John G. Fors
Department of Biochemistry and Biophysics Iowa State University Ames
Absorption, Dispersion, Circular Dichroism, and Rotary Dispersion
O n e of the great accomplishments of science has been to demonstrate the underlying unity among various superficially different phenomena. One of the aims of teaching science should he to point out this unity whenever possible. The purpose of this paper is to indicate a neglected opportunity to do just this in elementary physical chemistry. The topics to be discussed are light absorption, dispersion, circular dichroism, and rotatory dispersion. These very closely related phenomena are all of importance in chemistry and yet, to the writer's howledge, no elementary physical chemistry texts discuss them as a unified topic. This is especially unfortunate since on a phenomenological level it could he very easily done.
On the other hand if the same type of curves are compared for compounds having a strong absorption band, there is clearly a relationship. For example Figure 2 shows the absorption and dispersion curves for the strongly absorbing permangauate ion (2).
Absorption and Dispersion
Let us first consider the relationships between ordinary light absorption and dispersion' measurements. If the dispersion curve and absorption spec-
Figure 2. Absorption and dispersion curves for aqueous potassium permongonote. Redrown from Toylor and Glover (21.
Figure 1. Absorption and dispersion curve3 for cyclohexanone. drawnfrom Allropp (7).
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trum of a compound with a weak absorption band are compared, there will be no apparent relationship between them. For example Figure 1 shows such curves for cyclohexanone which has a very weak absorption band near 290 mp (I). The dispersion curve rises monotonically on going to shorter wavelengths, apparently even in the vicinity of the absorption band. This research was supported by a United States Public Eenith Service grant. ' A graph of refractive index versus wavelength is called a dispersion curve, bemuse it indicates how light of various wave lengths would be dispersed by a prism of the material being atudied.
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This is an example of a general phenomenon which is weU understood in both classical and wave mechanical terms (3). Figure 3 shows the behavior to he expected with the idealization that the index of refraction is determined by a single absorption, and that the conversion of radiant energy to heat follows a simple law. There are several points to be noted in this figure. First, the dispersion curve rises on going to shorter wavelengths, i.e., this part of it is a "normal" dispersion curve. Second, in the absorbing region the dispersion curve falls on going toward shorter wavelengths, and therefore, this portion of it is caUed an "anomalous" dispersion curve. Third, in the middle of the abscrption band the refractive index becomes equal to its value in a vacuum and a t still shorter wavelengths it can actually become less than unity.2 A very important aspect of this relationship between abscrption and dispersion is that a strong absorption band will always give rise to a large anomalous dispersion and a R-eak absorption a small anomaly. This aThis nleans that the velocity of light is greater than in a vacuum which is an appnrent violation of relativity theory; but this velocity ia the whose velaeitv. whereas relativity theow is concerned with the group velocit;.'
means then that in the case of the cyclohexanone data shown in Figure 1, if extremely accurate measurements were made, a small wiggle should he found in the dispersion curve near the weak absorption band. (There is actually a small break in Allsopp's data but it is not easily seen on the scale used in the present drawing.) As would be expected, it is possible to develop theoretical relationships between these curves and thus to calculate one curve from the other. These are the Kronig-Kramers equations. It is also possible to discuss these relationships very nicely qualitatively or quantitatively in terms of a simple damped harmonic nscillator model. In order not to detract from the basic simplicity of the phenomenological relations, a further discussion of the physical origin of the absorption-dispersion relationships, together with pertinent references, is included in the appendix.
would be said that the unsaturation causes an "exaltation" of the refractive index. By using the Sellmeier relationship (5) between refractive index and wavelength, it might even be possible on occasion to estimate the location of the absorption hands. But now the manifestation of dispersion effects over large wavelength regions can become troublesome, because it is difficult to separate contributions from distant, strongly absorbing bands. For this reason it is more desirable (and much simpler) to measure the absorption hands directly with an ultraviolet spectrophotometer. Since these are now so commonly available, neither the qualitative nor quantitative applications of refractive index measurements are as important as they once were. Circulnr Dichroism and Rotatory Dispersion
Until now in the discussion it has not been crucially important to specify whether or not we are considering measurements made with unpolarized or polarized light. We will now consider different effects which arise from using polarized light and will show that "circular dichroism" and "rotatory dispersion" are absorption and dispersion phenomena analogous to ordinary absorption and dispersion. There are two types of polarization which will he discussed. These are plane and circular polarization. Plane polarized light has its electric vector vibrating in
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Theoretical absorption and dispersioncurvet.
