PROTON CHEMICAL SHIFTSAND REACTIVITY OF POLYNUCLEAR AROMATICHYDROCARBONS
293
Proton Chemical Shifts and the Reactivity of Polynuclear Aromatic Hydrocarbons by K. D. Bartle and D. W. Jones School of Chemistry, University of Bradford, Bradford, England
(Received February 27, 1968)
The apparently significant correlations in 22 alternant and 7 nonalternant hydrocarbons between pmr chemical shifts (6) and the corresponding values of the LCAO index of free valence (F,) have been investigated. They are found to arise as a fortuitous consequence of the geometry of these molecules so that, in a causative sense, 6 is unrelated to F, and hence to other molecular orbital indices of chemical reactivity. F, can also be correlated with 6 for the more distant CH, and CH2CHs protons in substituted hydrocarbons. In general, F , is larger for positions closer to ring centers because such positioiis are flanked by one or two ring-junction carbon atoms. Those chemical shifts in alternant hydrocarbons which deviate markedly from the 6 us. F, regression line are well explained by ring-current theory.
Introduction Proton magnetic resonance spectroscopy has been applied to the direct study of chemical reactivity in aromatic systems through determination of the nature and structure of substitution products as, for example, in the reactions of phenanthrene1 and of dibenz[b,f]o x e p h 2 Recently, comparisons of reactivity in aromatic substitution reactions have been made with pmr chemical shiftsap4 (6) and with esr hyperfine coupling constants.6 An interest both in the origin of pmr chemical shiftse and in the carcinogeriic properties of polynuclear aromatic hydrocarbons has led us to investigate reported correlations between 6 and a number of Huckel LCAO indices for relative chemical reactivity in substitution reactions, Choice of Molecular Orbital Reactivity Indices for Comparison Many indices of intermolecular and intramolecular reactivity have been proposed and their applications to various classes of mechanism (e.g., electrophilic and free radical) have been reviewed.’-I0 Broadly, both well-established and more recently proposed indices may be grouped under one or other of tm7o somewhat extreme quantum mechanical approaches : (i) isolated molecule methods, based on the initial states of the reaction, and (ii) localization methods, based on energy changes involved in the formation of the substitution transition-state complex. Thus for electrophilic substitution in, say, benzene, contributory hybrid I corresponds to approach i, while structures I1 and 111, respectively, emphasize the transfer of charge and delocalization aspects of approach ii.
6 & 8 H
y+
I
Y
Y’
11
I11
Greenwood and R4cWeenyQascribed the similarity in reactivity predictions made by superficially distinct indices, summarized by Streitwieser,’ to analytical properties of the equations from which the indices are derived. In particular, the close agreement between these indices and the experimental reactivities in alternant hydrocarbons arisess3l1because of a fortuitous correspondence between reactivity indices and the more fundamental energies of reaction and activation, AE. In favorable cases, differences in AE may be dominated by changes in the .Ir-electron energy, E,, as compared with changes in E arising from all other causes. Thus the reaction rate, k, relative to some standard such as benzene, at an alternant position r is given by8
Here p, the LCAO resonance integral of the C-C bond,
(1) P. M. G. Bavin, K. D. Bartle, and J. A. S. Smith, Tetrahedron, 21, 1087 (1965). (2) P. M. G. Bavin, K. D. Bartle, and D. W. Jones, J. Heterocyclic Chem., 5, 327 (1968). (3) J. Kuthan, 2. Chem., 6 , 150,422 (1966). (4) J. Kuthan, Collect. Czech. Chem. Commun., 33, 1220 (1968). (6) C. P. P o o h Jr., and 0. F. Griffith, J. Phys. Chem., 71, 3672 (1967). (6) K. D. Bartle and D. W. Jones, Trans. Faraday Soc., 63, 2868 (1967). (7) A. Streitwieser, Jr., “Molecular Orbital Theory for Organic Chemists,” John Wiley & Sons, Inc., New York, N. Y., 1961,Chapter 11. (8) M. J. 9. Dewar in “The Application of Wave Mechanical Methods to the Study of Molecular Properties,” R. Daudel, Ed,, Interscience Publishers, Ltd., London, 1966, p 65. (9) H.H. Greenwood and R. McWeeny, Advan. Phys. Org. Chem., 4, 73 (1966). (10) L. Salem, “The Molecular Orbital Theory of Conjugated Systems,” W. A. Benjamin, Inc., New York, N. Y.,1966,Chapter 6. (11) F. Burkitt, C. A. Coulson, and H. C. Longuet-Higgins, Trans. FaTaday Soc., 47,863 (1961). volume ‘73,Number B February 1069
