Philip E. Stevenson
-
Universitv of Chicago Chicago, Illinois
I
The Ultraviolet Spectra of
I
Aromatic Hydrocarbons
II
Predicting subrfifufion a n d isomerism changes
The ultraviolet spectra of thousands of aromatic hydrocarbons have been measured, recorded, and catalogued. But it does not seem to he generally appreciated that there is a fairly simple phenomenological theory which is capable of predicting many of these spectra, or a t least the differences among them, in a quantitative way. This theory was developed by Sklar (I), Forster (2), Platt (3, 4), Moffitt (5), and Petruska (6, 7). It uses perturbation theory to treat the changes in the absorption wavelengths and intensities in going from the spectrum of benzene to that of a derivative or from one polynuclear hydrocarbon to an isomer.
(3). This set of three transitions corresponds to the absorption of energy by excitation of a single elecdron from the highest occupied molecular orbital of benzene to the lowest unoccupied molecular orbital. The spectrum of paraxylene, shown in Figure 2, shows a typical change in spectrum caused by substitution, the 'Lb, 'La,and absorptions shifting to 275, 214, and 193 mp, respectively. The intensity of the 'L, transition is seen to be about five times greater than it is in benzene. FREQUENCY I N 35
375 4 0
cm-' x lo-' 45
50
55
Effects of Substitution on the Spectrum of Benzene
It is easy to understand the general principles of the theory by studying its application to the spectra of benzene and its derivatives. The near ultraviolet spectrum of benzene consists of three electronic transitions, or "absorption bands": a very weak one, near 260 mp, a much stronger one a t 202 mp, and an even stronger one a t 185 mp, as shown in Figure 1. These three regions, or more precisely these excited states which are shown on the energy level diagrams of Figure 3, are designated 'Lb, 'Lo, and 'B,,D,respectively, in the Platt notation FREQUENCY IN c m - '
i
x 10''
WAVELENGTH IN
x Figure 2.
lo-'
Absorption spectrum of pmraxylene.
A The flne struduro of the
' b transition is two rerier of peaks the A series, or is found in benzene. and the B series, which hor as its lowest energy member, the 0-0peok. Spectrum is after Petrurko (7).
Changes of Intensity in Substituted Benzenes
The intensitv chanees in such substituted benzenes can be explained by an ingenious diagram, shown in Figure 4, originally by Sklar (1). This diagram shows the directions of a set of vectors for the 'Lbtransition a t each carbon atom about the ring. These are dipole vectors which point from a (+) region to a (-) region on a so-called "transition density diagram," also called a "polarization diagram" (3) or a "dipole map" (8). Both the vectors and the transition density diagram display the symmetry of the transition, which in t,he case of the 'Lo transition is classed as IB1, in the D m symmetry group of benzene (in group theory notation) ; u
WAVELENGTH IN x lo-=
4
Figure 1. Abmrption rpechvm of benzene. The floe rhvcture of the 'Ls transition is a rerier of peaks labeled A. The estimated location of the 0-0 peak is indicmted. Spectrum is ofter Patrurka (7).
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Journol of Chemical Education
that is, a state which changes its sign when reflected through a plane drawn perpendicular to the plane of the molecule through any pair of carbon atoms in a para relationship to each other. This symmetry characteristic is evident from Figure 4. The intensity of an electronic transition is proportional to the square of the transition dipole moment vector, i.e., proportional to the square of the sum of dipole vectors like those in Figure 4. It is evident, by inspection, that in benzene itself, this sumis zero; therefore, the intensity of the '4 transition in benzene is zero and is thus said to be "forbidden." Vibrational perturbations cause small distortions in the molecule resulting in a small net transition dipole moment, which accounts for the intensity actually ohserved. The 'Lb transition is, however, several orders of magnitude weaker than the allowed IB.,, transition, as can he seen in Figure 1.