Before our discussion of the analogous relationships between circular dichroism and rotatory dispersion a few additional important features of the absorptiondispersion curves will be considered. One very striking difference is that the absorption phenomenon is exhibited over a relatively small wavelength region hut the dispersion manifests itself a t wavelengths very far removed from the absorption band. This can be turned to advantage for chemical studies. For example, it is sometimes convenient to determine concentrations of solutions or the purity of compounds having absorption bands in the ultraviolet by measuring their refractive indexes in the visible region. Furthermore, it should be clear that since the dispersion and absorption curves are related, it might be possible to use refractive index measurements in the visihle as aids in molecular structure determinations just as absorption spectra are often used. Thus an nnsaturated compound with an absorption band in the near ultraviolet could be recognized not only by the absorption characteristics of this band but also by the increase in refractive index in the visible compared to a similar saturated compound lacking the absorption hand. In the terminology used in this type of study it
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Figure 4. Top, theoretical absorption ond dispersion curves measured with left and right handed circular light. Bottom, difference curves for a comexhibiting anomolow rotatory dispersion and circular dichroirm.
one plane, while the electric vector of circular light rotater as the light beam advances. The vector can rotate clockwise or counter-clockwise (as observed when facing the light source) and the light is said to be rightor left-handed circularly polarized respectively. (The appendix contains a brief description of the relationships among various types of polarized light and the methods used to produce polarization.) The upper graphs of Figure 4 show the results of a typical dispersion and absorption measurement using left- and right-handed circular light. The results are clearly very similar. In fact unless the compound studied is optically active the two sets of data will be Volume 40, Number 1 1 , November 1963
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identical to the same measurements made on a gaseous or dissolved material with unpolarized light. But, if an optically active compound is studied, there will be very small but important differences between these curves. When a substance has a difference in its refractive index for right and left handed light, it is said to exhibit "circular birefringence." As discussed in the appendix, this leads to what is commonly described as "optical activity." By analogy with ordinary dispersion, a curve showing the wavelength dependence of circular birefringence is called a "rotatory dispersion curve." When a substance absorbs right- and lefthanded light differently, it is said to exhibit "circular dichroism." This name is used because the original studies of circular dichroism were made in the visible and it was found that when viewed by transmitted right- and left-handed light a solution of such a substance would be colored differently. A curve showing the wavelength - dependence is called a circular dichroism spectrum. The difference curves for refractive index and absorotivitv are shown in the two small rrra~hsat the bottom of " ~ i ~ u4. r e The lower graphsweie deliberately made smaller to emphasize the fact that the differences are small. For example, the differences between two refractive index curves are usually in the sixth decimal place! The differences in the absorption curves will commonly be about one hundreth as large as the absorption curves themselves (though they can be as large as 10% in favorable cases). Figure 5 shows
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Figure 5. Absorption, rotatory dirpomion m d circular dichroisn of camphor in hexone. Redrawn from Kvhn mnd Goram (4).
some data for camphor as an illustration of the relationships among ordinary absorption, circular dichroism and rotatory dispersion (4). In this case measurements of rotatory dispersion were made through the entire band because the carbonyl group has a large rotation associated with this weak absorption. (The circular dichroism is not centered in the absorption band as it should be according to the simpler theories relating the two, but the reason for this is now understood (6).) 594
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Many of the comments made earlier about ordinary dispersion curves also apply to rotatory dispersion. For example the optical activity of most compounds increases on going to shorter wavelengths because they have optically active absorption bands in the ultraviolet. For this reason, when a rotatory dispersion curve rises on going toward shorter wavelengths it is said to show "normal" dispersion. Near the optically active absorption band the dispersion curve falls with a decrease in wavelength so it is said to exhibit "anomalous" dispersion. In the middle of the absorption band the optical activity commonly goes to zero, and at shorter wavelengths changes sign. The name given to this combined phenomenon of anomalous rotatory dispersion and circular dichroism in an absorption band is the Cotton effect (6). Thus far the analogies between ordinary absorption and dispersion, and circular dichroism and rotatory dispersion have been emphasized. But there is one differenceof great practical and theoretical importance. With ordinary dispersion a large absorption band leads to a large anomalous dispersion. A small absorption band can only give a small anomalous dispersion. This is not true with the circular analogues. A strong absorption band may or may not give a large anomaly in the rotatory dispersion while a small absorption