JOHN E. BLOOR AND DONNA L. BREEN
716 water-acetone solutions is lower than its energy when it is in pure acetone.20 The degree of dissociation of LiCl in the penultimate columns of Tables I and I1 was calculated by successive approximations from the law of mass action and the Debye-Huckel equation for the activity coefficient.21 The values 21.7, 20.7, and 19.8 were used for the dielectric constant22of the solvent at 15, 25, and 35’, respectively, and 2.4 A for the a parameter in the DebyeHuckel equation (the sum of the crystallographic radii28 of Li+ and C1-). The 25’ value for the dissociation was used for all temconstantz4of LiC1, 3.3 X peratures, because the conductivity data in the liter& ture for other temperatures were thought to be of insufficient accuracy. When the temperature dependence of the dissociation constant becomes available, it will then be necessary to revise the a values in Table I1 (except at 25’) and, hence, the activation energy 17.9 kcal mole-1 quoted above. An equation in which the dissociation constant is expressed as a function of temperature has been re-
ported.26 Rate constants, ki, evaluated using a values from this equation, yield an activation energy of 19.2 kcal mole-’. The upon which this equation is based appear, however, not to be of comparable accuracy to those reported in ref 24.
Acknowledgment. The authors wish to thank the Swedish Natural Science Research Council for financial support. (20) J. A. Leary and M. Kahn, J . Am. Chem. SOC.,81,4173 (1959). (21) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,“ Butterworth and Co., Ltd., London, 1959, pp 229-230. (22) R. C. Weast, “Handbook of Chemistry and Physics,” 46th ed, The Chemical Rubber Publishing Co., Cleveland, Ohio, 1965-1966, E-50. (23) L. Pauling, “The Nature of the Chemical Bond,” Cornell University Press, New York, N. Y., 1940, Chapter X. (24) L. G. Savedoff, J . Am. Chem. Soc., 88, 664 (1966). (25) Farhat-AIL and E. A. Moelwyn-Hughes, J . Chem. SOC., 2635 (1959). (26) 8. V. Serkov, J . Russ. Phys. Chem. Soc., 40, 413 (1908). (27) N. L. Ross Kane, Ann. Rept. Progr. Chem. (Chem. Soc. London), 27, 351 (1930). (28) P. C. Blokker, Reo. Trav. Chim., 54, 975 (1935).
Valence Shell Calculations on Polyatomic Molecules. 11.
CNDO SCF Calculations on Monosubstituted Benzenes1 by John E. Bloor and Donna L. Breen Cobb Chemical Laboratory, University of Vdrginia, Charhtteevilk, Virginia dd901
(Received July 19, 1967)
The results of SCFMO calculations, which include all valence electrons with the assumption of complete neglect of differential overlap (CNDO method), are described for substituted benzenes CaHsX where X is CH3, F, OH, NH2,NOz, CHO, and CF3. The dipole moments are in good agreement with experiment. The changes in the u- and ?r-electron densities of the C6H5X compounds compared to the corresponding HX compounds, which give rise to mesomeric moments, are discussed. It is shown that there is good agreement between total electron densities and C13 chemical shifts for all positions including the carbon atoms bonded to X. There is not a good correlation between orbital energies and ionization potentials.
Introduction Many of the qualitative and quantitative concepts of physical organic chemistry are based on experimental studies on the nature of the interactions between substituents and the benzene ring.2 Nevertheless, although there have been very many theoretical investigations on monosubstituted benzenes,zJ previous theoretical methods have considered explicitly only The Journal of Physical Chemietry
the ?r electrons and have either ignored entirely the effect of the u electrons or have taken them into account (1) Abstracted in part from the M.S. Thesis of D. L. Breen, University of Virginia, Charlottesville, Va., 1967. (2) (a) A. Streitwieser, “Molecular Orbital Theory for Organic Chemistry,” John Wiley and Sons, Inc., New York, N. Y., 1961,; (b) C. K. Ingold, “Structure and Mechanism in Organic Chemistry, Cornell University Press, Ithaca, N. Y., 1953.
