chosen. In actual practice it has the addition of “ionic” terms in this case was 95% been shown that even fairly crude approximations utilized in improving the “covalent” representation, to the exact wave function lead to very similar or indeed that the original “covalent” function was 95% ionic in the first place. One can easily show (1) Supported b y contracts a n d grants from t h e U. S. Air Force that if one is not particular about the precise nature OSR a n d from t h e National Science Foundation. of the “covalent”--“ionic” criterion, that there (2) H. Shiill, J . Am. C h ~ mS. n c . , 82, 1287 (1060). We refer t o this pnper 8 8 I. cxists almost any degree of ionic character that one (3) (a) P.-0. Lowdin a n d H. Shull, Phys. Rev., 101, 1720 (1956): chooses. (b) H. Shull a n d P.-0. Lowdin, J . Chem. Phys., 30, 617 (1959). (4) Excepting, of course, certain cases of degeneracy which are not of importance here.
( 5 ) H. Shull, J . Chem. Phys., 30, 1405 (1959). ( 6 ) J. Rraunstein a n d W. T. Simpson, ibid., 83, 174, 176 (19%).
