Quantitative infrared Determination of Geometrical isomers through Add itive Absorbance R. M. Gendreau and P. R. Griffiths’ Department of Chemistry, Ohio Unlversity, Athens, Ohio 4570 1
L. E. Ellis and J. R. Anfinsen Merrell-National Laboratories, Division of Richardson-Merrell, Inc., Cincinnati, Ohio 452 15
An infrared spectrophotometrlc method for determlnlng the ratlo of two geometrical isomers In a pharmaceutical compound, clomiphene cltrate, Is described. The isomer shlfts between the infrared spectra of this compound are small, and no bands due to the individual Isomers are resolved In the spectrum of the mixture. Even so, provlded that the anaiytlcai frequencies are carefully chosen, It was found that the isomer ratlo could be determined to a probable accuracy of hi%. Results were in good agreement with an HPLC method, and less sample preparation was required for the Infrared method.
Because the physiological activity of pharmaceutical compounds is often dependent on their geometrical and stereochemical configuration, the capability of accurately determining the proportion of closely related isomers present in a mixture can be very important. Often the isomers are so similar that their determination by standard techniques such as ultraviolet spectrophotometry, nonaqueous titrations, or separation methods (GLC, HPLC, etc.) is quite difficult. Infrared methods are rarely thought of for determinations of this kind, although ir has, of course, been used for several determinations of chemically dissimilar pharmaceutical compounds (1-5). However, we have developed two methods whereby the ratio of two closely related isomers can be determined using ir spectrometry, and they will be described in this and the following paper. The first method is dependent on the well-known fact that for any mixture of N components in which the absorption of each component obeys Beer’s law, the absorbance a t any frequency, v2, is given by: N
A , , = C agbcm m=l
(1)
where at is the absorptivity of species m at vl, b is the pathlength of the cell, and c m is the concentration of species m. If the absorbance is measured at at least N frequencies, the concentration of each species may in principle be determined provided that the absorptivity of each pure component is known at each analytical frequency vl. This method has been successfully applied to many determinations using ultraviolet-visible spectrophotometers, where absorption bands are broad and accurate values of the absorptivity can be measured without introducing a serious error due to the finite resolution of the spectrometer. The method has also been applied to the quantitative analysis of multicomponent mixtures by infrared spectrophotometry (6);Bauman (7) has summarized the methods for calculating the concentration of each component and reviewed the experimental conditions required to achieve the greatest accuracy. Both Bauman (7) and Potts (8) have stressed the need to select each analytical frequency to correspond to the maximum absorption of a band due to one component and to
be well separated from intense absorption due to other components. When all the analytical bands are well resolved, changes in the relative concentrations of each component will not appreciably shift the peaks in the spectrum of the mixture, and the absorbances can be read directly from the analog spectrum without introducing a serious error into the calculations because of a small wavenumber error. However, for two-component mixtures where none of the bands due to either component can be resolved, the wavenumber at which each resultant band has its maximum absorption depends on the relative concentrations of each component, and occurs between the frequencies of the two contributing bands; therefore peak absorbances should not be read directly from the chart unless great care is taken to ensure wavenumber reproducibility. In such determinations, several frequencies must be used where the absorptivity of one component is changing rapidly with wavenumber, so that very high abscissa reproducibility, of the order of 1%of the halfwidth of the bands, is required. It is believed that to date no accurate quantitative determinations have been reported on two-component mixtures in the infrared spectrum of which no bands due to either component are resolved, i.e., no dip is seen in any resultant band. For such determinations to be accurately performed, the instrumental requirements are fairly stringent; the spectrophotometer should have high wavenumber reproducibility, a digital readout (to provide the highest spectrophotometric accuracy), and fairly high resolution (so that no bands are distorted by the instrument line shape function). Both laser-referenced Fourier transform spectrometers and the recently introduced mini- and microcomputer controlled grating spectrometers appear to fulfil these specifications. We have studied the determination of the 2 and E isomers of a pharmaceutical compound, clomiphene citrate (9). The structures of the free base of these isomers is shown below.
Z isomer of clomiphene (CzH5),N--CH,--CH,-O
E isomer of clomiphene In the spectrum of a mixture of the two isomers, no band which can be assigned to a single isomer can be observed. A Fourier spectrometer was used in this study.
