LITERATURE CITED (1) W. H. Washburn and E.0. Kruger, J. Am. fharm. Assoc., Sci. Ed., 38,623
(1949).
(2)T. V. Parke, A. M. Ribley, E. E. Kennedy, and W. W. Hilty, Anal. Chem., 23,
953 (1951). (3) W. H.Washburn and E. 0. Krueger, J. fharm. Sci., 40,291 (1951). (4) W. H. Washburn, J. Am. fharm. Assoc., 43,48 (1954). (5) J. Carol, J. Assoc. Offic.Agr. Chem., 38, 638 (1955). (6) "Manual on Recommended Practices in Spectrophotometry", 36 ed.. A.S.T.M., Philadelphia, Pa., 1969, pp 35-44. (7) R. P. Bauman, "Absorption Spectroscopy", John Wiley and Sons, New York, 1962.
( 8 ) W. J. Potts, "Chemical Infrared Spectroscopy", Vol. I, Techniques,John Wiley and Sons, New York, 1963. (9) S. Ernst, G.Hite, J. S.Cantrell, A. Richardson, and H. D. Benson, J. Pharm. Sci., 65, 148 (1976). (IO) J. L. Koenig, Appl. Spectrosc., 29, 293 (1975). (11) T. Hirschfeld, 27th Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, March 1976, Paper No. 382. (12) J. R. Bodenmiller. Merrell-National Laboratories, Inc., Cincinnati, Ohio, personal communication, 1976. (13) P. R. Griffiths and R. J. Anderson, unpublished work, 1976.
for review March
49
lg7& Accepted August 5,
1976.
Quantitat ive Infrared Determination of Stereoisomers through Differential Absorbance R. M. Gendreau and P. R. Griffiths* Depaiiment of Chemistry, Ohio University, Athens, Ohio 4570 1
A method for determlning the mole fractions of stereoisomers present in a mixture Is described. Absorbance spectra of the pure isomers at a certain concentration are subtracted from the absorbance spectrum of the mixture at the same concentration. The ratio of the maximum value of one difference curve to the minimum value of the other dlfference curve is equal to the ratio of the mole factors of the isomers present. The method Is still accurate If the analytical bands of each Isomer have different absorptivities or half-widths. The effect of variations In the Instrumental baseline, Incorrectly prepared solutlons, and overlapplng bands Is discussed. The frequency repeatablllty of the spectrometer has to be very high whlch appears to limit the instruments on which measurements of this type can be performed to Fourier transform infrared spectrometers. It Is shown that even if the shift between the bands of two isomers Is less than 0.1 cm-', quantitative determinations of the Isomer ratio can still be found. The valldlty of the method Is verified by determlnlngthe mole fractions of Z and E clomlphene citrate In a comrnerclal sample.
The additive method for multicomponent analysis by infrared spectrometry described in the previous paper ( 1 ) is most useful when the peak absorbance of analytical bands is between 0.3 and 1.0 and when the position of the baseline of the spectrum is accurately known. When the analytes are only soluble in poorly transmitting polar solvents, the pathlength of the cell sometimes cannot be increased to the point that the peak absorbance of any solute band exceeds 0.3 without reducing the energy a t that frequency to the point where ratio-recorded spectra are too noisy for precise photometry. In this case, the determination must be carried out using shorter pathlengths than desirable, the peak absorbances of solute bands are low, and errors due to an incorrectly chosen baseline become important. Under these circumstances, the analytical bands must be carefully chosen to ensure that band shifts are of the same order as y, the half-width a t half peak absorbance of the bands. If the band shift, Av, is much smaller than y, the standard deviation of the solutions of the simultaneous equations become large, and less confidence can be placed in the final answer. Geometrical isomers often show relatively large shifts and the ratio of geometrical isomers may often be determined in this fashion. On the other hand, band shifts shown in the spectra of other types of stereoisomers may 1910
be much smaller than y, and the isomer ratio of these compounds cannot be accurately determined in this way. We have developed an alternative method for determining the isomer ratio of closely related stereoisomerswhich fall into this category. The principle of the method may be illustrated by the following simplified example. For a mixture of two stereoisomers, denoted I and 11,let the mole fraction of each isomer be XI and XI1,then