substituent; m is the carbon index (with the carbons numbered serially about the ring from 0 to 5); the exponential term is a representation in the complex plane of the d i c t i o n of the component dipole vector; and the summation is taken over a11 the suhstitnents. The results of this kind of summation are shown by the vector diagrams a t the bottom of Figure 5. It is easy to see that for mono-, 1,2di-, 1,3-di-, and 1,4-di- suhstitution, the predicted intensities are in the ratio of 1:1 :1:4, respectively, as Sklar first pointed out (1). Extension to the other substitution patterns is straightforward. These predicted intensitites are displayed as the solid line in the upper part of Figure 5. Experimentally, the electronic intensity of the 'La transition is proportional t o the extinction of the "0-0 peak," the lowest-frequency peak to he found in the lLb transition. This peak represents the energy of a pure electronic transition from the ground state to the 'hstate and does not appear in the spectra of benzene or of its 1,2,3-tri-, 1,3,5-tri-, or hexa-derivatives. The remaining peaks found in the 'L,band represent combined electronic and vibrational transitions. A vibrational analysis of the structure of these peaks indicates that in henzene and the above mentioned derivatives in which the 0-0 peak is not o b s e ~ e d ,its position is 520 cm-' to the red of the lowest frequency peak that is ohserved. The 0-0 peak is labeled in the spectrum of para-xylene and its location is indicated in the spectrum of henzene (Figs. 1 and 2).
Figure 3. Energy levels of the stater of benzene and poroxylene. The orrows indicate the hansitionr from the ground state to excited statesreen in the ultraviolet specha. The relotive lmation of a charge-transfer state is indicated for the paroxylene.
Replacement of one or more of the hydrogens by suhstituents can he thought of as changing the component of the transition dipole a t the substituted carbon. Since the benzene moment itself is zero, the changes in the component vectors then add vectorially to become the transition dipole moment of the molecule. The resultant electronic contribution to the intensity is of the same order of magnitude as the vihrationally induced intensity. According to the derivations of Moffitt (5) and Petruska (6), substituent perturbations cause the 'Lo transition to mix with the "allowed" 'B transition, and this mixing brings about the electronic intensity ohserved. Petruska's resultant formnla for electronic intensity is an algebraic representation of Sklar's vector model: f, = 1 zmy,e('rMW l a (1) In this equation, f, is the oscillator strength or intensity of the electronic transition; q is the magnitude of the change in the component dipole vector caused by the
Figure 4. Transition density diagram of benzene showing the hmndHon dipole vectors.
Whiie measurement of the extinction of the 0-0 peak gives the electronic intensity directly, other methods of measuring intensity give the total electronic plus vibrational intensity. This total intensity can be measured by smoothing out the fine structure of the transition and taking the maximum extinction of the smoothed out curve as proportional to the total intensity. This is called the method of the smoothed maximum. Petruska, however, used the more rigorous method of measuring total oscillator strength according to the standard formnla (9) f
=
4.32 X
f e(v)du
(2)
in which v is the frequency in ~ m and - ~e is the molar Volume 41, Number 5, May 1964
/
235
-
Wavelenath and lntensitv Parameters for Several Common Benzene Substituents for use with Formulas ( 1 ), (31, (41, and
Formula Parsmetera
F C1 Br OH CH, CN COOH IXT, ,L.,
(1)
(3) w('La)
-c
7.5 X 3.80 3.4 3.6 3.28 -7 -9 - 1A ,7
lo-'
0 x 101.0 1.3 1 4
...
4 1
-4) l(lLb)( m - 1 ) -125 840 940 700 430 1200 1470 - 14x0
( L ) c / 21.0 12.5 10 33 9 -22 - 13
--
-11
-6)
(6)
l ( L ( c m
~(~L.)(cm-'/?)
550 2600 3600 3000 1400 4700 6900 -xnn
17.0 11.0 11 27.5 8.0 - 15 - 18 -27 -.