EXPERIMENTAL Clomiphene citrate has only two bands for which appreciable iso-
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
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FREQUENCY ( CM“)
Flgure 1. Transmittance spectrum of N,Kdimethyl formamide at a pathlength of 96 pm. Most measurements were taken in the window between the strong sharp bands at 868 and 658 cm-’ mer shifts are exhibited when the absorbance spectra of KBr disks of the pure isomers are subtracted. These bands absorb near 770 and 750 cm-l and all other bands in the spectra of the pure isomers absorb within 1cm-I of each other. Of course, KBr disks, especially of amine salts, are unsuitable for quantitative work and solutions should be used. Solubility studies showed that while clomiphene citrate has a very low solubility in most solvents commonly used for infrared spectrometry, it dissolves readily in N,N-dimethylformamide (DMF) which has a spectral window from 700 to 1000cm-l, see Figure 1, so that the two bands which exhibited spectral shifts in the KBr spectra could be observed. Spectra were measured using a Model FTS-14 infrared Fourier transform spectrophotometer (Digilab, Inc., Cambridge, Mass.). All spectra were measured in double-precision (32 bits per datum point) in the double-beam mode at 2 cm-1 resolution and with a peak-topeak noise level of about 0.1% at 800 cm-I. Precision sealed KBr cells (Wilks Scientific Corp., S. Norwalk, Conn.) were used to contain the solutions and the same cells were usually used to contain the solvent reference; the use of a variable pathlength cell to contain the solvent reference was also studied. Two methods of solvent compensation were investigated. In the first method, transmittance spectra of the solutions and of the pure solvent were measured vs. an air reference using a single-cell for all measurements, and standard scaled absorbance subtraction techniques (IO)were applied to remove uncompensated DMF bands. The disappearance of the sharp DMF band at 868 cm-l was found to be the best indication that good compensation had been achieved. In the second method, a variable pathlength cell containing the solvent was held in the reference beam and its pathlength was adjusted until the 868 cm-I DMF band disappeared from the transmittance spectrum, which was then converted to the linear absorbance format and stored. After solvent compensation by either method, the absorbance spectrum of the solute was printed on a teletypewriter at equal intervals (approximately 1cm-1 apart); the frequencies at which ordinate values were printed out were constant to better than 0.003 cm-l ( I I ). Beer’s law plots were then made at each analytical frequency in order to find a: for the 2 and E isomers. To determine the isomer ratio of an unknown mixture, simultaneous equations similar to Equation 1were solved to give the best fit using a linear least-squares program for several analytical frequencies. One other equality was used in our programs, since it was known that the concentration at which the solution was made up, C, is equal to the sum of the concentrations of the 2 and E isomers, Cz and CE,i.e.: C=CZ+CE
(2)
It was assumed that no other solutions were present at appreciable concentration. Isomer ratios were calculated using as few as two and as many as all the analytical frequencies plus Equation 2, and the results for each solution were output. In this way, if the results calculated using absorptivitiesmeasured at a certain analyticalfrequency were inconsistent with the results from other frequencies for any reasor, the inconsistency could be readily spotted and those data could be eliminated from the final determination. 1908
Figure 2. Solvent compensated absorbance spectra of 9.77 % (w/w) solutions of clomiphene citrate in DMF; pathlength is 96 pm (A) E isomer, absorption maxima are at 765 and 750 cm-’; (B) 2 isomer, absorption maxima are at 771 and 744 cm-l; (C) Mixture of isomers for which results are given
RESULTS The greatest difference between the spectra of the 2 and E isomers of clomiphene citrate is between 800 and 700 cm-l, especially between the bands in the 2 isomer spectrum at 765 and 750 cm-l, and in the E isomer spectrum at 771 and 744 cm-l, see Figure 2. The absorptivities of each isomer at these four frequencies were measured using solutions of the pure isomers having concentrations between 2 and 8% (w/w), or approximately 0.03 t o 0.14 M. While linear Beer’s law plots with small standard deviations were measured at band maxima, some difficulty in obtaining good plots for data then on the slopes of bands was encountered. Two reasons can account for the deviations of individual points from the best straight line. Random variations in the Io line (of slightly less than f1%)occurred from run to run; this effect is probably due to short-term variations in the temperature of the triglycine sulfate (TGS) detector. Since the peak absorbance of each band was always less than 0.15, small variations in the baseline caused relatively large errors in the measured absorbance of weak bands. A s y s t e m atic error in the 10line is caused by the fact that contributions to the absorbance (measured against an air reference) are made not only by the solution or pure solvent but also by reflection losses from the cell window. When the solvent absorbance is numerically scaled for compensation, the reflectance component is also scaled. Since the concentration of the sample was typically about 6% and the reflectance of KBr is approximately 5%)an error in the baseline of the order of 0.3% (assuming a n ideal solution) could result from the digital method of solvent compensation. T h e effect of these systematic errors would, of course, be reduced since they occur both in the spectra of the pure isomers and in the spectrum of the mixture of isomers. In a n attempt t o eliminate this source of error, the use of a variable pathlength cell for solvent compensation was studied, but it was found that even when the pathlength of the reference cell was adjusted so that good solvent compensation was achieved, the standard deviation of the Beer’s law plots for wavenumbers on the slopes of the absorption bands was just as great as for the digital method of solvent compensation; even though the standard deviation was large, no systematic deviations were noted. Since accurate compensation of solvent bands using a variable pathlength cell is a time-consuming procedure on a Fourier spectrometer, the decision t o use the
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
Table I. Molar Absorptivities of E and Z Clomiphene Citrate Calculated from Direct Measurement of Absorbance and after Baseline Correction E isomer 2 isomer Frequency Direct Corrected Direct Corrected 744.5 cm-l 750.3 cm-l
37.3 48.3
103. 114.