K. D. BARTLEAND D. W. JONES
294 Table I: Scope and Sources of Chemical Shift Dataa ----ParentHydrogen position
Naphthalene Anthracene Phenanthrene Benz [a]anthracene Benzo [clphenanthrene Chrysene Naphthacene Triphenylene Pyrene Benzo[a]pyrene Benzo [e] pyrene Dibenz [a,c]anthracene Dibenz [a$] anthracene Dibenz[a,j] anthracene Per ylene Pentaphene Picene Coronene Biphenyl p-Terphenyl Biphenylene Acenaphthylene Fluoranthene Benzo [ k ]fluoranthene Benzo [ghi]fluoranthene Dibenso [ghi,mno]fluoranthene Acepleiadylene Azulene
Ref
---Methyl Methyl position
1-4, 9
24 24 25
I., 2 21 9 1-4, 9
1-12 1-6 1-6 1, 2, 5 1, 2 1, 2, 4 8 1-4, 9, 10 1-4, 9-11 7 7, 14 1-3 5, 6, 13 5, 6, 13 1 2-4 2’ 11 2 1, 3-5 1-3, 7, 8 1-3, 7-9 1,-5 1
26 27 28 29 6 24 29 30 30 29 31 24 29 30 24 32 32 33 27 15 15 15 34
1-12 1, 3* 5, 6
1, 2 1, 2, 9
1, 2, 5-7 1, 2, 4-6
derivative---Ref
---Ethyl Ethyl position
derivative-. Ref
31, 37, 40 31, 37, 41 25, 31, 36, 37, 39, 42, 43 31, 39 44, 45 46
2
41
2, 3, 9
25,42
27, 47 27, 37, 43, 48
2
51
1, 2, 4 10
31
1
49
1-3
52
1 2,c 4d
37, 43 40, 50
1 2, 3
43 40
1, 2
13 13, 35
a Alternant hydrocarbons, from naphthalene t o biphenylene, are listed first, followed by nonalternants from acennphthylene to azulene. Except for those marked with a superscript, all methyl derivatives are monomethyl; all ct,hyl derivatives are monocthyl. 3,10-Dimethylbenzo [clphenanthrene. 2,2’-Dimethylbiphenyl. 4,4’-Dimethylbiphenyl.
‘
is closely related to AE, and F,, the free valence index, is an example of a type i index. A chemical shift, 6, at a hydrogen atom is a measure of the total of shielding effects arising from the following, and possibly other, contributions: (1) diamagnetic circulations in the hydrogen atom, (2) paramagnetic circulations in the hydrogen atom, (3) a-bond circulations on the attached carbon and other atoms, and (4)n-system circulations. The q, index (one of type i) is based on the LCAO n density at the carbon atom and may influence term 1 above, despite12insulation of hydrogen from carbon by a bonds. While correlations between 6 and q,, are well established for hydrocarbon ions,ls nitrogen heteroc y c l e ~ ,certain ~~ nonalternant hydrocarbons, l a,l5 and substituted aromatic hydrocarbons,16 q, is unity for all positions in unsubstituted alternant hydrocarbons according to HRIO17 and some more realistic SCF theories;’S effects arising from changes in terms 1 and, a fortiori, 2, should therefore be small. Moreover, calculations on polycyclic hydrocarbons showa that, if shifts are referred to the appropriate monocycle, the contributions from term 3 are also small. The Journal of Physical Chemistry
Of the five indices with which I 6 b > 6,. Observed shifts do, indeed, follow this prediction, and the correlation between 6 and F , is merely a manifestation of this, just as the further correlations reported by Muthan3p4are assured by the interrelation of reactivity indices. The Journal of Physical Chemistry
[elpyrene H(2) are substantially greater than those calculated from the 6 os. F, regression equation. For both types of proton in biphenylene, the above equation predicts deshieldings with respect to benzene instead of the large shieldings observed experimentally. On the other hand, shifts calculated from ring-current theory agree well with experiment for all five protons (Table 111). Since coronene, pyrene, and benz [elpyrene are compact platelike hydrocarbons, ring-current contributions to 6 are larger than for the more open2
pyrene
2
coronene
benz[e]pyrene
chain compounds which comprise the majority of alternants in Table I. F , values, on the other hand, which reflect only the immediate environment of the carbon position, are typical of non-peri (pyrene and (56) J. A. Fisher and F. Yates, “Statistical Tables,” 6th ed, Oliver and Boyd, Edinburgh, 1963, p 63. (57) D. W. J. Cruiokshank, Tetrahedron, 17, 156 (1962). (58) J. A. Pople, J . Chem. Phys., 2 4 , 1111 (1956). (69) J. S. Waugh and R. W. Fessenden, J . Amer. Chem. Sac., 79, 846 (1957). (60) C. E. Johnson and F. A. Bovey, J. Chem. Phys., 29, 1012 (1968). (61) D.G. Farnum and C. F. Wilcox, J . Amer. Chem. Soo., 89,5379 (1967).