VALENCE SHELLCALCULATIONS ON POLYATOMIC MOLECULES in a very empirical f a ~ h i o n . ~In the previous paper,6 we demonstrahed, for heterocyclic compounds containing 0 and N, that the CNDO/2-SCFMO method, which was originally suggested by Pople, Segal, and Santry,6*7 and which includes all the valence electrons irrespective of their type, gave charge-density distributions, which could be used to calculate dipole moments in very good agreement with experiment. We also found it could be used successfully to interpret C13 chemical shifts. In this paper, we present the results of a similar study on monosubstituted benzenes. Prior to our work on heterocyclic corn pound^,^ the present work on monosubstituted benzenes, and the recent work of Dewar and Klopmans on some small hydrocarbons, SCFMO calculations, using all valence electrons, have been confined to molecules of the AB2 and AB3 type, to formaldehyde, and to ethane.6t7 However, the assumption of complete neglect of differential overlap (CNDO) makes it possible to avoid the difficult and expensive problem of calculating threeand four-center repulsion integrals so that it becomes reasonable to carry out calculations on quite large molecules (20-30 atoms) on even a moderate-sized computer .
Method The CNDO/2 method and its use in calculating dipole moments and C13 chemical shifts have been previously described.5~6 The dipole moment is assumed to be made up of a contribution pat from atomic charge densities and psp, a contribution from the atomic dipole. p,, arises from the mixing of the s and p orbitals on the same atom and includes the lone-pair moments (pLp) of heteroatoms. It is sometimes referred to as the hybridization moment. Although its importance COZ, has been recognized for small molecules (e.g., “3, and HtO) for many year~,~JO it has often been neglected in even very recent calculations on dipole moments. l1 These contributions are calculated from the orbital-bond orders P,, by eq 1-3. atoms
A
A
c
(103.573
+
bpA
+
Ud
2
/3(PffAffAPZASA
+
+
PSAZAPZAXA
-
2/8(PZAffAPffAZA) C2/3(PYAuBPzAzB
B #A
+
PZAZAPffAffA)
PZAZBPZAxB
PZAZBPffAffB)
+
+
- 4/3(PXAffBPYAXB)
(6)
where Aqtotal is the excess total charge density on atom A and P Z A v B is the bond order between a 2pz atomic orbital on atom A and a 2pu atomic orbital on atom B. In carrying out these calculations, it was found that nonnearest neighbor terms contributed very little to the &AB values ( OH > NH2 (i.e., a shortrange inductive effect). In addition t o this, our calculations predict a somewhat unexpected considerable long-range inductive effect resulting in a considerable positive charge at the para position in the order NH2 > OH > F. This positive r~ charge has a considerable effect on the magnitude of the total charges, since it is about half the size of and opposite in sign to the ?r-electrondensity a t the para position (Table 11). The possible existence of this effect, at present, can only be justified by the fact that the dipole moments calculated by including it are in good agreement with experiment (Table I). A comparison of the calculated dipole moment components for HX and G H s X (Table I) shows that in fluorobenzene there is a considerable rehybridization
+
VALENCESHELL CALCULATIONS ON POLYATOMIC MOLECULES of the F orbitals on replacing H by C6H5 and this causes the lone-pair moment, which is governed by the magnitude of the bond-order term between the 2s orbitals and the 2p AO's on the F atom, to be reduced to almost zero. The n-electron dipole moment, pn, is smaller than the corresponding dipole of the u electrons, but (because of the reduced pBPvalue) the total dipole moment is just a little lower than the moment for HF. In the case of phenol (planar conformation), the calculation predicts little change in the psp term. The p" moment induced in the ring is this time, however, greater than the p" increase and again results in a low total moment compared with the unsubstituted parent, HzO. In our calculations on aniline, we assumed two structures: (a) a planar form and (b) a pyramidal NHz group, as suggested by recent microwave measurem e n t ~ . The ~ ~ dipole moment for the planar form was much too low (0.98 D), due to a cancelling out of the n contribution by a very strong, entirely in-plane, u moment, On the other hand, the dipole moment for the pyramidal structure was in excellent agreement with e~periment.1~The charge distributions for the two forms were almost identical and the larger dipole moment in the pyramidal molecule was due to