band may actually give rise to a moderately large anomaious dispersion. (Compare for example the almost nonexistent anomalous dispersion of cyclohexanone in Figure 1 with the large anomalous rotatory dispersion of Figure 5 which is caused by the same carbonyl chromophore.) One of the consequences of this is that if an optically active substance has a small rotation associated with a strong absorption band, it will be either difficult-r impossible--to make rotatory dispersion measurements through the absorption band because of insufficientlight transmission. (For this reason during recent years considerable effort has been made to design more sensitive polarimeters. One has now been built with a sensitivity of approximately degrees (7).) Again, just as with ordinary dispersion and absorption data, theoretical relationships (the Kronig-Kramers equations) exist between circular dichroism and rotatory dispersion which permit calculating one curve from the other (8). This means that in principle no additional information can be obtained about a molecule by measuring both its rotatory dispersion and circular dichroism spectra. However, there are practical considerations which sometimes make it advantageous to measure one or the other. These considerations parallel the ones dip cussed for ordinary dispersion and absorption. For example the rotatory dispersion of a molecule can be measured a long ways from the optically active absorption band causing it. Such measurements in the visible region can be used to determine concentrations, optical purity, rates of reaction, etc., but basically what is being studied is the circular dichroism of an absorption band a t a shorter wavelength. When it is not possible to make measurements of rotatory dispersion through absorption bands, it is still possible to estimate the wavelength of the circular dichroism band by fitting the data to a Drude equation. This is analogous to using the Sellmeier equation for locating absorption bands with ordinary dispersion
data and it suffers from the same drawbacks, viz., that it is difficult to separate contributions from even rather distant bands. At the present time it is a simple matter to locate ordinary absorption hands with a spectrophotometer. Until recently, however, it was not possible to readily measure the circular dichroism spectrum, especially in the ultraviolet; but a t least one commercial instrument is now available which will do this. This promises to be very useful since it will permit the independent examination of the circular dichroism bands of molecules with several optically active chromophores.
type of polarization, is elliptical polarization. In this case the projection of the vector tip will give an ellipse. There are many relationships among these types of polarized light but only those of importance for this article will be mentioned. First, a plane polarized beam can be conceptually (and literally) resolved into right- and left-handed circular light components of equal magnitude. Second, if there is a phase shift between the two circular components this isequivalent to rotating the plane of polarization. And third, if there is a change of magnitude of one circular component relative to the other, elliptical light will result.
Conclusion
This now completes the brief discussion of the relationships among absorption, dispersion, circular dichroism, and rotatory dispersion. These relations and analogies are very simple, provided that only the phenomena themselves are considered and not their underlying causes. The author feels that the unified view this provides for these four superficially unrelated phenomena is very valuable. If, for example, the relationships between circular dichroism and rotatory dispersion were taught in all physical chemistry courses 50 years ago, would as much effort have been largely wasted by chemists on the interpretation of the optical activity of molecules a t the sodium D line? The author believes that a clearer understanding of these relationships would have hastened the development of methods for measuring both circular dichroism and rotatory dispersion in the ultraviolet. In order not to obscure the basic simplicity of the relationships already discussed a number of related topics will be considered in an appendix. The individual topics will he only briefly considered and referencesindicated for additional information. Applications to chemical problems have only been touched on since they are covered in great detail elsewhere. Weissherger's "Physical Methods of Organic Chemistry" has one chapter devoted to refractometry (9) and the interpretation of refractive index and dispersion data. There are a very large number of excellent books devoted to absorption spectmphotometry (10, 11). Applications of rotatory dispersion measurements are covered in some detail in a recent monograph (S), and similar applications can be made of circular dichroism spectra. This book also includes a very clearly written chapter by Moscowitz on the relationships between rotatory dispersion and circular dicbroism. A partial summary of the early experimental and theoretical work on circular dichroism and rotatory dispersion was recently published by a pioneer in this field, W. Kuhn (12). Appendix
Elliptical, Circular, and Phne Polarized Light. As judged by an observer stationed a t some point along an advancing light beam the electric vector of plane polarized light oscillates in one plane in a sinusoidal manner. Circularly polarized light has a rotating electric vector of constant magnitude. Thus the projection of the tip of the electric vector of circular light onto a plane perpendicular to the direction of propagation will give a circle. A third, more general
Figure 6. The circular components of light in vmrious stater of polarirotim) see k x l . The light beom is odvoncing towardthe observer.
