COMMUNICATIONS TO THE EDITOR
1963
Table I: Integral Diffusion Coefficientsfor KCl at 25"
6"x
c,
106,
c,
5" x 106,
c,
mole 1. -1
cmzsec-l
mole I.-'
cm2 sec -l
mole 1 . - 1
0.001 0.002 0.003 0.004 0.005 0.006 0.007
1.9734 1.9660 1.9607 1 .9563 1.9526 1.9494 1.9465
0.008 0.009 0.010 0.020 0.030 0.040 0.050
1.9438 1.9414 1.9392 1.9225 1.9113 1.9029 1.8961
0.060 0.070
coefficients, b, for these calibrations. Potassium chloride w51s chosen because precise optical2 and conductometrica data were available for its diffusion coefficient D at 25". There were, however, some gaps in the combined data and a much greater than average deviation between them near 0.1 M . Since 1951, the limiting value of D for KC1 a t 25" has been slightly altered and additional precise optical data have been p ~ b l i s h e d . ~Also improvements in diaphragm cell techniques in these and other laboratories have been made which make it desirable to use as precise b,"values as possible. Therefore, we have recalculated these coefficients. This was done by drawing a smooth curve through the combined D data from 0 to 1 M of ref 2-4 using the limiting value 1.993 X cm2 sec-'; the root-mean-square deviation, rmsd, between the data and curve was 0.0019 X cm2 sec-". An IBM Series 360 computer was used to obtain an equation5 for the curve of the form
0.080
0,090 0.100 0.200 0.300
5"x
106, cm2 sec-1 1.8904 1.8856 1.8815 1,8778 1.8746 1.8565 1.8501
rule the value of cm2sec-l.
c,
mole 1. -*
x 106, cm2 sec-1
B o
0.400 0.500 0.600 0.700 0,800
0.900 1.000
1 .8480 1. a 7 8 1.8486 1.8502 1.8524 1 ,8553 1 ,8585
will then be (1.840 h 0.001) X
(2) L. J. Gosting, J . Am. Chem. SOC.,7 2 , 4418 (1950). (3) H.S. Harned and R. L. Nuttall, ibid., 69, 736 (1947);ibid., 71, 1460 (1949). (4) D. F. Akeley and L. J. Gosting, ibid., 75, 5685 (1953);L. A. Woolf, D. G. Miller, and L. J. Gosting, ibid., 84, 317 (1962). (5)The coefficients Ai were: AO = 1.993,A I = -1.002337601* A2 = 3.235153497,As = -9.780514174, Aa = 24.34187091, A5 = -35.81551219, Aa = 26.75245668, Ai = -7.833317444, As = - 1.989929326 X 10-6. (6) A. R.Gordon, Ann. N . Y . Acad. Sci., 46, 285 (1945). (7) R. L. Robinson, Jr., W. C. Edmister, and F. A. L. Dullien, J . Phya. Chem., 69,258 (1965).
DIFFUSION RESEARCH UNIT RESEARCH SCHOOL OF PHYSICAL SCIENCES AUSTRALIAN NATIONAL UNIVERSITY CANBERRA, A. C. T., AUSTRALIA
L. A. WOOLF J. F. TILLEY
RECEIVED JANUARY 6, 1967
8
D X lo5 = EAd, where
z =
C"' with an rmsd
i=O
of 0.0008 X cm2 sec-l. The equation thus obtained was integrated exactly and the computer then used to calculate and print in tabular form values of b,". Results obtained a t round values of the concentration are given in Table I. The greatest deviations from Stokes' results' occur in the region 0.02-0.1 M and are of the order 0.2%. A Simplified Calibration Procedure. It is common practice to express data for the concentration dependence of b,"in the form of a graph and obtain values by interpolation as required. The difficulties of constructing and using such graphs may be circumvented entirely by using a standardized calibration procedure. The initial concentration of KC1 for the calibration experiment is chosen close to 0.5 M , the rule of Gordon6 used to determine the length of the preliminary period, and the equation due to Robinson, et aL17to fix the length of the experiment. As a general
Charge-Transfer Complexes of Polyenes
Sir: Lupinski has reported a band in a mixture of iodine and @-carotene which absorbs a t 10,000 A.' By varying the concentrations and the solvent, he showed convincingly that the absorption is due to a molecular species &carotene I+, which he considers may be a charge-transfer complex @-carotene I+. It appears that this new band might quite possibly be explained in terms of a shift in the absorption maximum of @-carotenerather than as a charge-transfer band. The two classes of compounds, the symmetrical polymethines and the polyenes, have quite different absorption maxima although in each the absorption is due to a chain of CC=C bonds. This is because the polymethines have two or more possible bond configurations or resonance structures which are isoenergetic while the (1)