the acquisition of a considerable out-of-plane u moment, i.e., in the x direction. The total energy for the nonplanar form was slightly more negative than for the planar form, but in view of our experience with the tetraz~les,~ we prefer not to attach any significance to the calculated total energy until more knowledge has been gained on calculations of conformation energies. We do believe, however, that the CNDO/2 method is potentially very useful for calculating conformations by comparing calculated dipole moments, for different assumed conformations, with observed dipole moments. l5 The methyl group of toluene is usually assumed to be an electron-donating group because of the possibility of hyperconjugation, which would cause an increase in the total n-electron density of the benzene ring by electron transfer from the CH bonds. Our calcul& tions predict that this occurs only to a small extent (the ring receives only 0.0125 n electron and this is not enough to counteract a flow of u electrons (0.205 e) in the opposite direction). The modified extended Hiickel calculations of Newton, et a2.,l6 gave values about double these quantities, but in the same direction. As a consequence of this high charge migration, their dipole moment was, as is usual with extended Hiickel calculations, more than twice the experimental values; the CNDO/2 method, on the other hand, gives a value lower than the observed one, a tendency we have found in other calculations on compounds containing methyl groups. 16 Electrow Withdrawing Groups. For the three electron-attracting groups, NOz, CHO, and CN, there is a considerable increase in dipole moment on replacing
719
hydrogen by phenyl. The analysis of the theoretical dipole moment into its u and n components suggests the reason for these changes (Table I). There is again a considerable charge polarization of the c electrons of the ring, especially a t the carbon to which the group is attached. Because of this, the u moment is usually increased with the negative end on the substituent. I n nitrobenzene, the u moment of the ring is in the opposite direction and is greater than that of the NOz group. The total u moment is consequently reversed in direction compared to HNOZ, so that it now reinforces the n moment, resulting in the prediction of a very high dipole moment for nitrobenzene, as is found experimentally. In all these three compounds, however, the increase in the calculated total dipole moment of the benzene derivative compared to the HX compound is mainly due to a significant increase in the n dipole moment contribution of the former. Another electron-attracting group we have studied is the CF3 group. Most of the dipole moment is due to the polarity of the CF bonds; there is, however, a total transfer of 0.08 e from the benzene ring onto the three fluorine atoms. Only a small part of this electron transfer is predicted as being due to the n electrons of the benzene and can be regarded as the MO interpretation of fluorine hyperconjugation. This is usually expressed in terms of resonance structures such as F I
The rest of the charge transfer (0.067 e) is the equivalent of inductive withdrawal. According to this picture, the observed increase in dipole moment (1.2 D) on replacing H in fluoroform by C6H5 is due to an increase in the electron density on the fluorines, accompanied by small positive charges appearing in the phenyl substituent. Our calculation does not support the previously proposed concepts of n-electron donation by the fluorine atoms into the benzene n orbitals and the idea of p-n interaction. l7 These results demonstrate that the final calculated dipole moment is a complex mixture of contributions from the u electrons (p"), the n electrons, (b"), and the lone pairs and bond hybridization moments (pap); the relative importance of each term is very specific for (13) D.Lister and K. Tyler, Chem. Commun., 152 (1966). A. L. McClellan, "Tables of Experimental Dipole Moments," W. H.Freeman and Go., San Francisco, Calif., 1963. (15) J. E.Bloor and F. P. Billingsley, unpublished data. (16) M. D. Newton, F. P. Boer, and W. W. Lipscomb, J. Am. Chem. Soc., 88, 2353 (1966). (17) W.Sheppard, ibid., 87,2410 (1965). (14)
Volume '7% Number 8 February 1968
720
JOHNE. BLOOR AND DONNA L. BREEN
I
L
8
3@
o-t*-
-40 Sc*exP(ppml-
Figure 1. Aq" values us. CY I chemical shifts: I, Auorobenzene; 2, benzaldehyde; 3, nitrobenzene; 4, toluene; 5 , phenol; 6, aniline; €3, a-carbon atom; 0, o-carbon atom; @, m-carbon atom; 0 , p-carbon atom; Q , benzene.