The ~ a r m e t e r for s formulas (I), (3), and (4) were reealcuhted by the author. Parsmeters for formula (6) are from Petruska.(7).
has a predicted electronic inteusity of 4q2. In the table, thus q for chloro substitution is seen to be 3.80 X the predicted electronic intensity is f, = 58 X lo-'. This compares to the experimentally determined value of 42 X lo-', obtained by application of formula (3) to the experimental data. This calculation is shown graphically in Figure 5. Inspection of Figure 5 shows that formula (1) holds within about 20% for alkyl and where fo is the vibrational intensity of benzene itself; halo substitutions. For other, more strongly perturbn is the number of substituents; and w, a small correcing substituents such as NH,, OH, COOH, SH, and tion for the increase in vibrational intensity brought C H 4 H 2 ,the assumption made in deriving formula (I), about by each additional substituent. The term fo that perturbations are small, begins to break down; as obtained from the spectrum of benzene has a value of so formula (I), though still qualitatively correct, as 17 X 10-4; and w is found from the spectra of benzene seen in Figure 5, is less accurate quantitatively for derivatives with no electronic intensity (1,2,3-tri-, these stronger substituents. 1,3,5-tri-, and hexa-; i.e., those with j, = 0) through Values of q for several substituents are given in the use of formula (3). table. Values of a similar quantity, the "spectroscopic Petruska obtained the electronic intensities of a moment," for use with "smoothed-maximum" intennumber of substituted benzenes using formulas (2) and sities, were given by Platt (4). (3). Some of these data are shown in Figure 5 in which The values of q in the table are positive for electronthey are compared with the predictions of formula (1). donor substituents and negative for electron-acceptor I n each case, the measured intensity is divided by the substituents, such as COOH, CHO, CN, and CFa (4). intensity measured for mono-substitution; this is This means that the vectors for the latter in Figure 4 equivalent to expressing the experimental data in would point in the opposite direction. This makes no multiples of q2. The predicted intensities are also given difference in the intensity patterns if all the subin multiples of q2. For example, paradichlorobenzene stituents are identical (homosubstitution) ; but i t changes them considerably I,b INTENSiTlES OF SUBSTITUTED BENZENES for heterosubstitution in the case when I some substituents are donors and some are acceptors. For example, para disubstitution then gives a lower intensity than ortho or meta, rather than a higher intensity as is the case of both substituents are acceptors or both are donors. An aza-nitrogen "substitution" (N), like that in pyridine and the diazines, behaves as a negative substituent. The interested reader is referred to the Platt (4) and Petrnska (7) papers for further details. The cancellation of intensity in the case of the 1,2,3-derivatives, as predicted and observed, is a particularly interesting consequence of the theory, as Sklar pointed out ( I ) , because it does not depend on Addition of symmetry, but only on the vector sum Vectors "accidentally" being zero. None The 'Latransition (IB,. in group theory TriTriPento Mono Dlnotation), observed a t 203 mp in benzene, 43 iK3 i,3,5 142.3.5 can be represented by a transition dipole Addifion of the transition dipole vectors is diagram similar to that of 'La (Fig. 3), Figure 5. 'La intensiti+$of wbrtitded bonzener Indicated at the bottom, and the squarer of the rewltont vectors are graphed at the top, iuxtabut with all the vectors rotated through posed against the experimental dot. on intensities, stmdordired so that tho intensity of the 9 0 ' . The intensity pattern should theremono-substituted derivative is unity.
