3672
CHARLES P. POOLE, JR.,AND 0. Ii’. GRIFFITH,I11
Relationship between Chemical Reactivity and the Hyperfine Structure of Polycyclic Hydrocarbons’
by Charles P. Poole, Jr., and 0. F. Griffith, I11 Department of Physics, University of South Cardina, Columbia, South Carolina
(Received February 67, 1967)
The hyperfine coupling constants ai of a polycyclic hydrocarbon are found to be closely related to the observed reactivity rates at various sites in the molecule. These coupling constants provide an experimental determination of the spin density a t the various molecular sites, and this is numerically equal to one-half the frontier electron density. A detailed comparison is made of the phenanthrene nitration reaction, and the coupling constants ai are found to be closely proportional to the logarithm of the reaction rate hi. The frontier electron densities scatter somewhat from a straight line and the other reactivity constants xii, Fi,Li,Si, and Ni exhibit a very poor correlation with these reactivity data. A general agreement is found between the experimental electron spin resonance hyperfine coupling constants and the observed order of reactivities at various sites in naphthalene, anthracene, phenanthrene, pyrene, chrysene, 1,2-benxanthracene1 3,4-benzpyrene, and perylene.
Introduction Several authors2-5 have reviewed the Use of molecular orbital theory to calculate chemical reaction rates. A number of indices of reactivity have been suggested and used t o explain the relative reactivities of the individual sites within a given molecule (intramolecular relative reactivity) and the reactivities derived from a comparison between different molecules (intermolecular relative reactivity). Salem4 has given an extensive discussion of phenanthrene, and Table I presents the data collected by him, using the molecule numbering: convention shown in Figure 1. The computational procedure often begins with the simple mathematical model Of the molecule the Huckel molecular Orbital (HMO) approximation, and it provides values of the various indices of reactivity. Most of the indices are functions of the Huckel coefficients C k i , but ordinarily no independent experinlental checks are made Of the values for these coefficients. Other indices depend upon postulated intermediate states jvith energies which are not accessible to measurement. Over the past few years a number of investigators have employed the technique of electron spin resonance (esr) to measure the hyperfine coupling constants of many ions‘ Of interest to us here are the measurements that have been carried out with The Journal of Physical Chemistry
polycyclic hydrocarbons. The measured hyperfine splittings correlate well in most cases with spin densities calculated by the Huckel method. We shall show the very close relationship between these measured hyperfine constants and the frontier electron densities suggested by Fukui, et aL6-’ as indices of chemical r e x tivity.
Hyperfine Structure and Reactivity The electron Spin resonance (esr) spectra arising from radical ions formed from polycyclic hydrocarbons have been widely studied. The subject has been reviewed (1) This work is supported by the National Institutes of Health, Grant NO.CA06401-05. (2) (a) B. Pullman and A. Pullman, Progr. Org. Chem., 4, 31 (1958); (b) H. H. Greenwood and R. McWeeny, Advan. Phys. Org. Chem., 4, 73 (1966), (3) B. Pullman and A. Pullman, “Quantum Biochemistry,” Interscience Publishers, Inc., New York, N. Y., 1963, pp 155-181. (4) L. Salem, “The Molecular Orbital Theow of Conjugated Systems,” W. A. Benjamin, Inc., New York, N. Y., 1966. (5) S. Glasstone, “Textbook of Organic Chemistry,” 2nd ed, The Macmiuan CO.,New York, N.Y., 1960. (6) K.Fukui, T. Yonezawa, and H. Shingu, J . Chem. Phys., 20,
722 (1952). (7) K.Fukui, T. Yonezawa, and H. Shingu, ibid., 22, 1433 (1954). (8) K. Fukui, T.Yonezawa, and C.Nagata, Bull. Chem. SOC.Japan, 27,423 (1954); J. chm. Phys., 26,831 (1957).