Table 11. Percentage of E Isomer Computed Using 2,3,4 and 5 Variables High value, No. of No. of different % variables equations 67.8 2 8 66.5 3 10 64.5 4 4 63.7 1 5
115. 63.5
166. 116.
Low value,
Average,
%
%
42.2 59.8 60.4 63.7
61.4 61.8 62.5 63.1
DISCUSSION digital method for solvent compensation was made because of its speed and convenience. For spectra in which the solvent bands had been compensated digitally, two different absorptivities a t each analytical frequency for each isomer were used for the computation of the isomer ratio of an unknown sample. One set of absorptivities was calculated from the absorbance values exactly as printed on the teletypewriter. The second set was calculated using a modified baseline method in which the smallest ordinate printed out for the absorbance minimum near 730 cm-l was subtracted from the printed absorbance values at the analytical frequencies. Both methods yielded linear Beer's law plots when the peak absorbances measured from the spectra of the pure isomers were plotted vs. concentration but the absorptivities calculated using the two methods were different. The absorptivity a t 771 cm-l for the E isomer and a t 765 cm-l for the 2 isomer, as measured using the modified baseline method, was small and therefore quite susceptible to errors caused by an incorrect baseline. In our work these absorptivities could not be determined with confidence because shifts in the IO line of f l %regularly occurred. On the other hand, the absorptivitity a t 744 cm-l for the E isomer was about one third the magnitude of the peak absorptivity of the 744 cm-l band for the 2 isomer. Similarly the absorptivity at 750 cm-l for the 2 isomer was greater than one half the peak absorptivity of the 750 cm-l band of the E isomer. Therefore the measured absorptivity of each isomer at these frequencies is less susceptible to errors due to small shifts in the IO line. If the absorbances a t 771 and 765 cm-l were included in the least-squares analysis to determine isomer ratios, consistent results were never found, whereas surprisingly consistent results were achieved from the 750 and 744 cm-l data using either set of absorptivities. In practice we had the greatest confidence in the results computed using both the uncorrected and baseline-corrected absorbances a t these two frequencies. The absorptivity values used in these calculations are shown in Table I, while Table I1 summarizes the results on a commercial sample of clomiphene citrate, the free base of which had been determined by an HPLC method (12)to have an E isomer content of 62 f 1%.Results are shown when two, three, four, and five simultaneous equations were solved. Significant deviations from the mean value were not observed in these calculations, although if data at 771 and 765 cm-l were included in the input, a much greater range of results was observed.
When two chemically different components are to be analyzed quantitatively by infrared spectrophotometry, it is customary to select analytical frequencies at which the absorption due to one component is a maximum while the absorption due to the second component is small. The pathlength must be accurately controlled so that samples are usually measured in the liquid phase, either as neat liquids or as solutions in infrared transmitting solvents such as C C 4 or CS2, so that little or no solvent compensation has to be performed and there is little uncertainty about the baseline. Finally, relatively long pathlengths can be used to.increase the solute absorbance to the optimum value of between 0.4 and 0.8. In our isomer analyses none of these ideal conditions are encountered, since a) the spectra of the isomers are very similar; b) the isomers are insoluble in CC14 or CS2; c) the use of DMF as solvent limits the pathlength and the solute has to be present a t a rather high concentration; d ) a t high solute concentration, the use of digital methods to compensate for solvent absorption is less accurate (13);and e) under these measurement conditions, the solute absorbance is low and most susceptible to errors due to an improperly chosen baseline. Nevertheless, remarkably consistent results were obtained provided that absorbance measurements were taken only at frequencies at which both isomers showed appreciable absorption so that baseline errors were minimized; it should be noted that this is just opposite to the way in which analytical frequencies are usually selected. To this end, the optimum shift between the peak frequencies of the analytical band should be approximately equal to the half-width a t half peak absorbance of the bands. Larger shifts cause increased baseline errors while smaller shifts cause the band parameters to become so similar that large errors can result. If baseline errors are decreased (either by stabilizing the detector or by being able to increase the solute absorbance) or if the analytes are more different chemically than the two isomers discussed above (allowing a greater number of analytical frequencies), the errors in determinations made in this way should be reduced below the level of f l %found in this study. Currently the measurement time and accuracy of this infrared method for the analysis of clomiphene citrate is comparable to that of HPLC determinations. However a major advantage of the infrared method over the HPLC method is that no sample preparation other than dissolution is required for the infrared method, whereas in order for the analysis to be performed by HPLC, the free base has to be liberated and extracted.
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
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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 stereoisomers which 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 vk is the peak frequency of the band of isomer I. Df = AI)" - AI
If Av = v; - v;', and Au