each molecule. It is therefore probably unwise to deduce the magnitude of mesomeric interactions on the basis of simple comparisons between the dipole moments of aliphatic and aromatic compounds as has often been done in the past.'O C18Chemical Shifts. The CIS chemical shifts of monosubstituted benzenes have been the subject of much discussion regarding qualitative correlations between experimental data and reactivity parameters.*8-20 These suggested correlations have provoked many ideas in the literature concerning the nature of C1* shifts. Because of the success of our dipole-moment calculations, we believe our calculated u and IT charge densities for a number of substituted benzenes are reasonably realistic. We have, therefore, used them to investigate the relationships between theory and experiment for the C18 shifts of monosubstituted benzenes. In our previous work on azines6 we investigated the relationship between C1* chemical shifts and (a) ?relectron densities A*", (b) excess total electron densities A\4tota', and (c) the theoretical chemical shift (up ud) calculated using the eq 4, which was derived by Pople and Karplus.12 In Figure 1, we have plotted the excess n-electron density A," against the observed shift relative to benzene for the 0-, m-,and p - carbons of
+
The Journal of Physical Chemiatry
Figure 2. Aqtotal us. CI*chemical shifts. and circle designations as in Figure 1.
Numbering
the ring. There is a fairly good relationship between the points. The graph goes through the origin but the slope of the best line is a little higher than the experimental value of Spiesecke and SchneiderI9 obtained C?H,+, and C8Hs-8 from measurements on CaHa-, COHO,
Le. SC18 = 160A,"
(7)
However, carbons ortho to the highly electronegative substituents Not, OH, and NH2 deviate noticeably from the line. Also, the a-carbons, to which the substituents are attached, are grossly off the line for the ortho and pura positions. In Figure 2 is plotted the total excess charge, Apt*', against the observed shifts. It can be seen that the ortho positions of phenol, nitrobenzene, and aniline are now much closer to linearity than in Figure 1. Spiesecke and Schneiderls had suggested that magnetic anisotropic effects at these positions are appreciable. However, the use of total electron densities, rather than n (18) (a) H. Spiesecke and W. G. Sohneider, J. Chem. Phys., 3 5 , 731 (b) T. K. Wu and B. I?. Dailey, ibid., 41, 2796 (1964); (c) J. B. Stothers, Quart. Rev. (London), 19, 144 (1966); (d) G. E. Maciel and J. J. Natterstad, J. Chem. Phys., 42, 2427 (1966). (19) H. Spiesecke and W. G. Schneider, Tetrahedron Letters, 14, 468 (1961);
(1961).
(20) T. D. Alger, D. M. Grant, and E. G. Paul, J. Am. Chem. ~ o G . , 88,6397 (1966).
VALENCE SHELLCALCULATIONS ON POLYATOMIC MOLECULES
p -200-
-210
-200
-
721
-
- 210-
/
I
O5
$?$ @9
- 220 -
-220j-
-230-
-24iJ0
>;-
-20
1 -;
6c" exp ( ppm)
-
A
io
2
- 240-40
-30
-20
0
-10
10
20
2 1
8cdl axp. (ppd-
Figure 3. Experimental G I * chemical shifts us. theoretical chemical shifts (q,f U d ) from eq 4, using AE = 10.0 eV for all compounds. Numbering and circle designations as in Figure 1.
Figure 4. Experimental C1* chemical shifts us. theoretical chemical shifts (vP U d ) using AE = 9.8 eV for nitrobenzene and benzaldehyde. Numbering and circle defgignations as in Figure 1.
densities alone, indicated that these anisotropic effects are much smaller than was originally thought. The main advantage of using the total excess charge, A:ota1, rather than APT is seen, however, when the points for a-c,srbon atoms are included. If one considers the approximate nature of the theory used to calculate the electron densities and the fact that the experimental data are uncorrected for solvent effects, ring currents, or any anisotropic effects, the graph shows a very definite, strong relationship between total electron density and C13 chemical shifts. We can now conclude that the apparent success of the relationship between A: for the para position and the observed shifts (Figure 1) is not so much due to the insensitivity to changing the substituent of the u-electron density a t these positions, particularly the para positions, but rather is due to a rough proportionality between A," and Apt'' (Table 11). The main disadvantage of Figure 2 over Figure 1 is that the former does not pass through the origin (Le., the point for benzene). This however, may be due to the presence of anisotropic effects of the substituent group, which would bring the line through the origin. I n Figure 3, we have plotted the up 4- Ud values, calculated using eq 4, against the observed shifts.