CHEMICAL RE.4CTIVITY AND THE
HYPERFINE STRUCTURE O F POLYCYCLIC HYDROCARBONS
Table I : Comparison of Phenanthrene Nitration Reactivities ki, with Several Theoretical Indices Theoretical Spin Densities,
Position
Log (kilkn)
9 1
0.02 -0.11 -0.19 -0.71 -0.77
3 2 4
(fi,
sii,
3673
Fi,L,, Si, N i ) ,
and Experimental Hyperfine Coupling Constants, ai
pi,
Exptl HFS constantb
HMO spin densityC
Frontier electron densitya
Selfpolarizabilitiesa
Free valence indexa
ai
Pi
/i
Xii
Fi
Localization energya Li
4.43 3.71 2.88 0.43 0.63
0.172 0.116 0.099 0,002 0.054
0.344 0.232 0.198 0.004 0.108
0.442 0.439 0,409 0.403 0.429
0.451 0.450 0.408 0.402 0.441
2.298 2.317 2.453 2.497 2.365
Superdelocalizabilitiesa Si
0.997 0.977 0.893 0.860 0.939
Reactivity no.a Ni
1.80 1.86 2.04 2.18 1.96
a Data from tabulations in ref 4 ; k , is the reactivity of the a position of naphthalene. * F. Mobius, 2. Naturjorsch., 20, 1102 (1965). From Huckel molecular orbital calculations. H. M.McConnell, J. Chem. Phys., 28, 1188 (1958); H. M. McConnell and D. B. Chestnut, ibid., 27, 984 (1967); 28, 107 (1958). See also T. C. Sayetta and J. D. Memory, J. Chem. Phys., 40, 2748 (1964).
9 -
empirical electron distributions may be postulated. Both theories provide about the same agreement with the available data on hydrocarbon radical i o n ~ . ' ~ J ~ An individual radical ion ordinarily has a Q value close to the appropriate average value. The experimental hyperfine coupling constants and theoretical HA10 spin densities for ~henanthrene'~ are shown in columns three and four, respectively, of Table I. The Huckel order was used in assigning the experimental coupling constants. Although errors in the assignment of spin densities to individual sites will be more likely if there are two values very close together, comparisons such as that shown in Figure 2a will not be significantly affected, precisely because of the closeness of the values.
3
2.
W
9
IO Figure 1. Polycyclic hydrocarbon molecules with sites of maximum frontier electron density (Huckel spin density) indicated: 1, benzene; 2, phenanthrene; 3, naphthalene; 4, chrysene; 5, pyrene; 6, 1,2:5,6-dibenzanthrscene; 7 , anthracene; 8, naphthacene; 9, 1,2-benzanthracene; 10, 3,4-benxpyrene.
(9) A. Carrington, Quart. Rev. (London), 17, 66 (1963).