J. H. Lupinski, J.Phya. Chem., 67,2725 (1963).
Volume 71, Number 6 May 1967
COMMUNICATIONS TO THE EDITOR
1964
Figure I. Possible charge-transfer complex of a polyene and I and the approximate isoenergetic ground-state resonance structures that will tend to reduce bond alternation. &Carotene is a diphenylpolyene with n = 11; (a) the principal ground-state resonance structure of the polyene; (b) the same state in the I + complex; (c) and (d) states whose contribution to the ground-state configuration will be much larger because of complex formation; (e) Platt’s D+.cart-A- complex with 13- could1 strengthen structure c. +
polyenes have only one principal resonance structure. Kuhn has derived a formula using the free-electron model fcr predicting the absorption peaks of polyenes as well as the symmetrical poIymethines.2 He introduces a Brillouin-type band splitting in the energy levels of the polyenes due to the unsymmetrical potential seen by the C atoms which causes the predicted wavelengths to be shifted to much shorter wavelengths than the corresponding polymethines. If &carotene is treated as a polymethine, then the predicted, , ,A is about 11,000 A, but if allowance is made for p-carotene to have a single resonance structure with alternating double bonds which dominates the ground state, then Kuhn finds good agreement between his calculation and the observed , , ,A of 4510 A. It may be possible to explain Lupinski’s spectrum as being due to a charge-transfer effect rather than being a charge-transfer band of the usual donor-acceptor kind. The spectrum looks very much like what would be expected for p-carotene with a mixture of isoenergetic resonance structures to make the bonds nearly equal with no-bond alternation. If, due to the formation of a charge-transfer complex with iodine, several bond configurations are possible, then the absorption maximum of @-carotene would shift to much longer wavelength:;. Previously, Platt has suggested a similar shift in pcarotene due to the formation of a donorcarotene-acceptor trimolecular comp1ex7Df *cart.*-I predicting also that this might absorb a t wavelengths asgreat as 11,000A.3~4 The interpretation of the Lupinski band as a “band shifted” 0-carotene absorption is suggested not only by the close agreement with the predicted wavelength The JournuE of Physical Chemistry
for no-bond alternation, but also by the narrow halfwidth of the band, only 2000 cm-‘ (compared to that of p-carotene itself, about 4200 cm-I) and by the shift in peak position by several hundred cm-I with changing solvent polarity. The latter features are typical of the polarized conjugated-chain spectra (merocyanines) studied by Brooker and co-workers near their isoconjugate points15s6and the narrowness has been shown theoretically to be a necessary consequence of the reduction of bond a l t e r n a t i ~ n . ~True charge transfer spectra, on the other hand, are commonly much broader than the spectra of the individual molecules. In Figure 1 there are diagrams showing the p-carotene I+ charge-transfer complex. This complex has several resonance structures for the @-caroteneground state that would equalize the bond length and shift the, , ,A of p-carotene to longer wavelengths. That the formation of a chargetransfer complex can cause large wavelength shifts in polyenes can be tested in several possible ways. One test is to try to form charge-transfer complexes with other polyenes and see if a band appears where the corresponding symmetrical polymethine would absorb. The band is predicted to move approximately 1000 A to longer wavelengths for every additional vinyl group in the chain.’ Another possible test would be to see if charge-transfer complexes formed with p-carotene and another acceptor similar to iodine would also have a band at 10,OOO A, since the, , ,A of this band depends principally on the formation of a complex which would allow several isoenergetic bond structures and not on the particular properties of the acceptor. Acknowledgments. I wish especially to thank Professor John R. YIatt for his interest and advice. I also thank Professors R . S. Mulliken and W. B. Person for their criticism. This work was supported in part by Public Health Service Grant GM 14035-02 and a Public Health Service predoctoral fellowship to the author. (2) H. Kuhn, J . Chem. Phys., 17,1198 (1949). (3) J. R. Platt, ibid.,25,80 (1956). (4) J. R. Platt, Science, 129,372 (1959). (5) L. G. S. Brooker, G. H. Keyes, R. H. Sprague, R. H. VanDyke, E. VanLare, G. VanZandt, F. L. White, H. W. J. Cressman, and S. G. Dent, Jr., J. Am. Chem. SOC.,73,5332 (1951). (6) L. G. S. Brooker, G. H. Keyes, and D. W. Heseltine, ibid., 73
5350 (1951). (7) L. G. Brooker and R. H. Sprague, ibid.,63,3203 (1941).
(8) Mental Health Research Institute, University of Michigan, Ann Arbor, Mich. 48104.
DEPARTMENT OF PHYSICS
THOMAS G. EBREY~
UNIVERSITY OF CHICAGO
CHICAGO, ILLINOIS60637 RECEIVED MARCH9, 1967