These three statements can be graphically demonstrated by reference to Figure 6. Figure 6a-c represent the resolution of plane polarized light with an electric vector E, into circular components with rotating vectors E, and E L The first three drawings indicate the appearance of the two circular and the one resultant linear component a t a particular point in space a t three different times. Notice in Figure Gb that the E, and El vectors cancel one another at one point in the cycle. If there is a phase shift of one circular vector with respect to the other, this will lead to a rotation of the plane of polarization of E, as shown in Figure 6d. If one circular component is reduced in magnitude relative to the other (as when a plane polarized beam passes through a solution exhibiting circular dichroism), the light will become elliptical as in Figure 6e, f. Notice that in this case there is no position comparable to Figure 6b in which cancellation occurs, so the resulting light cannot be plane polarized. Furthermore, since the magnitude of the resultant changes with time (compare Figure 6e and 6f),it cannot he circular light. Production of Ci~cularLight. Circular light can he produced by passing plane polarized light through an optical device known as a quarter wave plate. The quarter wave plate is made of a material having along two axes two different refractive indexes for plane polarized light. A light beam with a plane of polarization incident a t +45' to these axes will emerge from the plate with two orthogonal components traveling in the same direction, but with a quarter wave phase difference between them. The resultant of two such waves is a circularly polarized wave of either right- or left-handedness, depending on whether the orientation of incident light vector is plus or minus 45O to the axes. A typical quarter wave plate is a thin sheet of mica. Volume 40, Number
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For a very lucid introductory discussion of the properties of polarized light the reader is referred to "Optics" by F. W. Sears (IS). (Notice in particular Figures 7-16, 17, and 23 of this reference.) A more complete treatment of these topics can be found in any advanced level optics text (3). Measurement of Rotatory Dispersion and Circular Dichroism. Since optical activity is observed in any substance with a difference in refractive index for right and left handed circular light, it should be possible to measure this directly with a refractometer. For example, a Rayleigh interferometer could be used with a polarizer and quarter wave plate in each beam to measure the refractive index difference directly. However, the difference in refractive index is too small to make this a useful method. On the other hand, it turns out that the small difference can easily be measured indirectly by using a polarimeter which measures the rotation of the plane of polarization resulting from the phase shift between the right- and left-handed circular components of the plane polarized beam entering the sample. (In recent years there have been remarkable improvements in polarimetry. For examples see references (7) and (1L).) Circular dichroism can also be measured directly or indirectly. For direct measurements, polarizers and quarter wave plates (giving right- and left-handed circular light) could he inserted in the beams of a double beam spectrophotometer and the difference in absorbance measured mith the same circularly dichroic sample in both beams. There are practical difficulties in such a direct measurement but recently a commercial instrument has been produced which does measure dichroism directly. For the principle of its operation see Legrand and Grosjean (15). In the discussion of Figure 6e it was pointed out that circular dichroism leads to the production of elliptical light. By using a quarter wave plate in an appropriate manner it is possible to make an "ellipsometer" which will measure the ellipticity of light (and therefore, indirectly the circular dichroism of a sample (16)). Physical Origin qf the Absorption-Dispersion Relationships. When the relationships between absorption and dispersion were first discovered, explanations were proposed by analogy with the behavior of a damped harmonic oscillator. If such an oscillator is forced into motion by a force varying sinusoidally with time, the power consumption and displacement of the oscillator reach a peak when the frequency of the driving force is equal to the natural resonant frequency of the oscillator. It was proposed that molecules contain atomic or electronic oscillators with natural frequencies of oscillation. When these oscillators are set into motion by a light wave, they consume the maximum power at their resonant frequencies. This then is the origin of an absorption band. The oscillating electrons would also radiate light (since accelerated charged particles radiate), and the interaction of this scattered light mith the original light beam leads to the observed dispersion anomalies. A detailed discussion of this point is lengthy but involves no conceptual diffiulties. At a much later date these ideas were reformulated in wave mechanical terms. A very clear discussion of this problem in both classical and wave mechanical terms can be found in 596