PROTON CHEMICAL SHIFTSAND REACTIVITY OF POLYNUCLEAR AROMATIC HYDROCARBONS benz [eIpyrene) and peri (coronene) positions. Simple ring-current theory cannot explain why biphenylene protons resonate a t higher field than those of benzene. Recently, Figeys02 has found that, for the four-membered ring in biphenylene, the reverse or paramagnetic current characteristic63 of 4%n-systems more than outweighs the diamagnetic currents for the six-membered rings; thus both protons in biphenylene have a large net shielding compared with those of polyacene positions with similar F , values. Although the correlation between 6 and F, for alternant positions which are sterically hindered to varying degrees (Table 11, row 2) appears to be significant, it also is fortuitous. Of those protons which are similarly hindered in “bay” situations and hence presumably subject to comparable u-bond anisotropy-van der Waals influences, 11 are NN-NJ (F, = 0.439-0.455) and 4 are NJ-NJ; as argued above, the latter are more deshielded and, for different reasons, have larger values of F, (0.498-0.502). Of the three shifts which deviate most from the line, H ( l ) of perylene is less hindered than the other protons in group 2, owing to the long C-C bond,B4 while both H(l) of benzo [clphenanthrene (“fjord”) and H(14) of dibenz [a,j]anthracene (double “bay”) are more hindered.
297
-1.6 I
2
Y P
-0.4
4 ’5
.-D
I! -0.8
5
f Figure 1. Graph of methyl shielding (parts per million relative to toluene) vs. proton shielding (parts per million H 0 ~ . 5 1 6 ~- 0.13 relat,ive to benzene). The regression line, ~ C = is calculated with divergent points (1)2,2’-dimethylbiphenyl, (2) 1-methylbenzo[c]phenanthrene)excluded.
Table IV: Correlation ( r ) and Regression ( a and b ) Coefficients for Relation 6, =
+b
U ~ H
Significance
Xa
No. of compounds
r
a
b
Methyl CH, of ethyl CHs of ethyl
34 11 11
0.961 0.961 0.948
0.511 0.607 0.226
-0.130 -0.049 -0,043
level, %
0.1
0.1 0.1
a x includes compounds listed in Table I except where specified in the text.
Perylene Beneo [clphenanthrene Dibene [a,j]anthrancene
Chemical shifts of nonalternant hydrocarbons are only fairly significantly correlated with F , (row 3, Table 11); restriction of the values to benzenoid protons produces better correlation (row 4). Two factors make interpretation of these results more difficult than for alternants; first, nonuniform charge densities may make quite large shift contributions; second, the currents in rings containing fewer than six carbon atoms have not been calculated for all these compounds; for the cases where they have been calculated, these currents are diamagnetic.06 F, values for benzenoid positions in nonalternants also fall into three groups, corresponding to proximity to an increasing number of rings: (a) flanked by bonds NN and NN, 0.395-0.409; (b) flanked by bonds NX and NJ, 0.438-0.478; and (c) flanked by bonds NJ and NJ, 0.497 (one only). Plots of 6 for nonsterically hindered methyl and ethyl protons us. F , value a t the same position in the unsubstituted parent hydrocarbon, together with the regression data in rows 5-7 of Table 11, provide further support for the ring-current explanation of chemical shifts in polynuclears. Even though the CH, and CHzCHa protons are separated from the aromatic carbon atoms
by two Q bonds, their shifts still correlate well with the n index, F,. Moreover, those points which show greatest deviations from the regression lines are again well explained by ring-current theory. For 2-methylpyrene and ethyl- and methylcoronene, the same argument applies as was used with pyrene and coronene in Table 111. In 2,2’-dimethylbiphenyl and 2-ethylbiphenyl, substituent groups are shielded since, as uv evidence suggests,66-68they are held above the ring plane. Although the deviations for ethylcoronene and 2ethylbiphenyl evidently reduce the r value in the CH2CH3 graph of 6 us. F,, the degree of correlation for both the CI13 and CNzCH3 graphs is similar to these for aromatic protons (Table 11). This is not unexpected in (62) H. P. Figeys, Chem. Commun., 495 (1967).
