Paul Blalz, David ~ipperl', Larry Sherman, and V. Balasubramaniyan
University of Wyoming Laramie, 82070
I I
Carbonium Ions of Coniugated Molecules A physical organic experiment
Every undergraduate organic student is familiar with the concept of fleeting organic intermediates known as carbonium ions, but very few have ever had the experience of generating and detecting them. Because they are short-lived species, evidence of their participation as intermediates in organic reactions was found orginally from kinetic and stereochemical data. Only recently has it been possible to observe or isolate these intermediates experimentally. The last ten years have seen a tremendous increase in interest in the direct isolation and observation of these species. With the improvement of existing techniques (e.g., ultraviolet spectroscopy) and the development of new techniques (e.g., nmr spectroscopy), our knowledge of cationic intermediates has increased considerably. Reviews on carboninm ion generation, detection, stabilization, and characterization have been published recently by Deno ( 1 , 2 ) and Olah (3). More recently, considerable energy has been expended toward the preparation and characterization of polyenylic cations. Deno (4, 6) and Sorensen (6, 7) studied a series of aliphatic polyeuylic cations formed by protonation of polyenes of strnctnre I. The symmetrical cations, 11, give a progression of visible ahsorption maxima ranging from 305 mp for n = 0 to
702 mji for n = 5. In addition Blatz, et al., (8) studied carboninm ions generated from vitamin A-related polyenes. Because of difficult procedures of synthesis or complicated instrumentation, the student is rarely able to generate and detect carbonium ions. However, using the experimental procedures outlined in this paper, it is possible for the undergraduate student in the organic, physical, or anlytical chemistry laboratories to actually see the formation of a polyenylic cation, detect it spectrophotometrically and make certain measurements on it. To our knowledge, this is the first time such an experiment has been adapted to undergraduate laboratories. 'Present address: Department of Chemistry, Upper Iowa College, Fayetta, Iowa 52142. 1 Nomenclature proposed by the Commission on the Nomenclature of Biolagicd Chemistry of the International Union of Pure and Applied Chemistry (1960). Also called vitamin A acetate.
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Specifically, the experiment involves the generation and stabilization of a polyenylic cation formed by the addition of acid to retinyl acetate,? 111, a t reduced temperature. FHa ?Ha
CHs
111
All of the starting materials are commercially available and a minimum amount of equipment is required. Although the experiment may be adapted to the use of a manual spectrophotometer, a recording ultraviolet spectrophotometer is preferable. Theory
All carboninm ions are stabilized by an sp2 hybrid orbital configuration. As the ?r overlap of spZ orbitals increases, electron delocalization increases resulting in greater stability. Ions formed from conjugated polyenes allow resonance hybrids which distribute the charge over all the carbons of the conjugated system for increased stability. Inspection of the retinyl acetate molecule reveals two possible modes of protonation: (1) a t the end of the polyene chain and (2) on the ester oxygen of the acetate group. Under high acid conditions, protonation occurs preferentially on the acetate oxygen (9). Elimination of acetic acid from the polyeue results in formation of the retinylic cation, IV, V.
This leads to n values of energy E. This step is thought to be essentially irreversible in high acid concentration. The polyenylic cation is stabilized by five conjugated double bonds with two limiting resonance structures making the largest contribution to the stability of the ion. It was shown by previous investigators that retinol has a tendency to lose water to give anhydroretinol, VI, (10-18) in dilute acid. However, Blatz and P i p pert (9) showed that high acid concentration tends to stabilize the cation by hindering removal of the proton. The retinylic cation decays with time, but the exact nature of subsequent products has yet to he positively determined. There is evidence, however, that the cation takes part in polymerization reactions (IS). Retinyl acetate absorbs at about 330 mp, whercas the retinylic cation absorbs in the region of 600 mp. An experimentally derived formula for the estimation of the, ,X of polyenylic cations may be obtained from the absorption maxima reported by Sorensen (7). A.,
=
250
+ 7%
(1)
From this relation, it can be seen that the wavelength obtained is a function of the length of the conjugated chain since 7% is the number of double bonds contributing t o the stability of the cation. The observed red shift (bathochromic shift) was treated theoretically by Ruhu (14) for related conjugated systems. He employed the free electron molecular orbital model in his t,heoretical treatment of polymethine dyes. This treatment may also be applied to polyenylic cations; it is found that a direct correlation exists between the experimental A., of a carbonium ion and the wavelength calculated from the free electron model. The a system of a carbonium ion is comprised of an odd number of p orbitals on spZ carbons. The retinylic cation has eleven p orbitals in its a system. I n such a system the carbon to carbon bond lengths are all considered to be equivalent resulting in a condition of zero potential as the electron moves along the a system. These conditions are the conditions for a particle in a box with zero potential. I n the wave equation H$ = EJ. (2) the kinetic energy operator is
where h is Planck's constant and m is the mass of t,he electron. Substituting eqn. (3) into eqn. (2)
.