There are considerable deviations and the line cannot be said to be any better than the line for total charge densities (Figure 2), especially for the para positions of the electron-attracting groups CHO and NOz. These molecules, however, have low-lying excited states of n-a* type, which would make a smaller AE value reasonable. This would increase the magnitude of the up term and would move the points closer to the regression line. For example, a decrease in AE of only 0.2 eV changes the value of up Ud for the para position of nitrobenzene from -205.24 to -213.46 ppm. The graph of Figure 4 shows the effect of changing for nitrobenzene and benzaldehyde the AE value from 10 to 9.8 eV. The over-all result is better, except that the a-carbon of benzaldehyde is now off the graph. It does seem, though, that a possible solution to the apparent poor results for the electron-attracting groups CHO and NOS, shown in Figure 3, could be due to the presence of low-lying n-a* transitions, as corrected for in Figure 4. More experimental data, particularly for molecules containing electron-attracting groups such as CF3 and CN which do not have low-lying n-n* transitions, might help clarify the situation. Until such a time as more data are available, it seems that the use of the Karplus-Pople theory12 over the simpler
+
+
Volume 71,Number P February 1968
JOHN E. BLOOR AND DONNA L. BREEN
722 relationship between total charge densities and chemical shifts is only marginally justified for monosubstituted benzenes. Further support for the conclusion that the Karplus-Pople theory should be used with care can be found by comparing recent experimental data on polycyclic hydrocarbons*O with the original calculations by Pople and Karplus12 on these compounds. The correlation with experiment is very poor, especially for the central carbon atoms joined to three other carbon atoms. These atoms all exhibit chemical shifts of -10 to -14 ppm relative to benzene, whereas the predicted values are much too small (-2 to - 5 ppm) or even of the wrong sign (e.g., position 12 in phenanthrene.) Ionization Potentials. I n our work on heterocyclic5 and other16 molecules we found that the relationship between the experimental ionization potential and the energy of the highest occupied molecular orbital, E(HOMO), was not very satisfactory. This conclusion is supported by the results for monosubstituted benzenes summarized in Table 111. The general qualitative trend is correct for electron-donating groups, but for the electron-withdrawing groups CHO, NOz, and CN, the theory predicts -E(HOMO) values which are lower than for benzene, whereas the experimental values are clearly higher (Table 111). These incorrect predictions could be due to the breakdown of the assumption, implicit in equating the negative of E(HOM0) to the ionization potential, of neglect of reorganization energy of the electrons on ionization. Since the electron-withdrawing groups do contain easily polarizable nonbonded electrons, they would be expected to have considerable reorganization energy.
The Journal of Phgaical Chemiatry
Table I11 : Ionization Potentials of Monosubstituted Benzenes ( CeH&)
X
H CHa F OH 2"
NO, CHO
CN CFa
-E(HOMO), eV
13.89 12.93 13.29 12.43 11.84 13.17 12.97 13.16 14.17
AIP (Calcd),
IP
AIP
(exptl),
(exptl),
eVQ
eVb
eVO
9.24 8.84 9.20 8.46 7.71
0.40 0.04 0.78 1.53
0.96 0.60 1.46 2.05 0.78 0.92 0.73 -0.28
9.86 9.65 9.67
-0.62 -0.41 -0.43
a AZP (calcd) is the difference between the energy of 'the highest occupied MO of CoHsX and the corresponding value for benzene. Taken from D. W. Turner, Advan. Phys. Org. Chem., 4, 31 (1966). E AIP (exptl) is the ionization potential relative to that of benzene in electron volts.
It is interesting to note that for hydrocarbons (ems., methane, ethane, ethylene, and butadiene16) the CNDO/2 method gives relative energy values, even for the deeper orbitals, which agree with experiment just as well as in other calculations.*J6 It seems that it is only on the introduction of heteroatoms that the discrepancies appear. On the other hand, the discrepancies could be due to the inadequacy of the CNDO/2 method itself.
Acknowledgments. The authors are indebted to the National Institutes of Health and the Air Force Directorate of Scientific Research through Grant No. AFAFOSR-1184-67 for financial support for this work.