XI
+ X" = 1
(1)
Consider the spectra (measured linear in absorbance) of equimolar solutions of isomer I, isomer 11, and the mixture of the isomers to be analyzed. Let us assume that there is an isolated Lorentzian band in the spectrum of each isomer for which the peak absorptivities of the two isomers, a; and a;', are equal and the half-widths at half peak absorbance, 71 and ?I1, are also equal. Let the absorbance as a function of frequency, u, for each solution be represented as Af, A:' and A:,", respectively. If Ai is subtracted from AL,", a symmetrical difference spectrum, denoted by D!,results. Assuming that y1 = yI1 = y, and a; = a;' = ao, we have that:
(3) and
where b is the pathlength of the cell, c is the concentration of each solution, and LJ; is the peak frequency of the band of isomer I. Df = AI)" - AI
If Av = v; - v;', and Au XI1, out of all the maximal and minimal values on the difference curves, DL,,is the greatest affected, and DL,,/D~,, should be used in the evaluation of XI1/X1, see Figures 4C and 4D. It may be stressed that an advance knowledge in the most likely source of error will allow the determination to be optimized. The effect of an error either in C1 or CII or in the concentration of the analyte solution is to move the isoabsorbance point from zero to a point above or below the D,axis. When all measurements on the difference spectra are referenced to the isoabsorbance point, the absolute error in the determination of XI and XI1 due to an error in C1or C" is reduced to less than f0.2% for errors of up to 5% in C* or C'I. When the concentration of the analyte is in error, the effect of referencing the maximal and minimal values on the difference spectra to the isoabsorbance point is less spectacular, but errors are always somewhat reduced, see Figures 4C' and 4D'. If more than one of the solutions is incorrectly prepared, the errors in the calculated values of XI and XI1are increased, the worst case being when either C1or CII is high and the other is low. In this case the use of the isoabsorbance point does not significantly reduce the error. Effect of Neighboring Bands. If neighboring bands absorb a t the same frequency and have the same absorptivity for each isomer, no effect on the difference spectrum will be observed provided that measurements are performed at fairly high resolution. However large errors in the determination of isomer ratios may be introduced by overlapping absorption bands which also exhibit spectral shifts. The most drastic effects are observed when the shift for the neighboring bands, (Av)'is approximately equal to that for the analytical bands, Av,when their absorptivity is high, and when their absorption maxima are displaced by less than 4y
-
W a 0
,'
Figure 4. Absolute error in the calculated percentages of each isomer - xirue[, as a function of x'/x" for an error of present, i.e., 100 2.5% in making up one of the solutions: in each case XI is greater than
l ~ & ~ ~ ~
X" When d is incorrect, curve A shows the error if d,max/d~in is used to evaluate Xti/Xi, and curve 6 shows the error if dmIn/& is used. When the Concentration of the analyte is in error, curve C shows the error if dm/dAlnis used to evaluate Xii/Xi, and curve D shows the error if dmin/d,Aax is used. Curves and IY show the corresponding errors when the isoabsorbance point is used for the calculation of the maximal and minimal values of d,and d i
c
from the analytical bands. Under these circumstances, absolute errors in the calculated values of XI and XI1may exceed 5%. The error in the determination due to overlapping bands is reduced by any factor which tends to reduce the amplitude of the difference spectrum due to the interfering bands relative to that due to the analytical bands. Denoting the absorptivities of the interfering bands by (ab)' and (a;')', the accuracy of the determination is therefore greatest when ab >> (a;)', >> (a;')', and Au >> (Av)'.
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
1913
Difference spectra, ( A ) 0: and (B)Of,for the clomiphene citrate spectra shown in Figure 2 of Ref. 1
Figure 5.