(63) J. A. Pople and K. G. Untch, J . Amer. Chem. Soc., 88, 4811 (1966). (64) A. Camerman and J. Trotter, Proc. Roy. Soc., A279, 629 (1964). (65) J. A. Pople, M o l . Phys., 1, 175 (1958). (66) G. H. Beaven, “Steric Effects in Conjugated Systems,” H. B. Gray, Ed., Butterworth and Co. Ltd., London, 1958, p 22. (07) G. H. Beaven and E. A . .Johnson, “Conference on &‘Iolrcnlar Spectroscopy,” E. Thornton and H. W. Thompson. E d . , Perpainon
Press, London, 1959, p 78. (68) 9.F. Mason, Quart. Rev. (London), 15, 287 (1961). Volume 73, Number d
February 1060
PAULMILIOSAND JOHN NEWMAN
298 view of correlation between B C H ~and the corresponding unsubstituted BH noted earlier by RIacLean and I14ackorsgfor seven compounds and extended in Figure 1 to include additional methyl polynuclears; analogous plots can be made for CH? and CH3 shifts in ethyl polynuclears. The regression data in Table IV have been calculated for all positions given in Table I, apart from the special cases in which the methyl group suffers shielding from its location above the ring plane.6gJ0 All three groups of shifts are highly significantly related to BH; for CH3 and CH&H3, the gradients (a) are
similar, while, for the CH2CH3 protons more remote from the ring centers, the gradient is lower. Acknowledgments. We are grateful to Mr. R. L. Cureton, who provided a computer program for calculating regression parameters. This work was carried out during the tenure of an I.C.I. Fellowship by K. D. B. (69) M. 5. Newman and M . Wolf, J . Amer. Chem. SOC.,74, 3225 (1952). (70) A. W. Johnson, J. Org. Chem., 24, 833 (1959).
Moving Boundary Measurement of Transference Numbers by Paul Milios and John Newman Inorganic Materials Research Division, Lawrence Radiation Laboratory, and Department of Chemical Engineering, University of CalQornia, Berkeley, California (Received March 8, 1068)
A moving-boundary system is analyzed, and an equation, valid for concentrated as well as dilute solutions, is obtained for the transference number. When the partial molal volume of the solvent is constant through the boundary, the equation reduces to the approximate equation now in common use. The cation transference number in 0.213 M NH4NOa was experimentally determined at 25’ and found to be 0.5140 k 0.0024.
Introduction Rloving-boundary measurements date back to the nineteenth century.‘ The two-salt boundary mas analyzed in 1900 by the mathematician Weber.% I n 1910, the chemist Lewis3 presented an analysis which corrected for the boundary movement caused by the electrode reaction. His equation was thought to be restricted to dilute solutions’ until B e ~ m a n in , ~ 1962, showed that it actually applies to systems in which the partial molal volumes are constant through the boundary-a slight,ly less stringent condition. KO other theoretical progress has yet been made, and Lewis’s equation is still used today.5 I n the present work a more detailed analysis of the moving-boundary system yields an expression of more general validity for the transference number. Analysis of the Two-Salt Boundary Figure 1 shows the two-salt boundary a t steady state. Solution A is composed of ions 1 and 3 and, being the lighter of the two solutions, is above solution B, which is composed of ions 2 and 3. The solvent is referred to by “0.” The equations necessary to describe the movingboundary system are the continuity equation or material balance (1) The Journal of Physical Chemistry
an equation relating the current density to the fluxes
i
=
FCX,C~V~ i
a statement of electroneutrality
cx,ct
=
0
z
and a flux or transport equation ape
ce-- = bX
where
RTC--(vjClCl j
C T Q ~ ~
- v,)
(4)
is the electrochemical potential and where Dtj = D j l . These equations are discussed in detail by Sewman.6 When the motion of the ions is referred to the solvent motion, the transference number (relative to the solvent velocity) is defined as the fraction of the current carried by an ion in a solution of uniform composipe
L. G. Longsworth, Chem. Rev., 11, 171 (1932). (2) (a) H. Weber, Sitzber. Deut. Akad. Wiss. Berlin, 936 (1897); (b) H. Weber, “Die partiellen Differential-gleichungen der mathematischen Physik,” Friedrich Vieweg und Sohn, Braunschweig, 1900, pp 481-506. (3) G. N. Lewis, J. Amer. Chem. Soc., 32, 862 (1910). (4) R. J. Bearman, J. Chem. Phys., 36, 2432 (1962). (6) R. Haase, G. Lehnert, and H.-J. Jansen, 2.Phys. Chem. (Frankfurt am Main), 42, 32 (1964). (6) J. Newman, Advan. Electrochem. Electrochem. Eng., 5, 87 (1967). (1) D . A. MacInnes and