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"Quantum Chemistry" by W. Kauzmann (17) and in (10). Other Absorption-Dispersion Phenomena. In addition to the two "paired phenomena" discussed in the text there are a number of others of some chemical importance such as absorption-dispersion of the infrared, radio frequencies (electron spin and nuclear magnetic resonance), X-rays, and the Faraday effect. These will now be very briefly considered. The extension of the text's discussion of absorptiondispersion in the electronic spectral region to the infrared is very obvious. An understanding of infrared absorption-dispersion is useful in discussing the reasons for needing a number of prisms in infrared spectrophotometers to obtain adequate dispersion with reasonable prism transmission. At still lower (radio) frequencies one can observe electron spin resonance (18) and nuclear magnetic resonance (19) spectra. Both resonance phenomena exhibit absorption and dispersion modes exactly analogous to the ones already discussed. Just as in the ultraviolet, visible, and infrared regions, radio frequency absorption spectra are more important than dispersion measurements. But there are situations where conditions are more favorable for the latter (18). At very high frequencies, in the X-ray region, absorption-dispersion is also observed. An understandmg of this is helpful in studying the technique used by Bijvoet in determining the absolute configuration of tartaric acid (20). The induction of optical activity in a substance by a magnetic field is known as the Faraday effect. It also shows the expected relationships between its magnetic rotatory dispersion and magnetic circular dichroism (21). Recently it has been suggested that a study of the anomalous dispersion of the Faraday effect might provide a useful method of identifying singlet-triplet transitions (22,tS). Another example of a paired phenomenon of chemical importance is the dielectric loss factor and the dispersion of the dielectric constant (24). Also of importance are the absorption and dispersion of sound (25). Sound dispersion measurements have recently been exploited for studying very fast chemical reactions ($6). Finally two systems which are useful in discussing the physical basis for the absorption-dispersion phenomena are the damped harmonic oscillator (17) and the resonant RLC electrical circuit. A general treatment of the formal mathematical relationships (such as the Kramers-Kronig equations) between all of these paired phenomena can be found in a paper of Macdonald and Brachman ($7). Literature Cited
( 1 ) ALLSOPP, C . B., Pme. R o ~ aSoc. l (Lmdon),A146,300 (1934). A. M., AND GLOVER, A. M., J. Opt. SOC.Am., 23, ( 2 ) TAYLOR, 206 (19331. (3) DITCHBURN, R. W., "Light," Blackie and Son, London, 1952. (4) KUHN,W., A N D GORGE,H. K., 2. Phys. Chem. (Leipzig), (B)12,389 (1931). (5) MOFFITT, W., and Moscowr~z,A,, J. Chnn. Phys., 30, 648 (1959). ( 6 ) COTTON; A,, Ann. Chim. Phys., 8 , 360 (1896). ( 7 ) RIDGEWAY, D., Proc. Nat. A d . Sei. U.S.,48, 1482 (1962). ( 8 ) DJERASSI,C., ''Optical Rotatory Dispersion," McGrawHill, New York, 1960. (9) BAUER,N., FAUNS, K., AND LEWIN,S. z., in "Physical
(10) (11) (12) (13) (14) (15) (16) (17)
,Methods of Organic Chemistry," 3rd ed., A. Weiss-, berger, ed., Interscience Publishers, New York, 1960, Vol. 1, Part 2, chap. 18. BAUMAN, R. P., "Absorption Spectroscopy," John Wiley, New York, 1962. GILLAM,A. E., AND STERN,E. S., ,'An Introduction to Electronic Absorption Spectroscopy in Organic Chemistry," Edward Amold, London, 1957. KUHN,W., "Optical Rotatory Power," Ann. Re.. Phys. Chem., 9,417 (1958). SEARS, F. W., "Optics," Addison-Wesley, Cambridge, Mas., 1949. GILLHAM, E. J., J . Sn'. Inst., 34, 435 (1957). GROWEAN, M., AND LEGRAND,M., Comptes Rend. .4cad. Sci., 251, 2150 (1960). JAEOER,F. M., "Spatial Arrangements of Atomic Systems and ODtied Activitv." hleGraw-Hill. New York. 1930. K A U Z M ~ N N , W., " ~ u & t u m chemistry," Academic Press, New York, 1957.
(18) FFAENKEL, G. K., in "Physical Methods of Organic Chemis(19)
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(20). (21) (22) ~, (23) (24)
try," A. Weissberger, ed., Interscience Publishers, New Ymk, 1960, Vol. 1, Pert 4, p. 2801. GUTOWSKY, H. S., "Physical Methods of Organic Chemistry," ed. A. Weissberger, Interscience Publishers, New York, 1960, Vol. 1, Pmt 4, p. 2663. BIJYOET.J. M.. Endear,our.. 14.. 71 (1955). . . LOWRY,T. M., "Optical Rotatory Power," Longmanw, Green, London, 1935. SHASHOUA. V. E.. J. Am. Chem. Soc... 82.. 5505 (1960). SMYTH, C. P., ((DielectricBehavior and S t ~ c t u r e , "McGraw Hill, New York, 1955. E B E R ~ R DW. T , H., A N D RENNER,H., J . Molee. Spectrosc.,
6, 483 (1961). (25) R r c w ~ o s o E. ~ , G., Rev. Mod. Phys., 27, 15 (1955). (26) EIGEN,M., Disc. Paraday Soc., 17, 194 (1954). M. K., Reu. Mod. (27) Mac~oNAm,J. R., A N D BTULCHMAN, Phys., 28, 393 (1056).
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