Values of D L , and DLlnfrom the isoabsorbance point (which is indicated by the broken line) are shown
In view of the fact that this analytical method is most useful for large molecules (with a correspondingly large number of absorption bands in the infrared spectrum), some care has to be exercised in selecting the band which will yield the most accurate results. Since a change in solvent will often cause frequency shifts, it may even be possible to optimize the analysis by the correct choice of solvent. In the presence of perturbations to the difference spectra by neighboring bands, the possibility of choosing which lobes to use for the analysis, as discussed in the previous section, is often eliminated. If neighboring bands are on the high frequency side of the analytical bands, the maximal and minimal values of Di and 0:'on the low frequency side of the isoabsorbance point must be selected to minimize the errors, and vice versa. Experimental Verification. The validity of the method was studied using cIomiphene citrate for reasons discussed in the Experimental section. The spectra of the 2 and E isomers and of an unknown mixture from 800-700 cm-l are shown in Figure 2 of Ref. 1.Although the bands in the spectrum of the E isomer at 765 and 750 cm-l are of comparable intensity and overlapping significantly, the 745 cm-l band in the spectrum of the 2 isomer is stronger than its neighboring band a t 771 cm-l and also better separated. The determination of the isomer ratio would therefore be best carried out using the lobes in the difference spectrum for which the contribution of the 745 cm-l band is the greatest. The difference spectra are shown in Figure 5; as expected, the most intense feature in each spectrum occurs close to 745 cm-l. Measurements taken from the isoabsorbance point lead to a value of X1/XI1= 1.71, so that XI' = 0.369 and XI = 0.631. Since the amplitude of Dl (the difference plot when the absorbance spectrum of the E isomer is subtracted from that of the mixture) is less than that of D:, it may be deduced that the mole fraction of the E isomer is greater than that of the
1914
2 isomer. The calculated value of the mole fraction of the E isomer is therefore 0.631, which may be compared with the values of 0.637 calculated using the additive method ( I ) and 0.62 as measured by HPLC ( 4 ) . Comparison with Other Methods. The method described in this paper for the determination of the isomer ratio of stereoisomers compares very favorably in many respects to other analytical methods, although the instrumentation is not inexpensive. A Fourier transform spectrometer with a good data system is needed, both because of the high frequency repeatability needed when the band shifts are small and also because spectra of the pure isomers must be stored over long periods of time if they are not to be measured for each determination. With this equipment, the analysis can be performed relatively quickly: in the example above at least four determinations per hour could be performed and, if bands in a more favorable spectral region were available, the analysis time could be reduced. The method can be applied even when the isomers have very similar properties, although it may be noted that the smaller the band shift, Au, the longer will be the time required to achieve a given accuracy. It might also be mentioned that even if pure samples of the two isomers are not available, it is possible to synthesize their spectra using the data system of a spectrometer with array-based software (5))provided that solutions of samples where a partial separation has been achieved (say, XI = 0.8 for one sample and XI = 0.2 for the other) are available. Methods for the analysis of closely related stereoisomers based on the use of HPLC usually require long columns (with correspondingly long elution times), and even then the peaks due to the two isomers may not be fully resolved so that baseline corrections are needed before accurate values for XI and XIxmay be obtained. Other currently used ir and uv-visible spectrophotometric methods do not yield accurate results for this type of determination because of the similarity of the spectra of the two isomers. The method described in this paper therefore shows promise for a wide variety of difficult analytical applications, especially for the determination of pharmaceutical compounds where small stereochemical changes can cause large changes in physiological activity.
ACKNOWLEDGMENT The cooperation of Jon Anfinsen, John Bodenmiller, and Larry Ellis of Merrell National Laboratories, Cincinnati, Ohio, in providing samples of the pure isomers of clomiphene citrate and analyzed samples of mixtures is gratefully acknowledged. LITERATURE CITED (1) R. M. Gendreau, P.R. Griffiths, L. E. Ellis and J. R . Anfinsen, Anal. Cbem., 48, 1907 (1976). (2) T. Hirschfeld, Appl. Spectrosc., 29, 524 (1975). (3) T. Hirschfeld,"Wavelength accuracy of Fourier transform spectrometry". Pittsburgh Conference on Analytical Chemlstry and Applied Spectroscopy, Cleveland, Ohio, March 1975, Paper 382. (4) J. R. Bodenmiller, Merrell National Laboratories, Cincinnati, Ohio, personal communication, 1975. (5) T. Hirschfeld, Anal. Chem., 48, 721 (1976).
RECEIVEDfor review March 4,1976. Accepted August 5,1976. This work was supported by Grant GP 38728X from the National Science Foundation. One of us (RMG) also gratefully acknowledges summer support under the National Science Foundation Undergraduate Research Program, Grant EPP 04407 to Ohio University.
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