extinction coefficient in liters/mole centimeter, as a function of frequency. The electronic oscillator strength, f,, can then be found from this total f by subtracting out the vibrational intensity as follows (7) :
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Journal of Chemicol Fducofion
fore be the same as for the 'Lb,and formulas (1) and (2) should also hold in this case. However, the vibrational intensity of this transition of 100 times greater than the vibrational intensities of the 'L, transition, and the predicted electronic intensities are no more than 1% of this total intensity. So far, the uncertainties in measuring such small changes have prevented any definitive test of the predictions in this 'L. transition. Frequency Shifts in the Substituted Benzenes
Substituents on benzene cause changes in the transition energies as well as in the intensities. I t appears that frequency shifts in both the 'L, and 'L. transitions, as they depend on the type, number, and geometric arrangement of the substituent groups, can both be accounted for by simple two-term formulas. The 'Loformula was first derived by Forster (I?) and is also easily derivable from the work of Moffitt (5). Its two terms contain, respectively, thr: first- and second-order contributions t o the frequency shift. -A" = Z,l, + l Z,v,e'2"kiSl 1 % (4) I n formula (4), -Au is the frequency shift in cm-l. The minus sigu makes this term positive for a "red shift" or shift to longer wavelengths and lower frequencies, which is the direction of the observed shifts for most substituents. The first-order contribution of a single suhstituent to the frequency shift is 1. For multiple substitution, the first-order term is proportional to the number of suhstituents. The second-order term is a vector sum of exactly the same form as the expression for electronic intensity since it arises from the same mixing of the ' B state with the '4. Thus, this second-order term is a multiple of v2 (where v is the magnitude for a single suhstituent) in the same way that the electronic intensity is a multiple of q2. Again the pattern 1 :1 :1 :4 is found for the
second-order contribution to the frequency shifts of mono-, 1,2-di-, 1,3-di-, and 1,4-di-substitution, respectively. The observed frequency shift is measured relative to benzene. Preferably this should be done by measuring the shift of the 0-0 peak, hut in some of the more highly substituted derivatives of benzene, none of the fine structure can be seen. I n these cases, the position of maximum extinction in the derivative is compared to the position of the "smoothed-out maximum" in benzene. I n Figures 6,7, and 8, such measured frequency shifts of methyl-, chloro-, and fluoro-benzenes are plotted for the twelve possible patterns of substitution. These actual shifts are compared with the predicted values obtained from formula (4). The parameters 1 and u for each substituent are the best values obtained for fitting all the data. I t is evident from Figures 6, 7, and 8 that formula (4) gives a good quantitative
Figure 7. Figure 6.
Frequency rhifh of the methylbenzene..
Designations are as in
description of the relation between the observed shifts. The formula was especially interesting when it was first applied to the fluorobenzenes, which have a negative value of 1 because it immediately explained why some of the fluoro-benzenes have blue shifts and others have red shifts (10). A possible reason for the negative value of 1 is that the ionization potential of singly bonded F is higher than that of singly bonded H, with a resultant blue shift of the higher charge-transfer states, as discussed later. As an example, we can use formula (4) to calculate the frequency of the 'Latransition in paradichlorohenzene. From the geometry of the molecule, the shift of the transition from its position in benzene should he (21 4v2). Since 1 is 840 em-' and u is 12.5 em-% according t o the table, the shift is calculated to he 2320 cm-'. This compares to the observed shift of 2340 em-' (7). This calculation is shown graphically in Figure 6. Formula (4) holds within about 10% for substituents whose shift caused by mono-substitution (L'monoshift")
+
Figure 6. Frequency shifts of the chlorobenrener The flrrt order contribution h indicated by the solid bar; the second order by the ho!low bar. The erperimento! valuer of the shifts are indicated by crosser.
Volume 4 1 , Number 5, Moy 1964
/ 237
is less than 2000 cm-'. This includes alkyl and halo substituents as well as OH, OCH1, and the electronacceptor substituents such as CN. A few substituents such as NH2, CHFCH, SH, and the acceptor groups COOH and CHO, cause such large perturbations that formula (4) loses its quantitative accuracy although it continues to give a good qualitative description of the relative shifts. Petruska had refined formula (4) by addition of a third term and by considering interactions between substituents in an "ortho" relationship to each other. To compensate for the "ortho" effect, Petruska found he had to assign 1's for ortho substituents which were somewhat smaller than the 2's for the nonortho cases. His resultant formula is (7) -A"
= Z,1,
+ IZ,u,e(2Tk")
1
for the higher energy 'L. transition than for the 'Lb transition. Petruska (7) gives the following formula for 'L. in which the values of u are the same as for formula (5) but for which there is a new set of first-order parameters 1': -av = z',l,f - 1.2 1 z,z~,,(-I)~I~ (6) He found that this improved formula described the 'Lo shifts quite well; the qualitative behavior is, of course, very similar to that shown in. Figures fi-8 for the 'Lbtransition.