through 1963 by Carringtong and recently by Bowers.'O (10) K. W. Bowers, "Advances in Magnetic Resonance," Vol. 1, Academic Press Inc., N e w York, N. Y., 1966, p 31. Xegative radical ions form readily by polarographic technique^^^-'^ and in alkali metal s o l ~ t i o n s . ' ~ ~(11) ~ ~A. H. hfaki and D. H. Geske, J . Chem. Phys., 30, 1356 (1959). (12) D. H. Geske and A. H. N a k i , J . Am. Chem. SOC.,82, 2671 Positive radical ions have been prepared in sulfuric (1960). a ~ i d ' ~and , ' ~ by other methods such as oxidation with (13) P. H. Rieger, I. Bernal, W.H. Reinmuth, and G. K. Fraenkel, ibid., 85, 683 (1963). SbC15.'9 The hyperfine splittings of the esr spectra are (14) R. Dehl and G. K. Fraenkel, J . Chem. Phys., 39, 1793 (1963). often sufficiently well resolved to provide experimental (15) See Table I, footnote b. hyperfine coupling constants, and many such constants (16) G. J. Hoijtink, J. Townsend, and S. I. Weissman, J . Chem. have been tabulated in the literature. 1\4cConne1120~21 Phys., 34, 507 (1961). related the hyperfine coupling constant a i to the un(17) E. de Boer and S. I. Weissman, J . Am. Chem. SOC.,80, 4549 paired Hiickel spin density pi residing at an atom by (1958). (18) J. S. Hyde and H. W. Brown, J . Chem. Phys., 37, 368 (1962). eq 1. The spin density may be calculated by the simple ai
= &pi
(1)
Hiickel a p p r o ~ i m a t i o n ~ ~and a ~ 3Q is a semiempirical constant with the values Q- = 28.6 gauss for negative ions and Q+ = 35.7 gauss for positive ions. The measured hyperfine coupling constants are usually compared to calculated spin densities, through either the McConnel120*21 or C ~ l p a - B o l t o n ~theories, ~ and
(19) I . C. Lewis and L.S. Singer, ibid., 43, 2712 (1965). (20) H. .\I. hlcconnell, ibid., 24, 764 (1956). (21) See Table I , footnote c. (22) A. Streitwieser, J. I. Brauman, and C. A. Coulson, Supplemental Tables of Molecular Orbital Calculations with Dictionary of Electron Calculations, Pergamon Press Inc., Kew York, N. Y., 1965. (23) E. Heilbronner and P. A. Straub, "Huckel Molecular Orbitals," Springer-Verlag, N. Y., Inc., New York, N. Y., 1966. (24) J. P. Colpa and J. R. Bolton, Mol. Phys., 6,273 (1963).
Volume 71,Number 11 October 1967
3674
CHARLES P. POOLE, JR.,AND 0. F. GRIFFITH,I11
*/
95
/
/
/
PI
1
7 /
*/
1.8 L
,
1.9
- Ni
z
2 2.0 -
/
/
i/
Figure 2. Graphs showing the data in columns 3-10 of Table I plotted against the logarithm of the relative reactivities ki/kn. Note that some ordinate scales are inverted to allow graphic comparison.
Table 11: Comparison of Various Reactivities with Hiickel Spin Densities
pi
a t the Molecular Sites Indicated
Compound
Reaction
Order of reactivitya
Naphthalene Anthracene Phenanthrene Phenanthrene Phenanthrene Pyrene Chrysene 1,%Benzanthracene
Acylation Ketone formation Nitration Acetylation, CS2 solvent Acetylation, C2HaC12solvent Acylation Acylation Acylation
1>2 9 > 1 > 2 3 > 1 > 2 3 > 9 > 2 > 1 > 4 9 > 3 > 2 > 1 > 4 1 > others 6 > 3 = 2 > others 7 > 10 > 9 > 3 = 2
3,PBenzpyrene 3,4-Benzpyrene Perylene
Normal substitution Acylation Acylation
6 > others 1 > others 3 > others
Order of Hiickel spin densities
1 > 2 9 > 1 > 2 9 > 1 > 3 > 4 > 2 1 > 4 > 2 6 > 1 > 4 = 3 = 5 > 2 8 > 7 > 9 > 12 > 5 > 2 6 > 10 > 4 > 3 > 1 1 > others
> 11 >
>6
3 > 1 > 2
a These data were compiled from “Freidel-Crafts and Related Reactions,” G. A. Olah, Ed., Vol. 3, John Wiley and Sons, Inc., New York, N. Y., 1964.
It is interesting to compare quantitatively the various indices in columns 6-10 in Table I with the logarithm of the relative reaction and this is done in Figure 2. A glance a t this figure reveals four things: (1) the five indices calculated by molecular orbital methods do not correlate well with the reactivity; (2) the spin densities pi calculated by the molecular orbital theory do correlate well; (3) the frontier electron densities f i equal twice the respective spin densities p i and hence give the same correlation; and (4) the experimentally determined hyperfine coupling constants ai provide an The Journal of Phgsical Chemistry
excellent linear fit to the reactivity data. Note that it is no longer necessary to invoke steric hindrance26to explain the very low reactivity of position 4 when one uses the hyperfine coupling constants determined by esr data. Detailed reactivity data of the type discussed for (25) E. C. Kooyman and E. Farenhorst, Trans. Faraday Soc., 49, 58 (1953). (26) M. J. Dewar, T. Mole, and E. W. T. Warford, J. Chem. SOC., 3581 (1956).
CHEMICAL REACTIVITY A N D THE HYPERFINE STRUCTURE OF POLYCYCLIC HYDROCARBONS
3675
- 5 6
4,
1
8,
6,
: 0 ’ -5
1
-4
-2
-I
0
I
1
,
-4
45
I
-3
1
,
,
,
-2
-3
,
-I
1
,
2
I
0
2
Log,, Figure 3. Calculated Huckel molecular orbital spin density as a function of the logarithm of the reaction rate for the radical reaction (CCl, * hydrocarbon). Numbers indicate compounds shown in Figure 1.
(pi)
+
phenanthrene are not available for a large number of have been measured for many of them. Table I1 compares some of these data with the order of the HMO spin densities, and a good over-all correlation is evident. I n the case of 1,2-benzanthracene the order of reactivity 7 > 10 > 9 > 3 = 2 tends to follow the order 7 > 9 > 2 > 10 > 3 of these Huckel coefficients except for position 10, but many high-spin density positions do not appear in the former list due to the lack of detectable reactivities. The preceding discussion shows that the spin densities and hyperfine coupling constants provide self-consistent
cule. The value of these indices for comparing different molecules is shown in Figures 3 and 4 where pi and ai, respectively, are plotted against log k i for the most reactive sites of several polycyclic molecules. When a least-squares fit is attempted, the large scatter in these data prevents us from drawing definite conclusions regarding the correlation of the reactivity with the charge density pi and the coupling constant ai for different molecules. There does appear, however, to be a slight correlation between the hyperfine coupling constant and the reactivity, as indicated in Figure 4. Thus we see that the hyperfine coupling constants ai and spin densities pi exhibit a very good intramolecular correlation and a possible intermolecular correlation with reaction rates. In each case the experimentally determined hyperfine coupling constants correlate
K&,
Figure 4. Experimentally determined hyperfine coupling constants ai for the most reactive site plotted against the logarithm of the reactivity for the compounds listed in Figures 1 and 3: 0 , obtained from the experimental hyperfine coupling constants; W, computed from experimentally determined Q values and Huckel spin densities (cf. Salem,4 p 295, and Kooyman and FarenhorstZ6).
L
.25
.I5
I
-
/
’
v)
4 .to c
5.05-
/
r:
- 20 9
,‘ /
/
/
1
Io 0 ’
,
,/
/ O
w
, , ’
A
Naphtholma
0 Pentacene
0 Anthracene
0-
0
p’
,e/
’ /’,’
//
A,/
&’
0
0 Tetrocene I
I
I
I
L
Figure 5 . Relationship between spin densities pi calculated by the Huckel method and the atom-atom self-polarizabilities xii for the series of linear polycyclic hydrocarbons.
better than the calculated spin densities. This correlation means that we may expect ai and pi to be closely related to the various molecular indices for a series of atomic sites. The spin density is half of the corresponding frontier electron density, as observed above. Another example of such a correlation is shown in Figure 5 where we plot pi against the atom-atom self-polarixability xii. The figure shows the regular trend of each individual molecule (intramolecular effect) and the differences between molecules (intermolecular effect) noted above. For even alternate hydrocarbons, the four Volume 71. Number 11
October 1967
3676
indices rii,Fi, Li, and Si all predict the same order of activity, SO they should all exhibit correlations with spin density of the type shown in Figure 5 - %me rnOlecules such as Phenanthrene do not show a regular intramolecular correlation, but in this case it is the hyperfine coupling constants which follow the reactivities.