- 0.21 Z ~ Q ~ ( - ~ (5) ) " ~ ~
It is qualitatively similar to equation (4) but gives an appreciably better fit to the experimental data in some cases. In this formula, the blue shifts of the fluorobenzenes are described by the third termratherthan by the first term as they were in formula (4). The parameters for formula (5) are, of course, different from those for formula (4).
Figure 9. The Plan perimeter model cane ond phenmthreno.
Cl4Hlr ond i h relationship to onthra-
Figure 10. The Plan perimeter model C I ~ H and~ ik ~ relotionship to naphthalene and azulene.
Shifts in the Spectrum of Polynuclear Aromatics with Isomerism
Figure 8. Frequency shifts of the fluorobenzener Designations ore 0 %in Figure 6. Note that the Rrrt order shift is toward the blue and the second order to the red.
Moffitt (5) predicted that the frequency shift of the 'L. transition should be equal to the first-order contribution of the 'La frequency shift, but this prediction is not supported by the experimental data, which show in most cases that the 'Lo shift is several times greater than the entire 'LB shift. Petruska's theoretical treatment of benzene substitution (6, 7) showed, however, that the first-order term included an interaction of the particular state ('Lo or IL,) with a higher energy "charge-transfer" state of the substituent (see Fig. 3), and that this effect was larger 238
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Journol o f Chemical Educofion
The 'Lo, 'La, and 'B.,, transitions are found not only in the spectra of benzene and its derivatives but also in the class of polynuclear aromatic hydrocarbons known as the catacondensed hydrocarbons. These hydrocarbons are of the general formula C I ~ + l H I ~ + I and have the characteristic that all the carbons are located a t the perimeter of the molecule. Examples of such molecules are naphthalene, anthracene, phenanthrene, and triphenylene, but not purene or coronene. Replacing of each cross-link in such hydrocarbons by two hydrogen atoms converts these molecules into cyclic aromatic polyenes resembling benzene. This concept of the "cyclic polyene" was first proposed by Platt (5) as a basis for a perturbation treatment of cross-link isomerism, and was employed by Moffitt (6) for that purpose. Figure 9 shows how anthracene and phenanthrene (CvHlo) are related to the cyclic
polyene CIPHIP;the Figure 10 relates naphthalene and aznlene (C10H8) to the cyclic polyene C~oHlo. Moffitt's analysis ( 5 ) , which is fairly complex, need not concern us here. Nevertheless, his results are fairly simple and serve to explain the frequency shifts found for cross-link isomers. The shifts are given relative to the positions of the corresponding transitions in the hypothetical cyclic polyene, which was estimated by Moffitt to lie a t about 6 / ( 4 n + 2 ) of the energies of the corresponding benzene transitions. The following two formulas apply to hydrocarbons in which all rings have six carbon atoms. For the 'La transition, -A,
=
A (N)
(7)
the energies of the states of the hypothetical cyclic polyene CloHlo(11). Again the prediction of this theory is quite good. The general theory that has been discussed in these pages is a good example of a phenomenological theory. The formulas can he derived fairly rigorously from basic principles, but the numerical parameters for the various suhstituents then must he determined from the experimental data. This procedure is quite useful for the experimental spectroscopist and gives valuable parameters for the pure theorist to try to interpret. As we have seen, the frequency shifts of the ' L b transition, for example, for twleve different patterns of substitution can he described by one formula and two parameters;
I n words, the frequency shift of this transition from the cyclic polyene position is dependent only on the number ( N ) of rings in the compound and not on the cross-link geometry. The equation for 'L. is = A (N) + B ( N ) e(Zr' W + I l ( m + n l i ( ( ~ + ~ ) ) l f (8)
With ~irst
Ordn
Ix
Shift FOR IAPYTHLLENE
With Fird
Ordsr
Anfhrncere
Phemnthrene
Shift
TOR AZULENE
m