NOTES
Conclusions I n this paper we have shomn that the hyperfine coupling constants are good quantitative indices of relative chemical reactivity rates at various sites in a polycyc~ic hydrocarbon molecule. Various conventional molecular orbital reactivity indices are found to be unsatisfactory in this respect.
NOTES
Exact Geometrical Parameters for Pendular Ring Fluid
by James C. l\Ielrose and George C. Wallick Mobil Oil Corporation, Dallas, Texas 75221 (Receired A p r i l 5 , 1967)
That a fluid can be confined in the region of the contact point between two spherical solid particles by means of “capillary action’’ is well known. Such fluid is often said to be in a pendular ring configuration, and the problem of specifying the volume, meniscus area, and pressure deficiency is a classical problem in the theory of capillarity. The shape of the meniscus separating the pendular ring fluid from the surrounding fluid (vapor or liquid) is described by an equation due to Laplace,’**which relates the pressure deficiency to the A uid-fluid interfacial tension. From this equation it follows that, if gravitational distortion can be ignored, the meniscus must assume the form of a surface of constant mean c ~ r v a t u r e . ~ For many cases of interest it can be supposed that the two spheres are identical in size and that the properties of both solid-fluid interfaces are uniform a t all points in the region in which the meniscus meets the solid surface. It follows from the latter specification, together with Young’s equation14that the three-phase line of contact is characterized by a uniform contact angle. When this is so, the boundary conditions for Laplace’s equation have cylindrical symmetry. This establishes the fact that the meniscus will also take the form of a surface of revolution- Among surfaces of only the sphere, cylinder, unduloid, catenoid, and T h e Journal of Physical Chemistry
nodoid are also surfaces of constant mean curvature.jrs In the case of pendular ring fluid, the appropriate configuration of the meniscus is that of the nodoid. Since the two spheres are identical in size, the section of the nodoid involved is symmetrical with respect to the contact plane. The availability of these classical resuits7s8makes it possible to assess both the mathematical nature and the importance of various approximations which have been used in obtaining numerical solutions to the nodoid problem. Recently, AIayer and Stoweg have treated the problem by assuming the meniscus profile to be a circular arc. They then relate the curvature to differential changes in the volume, meniscus area, and area of contact between the solid and the confined fluid. The toroidal meniscus configuration was also assumed by Roselo and by earlier authors. In this previous work, it was recognized that the torus surface is not (1) J. C. Maxwell, “Capillary Action,” in Encyclopedia Britannica, 9th ed, 1875; “Scientific Papers,” Vol. 11, Cambridge University Press, London, 1890, p 541. (2) The classical hydrostatic and thermodynamic theories have been reconciled and extended by F. P. Buff, “The Theory of Capillarity,” in “Handbuch der Physik,” Vol. 10, Springer-Verlag, Berlin, 1960. (3) J. A. F. Plateau, “Statique exp6rimentale et thBorique des liquides,” Vol. 1, Gauthier-Villars, Paris, 1873, p 6. (4) T. Young, Phil. Trans. Roy. SOC.London, 95, 65 (1805). (5) J. A. F. Plateau, ref 3, p 131. (6) A lucid review is given by D. W.Thompson, “On Growth and Form,” J. T. Bonner, Ed., Cambridge University Press, London, 1961, pp 53-61. (7) H. Bouasse, “CapillaritB, phenomhnes superficiels,” Delagrave, Paris, 1924, pp 49-66. (8) G. Bakker, “Kapillaritat und Oberflachenspannung,” in “Handbuch der Experimentalphysik,” Vol. VI, Akademische Verlagsgesellschaft, Leipsig, 1928, pp 120-124. (9) R. P. Mayer and R. A. Stowe, J . P h y s . Chem., 70, 3867 (1966). (io) w. Rose, J . Phys., 2 9 , 687 (1958).