This equation involves a single v a r i a b l e t h e length of the well, L. For purposes of calculation, the length of the well can be approximated as one bond length beyond either terminal sp2 carbon. Delocalization of a a electron occurs when it is in the vicinity of a carbon atom bound in the sp2 state. When the electron moves from the vicinity of an sp2 to an sp3 orbital arrangement, the boundaries of an infinite well occur. To illustrate the methods involved in the determination of the length of the well for a polyenylic cation, refer to Figure 1. A dienylic cation, as represented by
Figure 1. Boundaries of the inRnite well for o con/ugokd triene, 2,4,6octotriene, VII, and o dienylic cotion, VUI, IX.
resonance structures VIII and IX, may be generated from the conjugated triene, 2,4,6-octatriene, VII, by the addition of a proton to a terminal double hond. Conjugation of the cation with a series of double bonds results in delocalization of the charge between carbon atoms C-2 and C-6. Structures VIII and I X are the major contributors to the stability of the ion. Delocalizat,ionhas the effectof equalizing the C-C bond distances. I n the polyene, the bonds havc roughly alternating double and single bond distances; in the polyenylic cation, all bond distances (wit,hin the area of conjugation) are assumed t.o be those of aromatic C-C bonds such as are found in benzene. As already stated, the length of the well is one bond distance past the deloralizecl chain on either side. Therefore, the lengt,h of the well, L, for the dienylic cation is 6(1.40 A) or 8.40 A, when it is p n n e d t,hat the aromatic C-C bond distance is 1.40 A. In general, for polyenylic carhonium ions cont,aiuing 21c T electrons (or k double bonds stabilizing t,he cat,ion), L can be defined by t,he equation 1, = (2k
,
The wave function J., which is a solution to eqn. (3) is
where L is the length of the box (in this case the length of the a system), n is the quantum number and x is the distance along the box. The value for J., may now be substituted into eqn. (4).
+ 2)d
(8)
where d is the average hond lengt,h in the conjugat,ed system and k is the number of douhle bonds nt,ahilizing the cat,ion. The Pauli cxclusion principle prohibits more than t,wo elect.rons of opposite spin from occupying any given orbital; thus in its lowest energy state, the first lc orbitals of the carbonium ion will be doubly occupied. The first electronically excited state of a conjugated molecule is the result of the promotion of one a electron Volume 46, Number 8, August 1969
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51 3
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from the highest occupied level (n = k) to the lowest ulioccupied level (n = k 1). The energy of excitation, AZ, is therefore
+
Since AE
=
ergy is assumed to rise t,o infinity as in the case of the free electron gas model. Using the procedure developed by Morse (15), it can be shown that Ah', the energy difference between the lowest unfilled orbital and the highest filled orbital for t,his model, is closely approximated by the equation
h v = ~ C I A where , c i s the velocity of light
Again making the subst.itut.ion AE for A, t,heequation becomes When a comparison is made of the calculated values of A,, with the observed values for a series of carbonium ions, it becomes apparent that while eqn. (10) correctly predicts an increase in A,, as the length of the conjugated chain increases, the predicted values do not agree exactly with the observed values. The table makes a comparison between experimental and calculated values for the seriesof polyenylic cations which were studied by Blatz, et al. (8) and Sorensen (7). Iiuhn (14) found similar discrepancies when he used free elctron calculations to determine the energy levels of unsymmetrically substituted polymethine dyes or the polyenes themselves. He reasoned that a model for these species must be selected which allows for single-double bond alternation. This alternation of C-C bond lengths brings about a disturbance in the h e havior of the T electron gas along the chain. Thus a s electron traveling along the chain undergoes a periodic variation which is complete only after passing two carbon atoms (Fig. 2). It is permissible, however, as
C-C=C-c=c-czc-C
1
C-C=C-c=c-c=c-C Figure 3. Sine wove approximation of the potential energy of o r electmn moving along a conjugated polyene chain.
an approximation, to assume a one-dimensional potential field which has a sine wave variation along the chain, as indicated in Figure 3. The maxima of this sine curve correspond to the centers of the longer C-C bonds; the minima correspond to the centers of t,he shorter honds. V, corresponds to the amplitude of the sine curve or the perturbed sinusoidal potential. At both ends of the conjugated chain, the potential en514
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Journal of Chemical Education
and solving
Equation (12) reduces to eqn. (10) when V ois zero. Indeed T'o must be zero for the polymethine dyes since eqn. (lo), which has a zero value of Vn, gives calculated wavelengths which are in very close numerical agreement with experimental values. On the other hand, Kuhn evaluated Vn for a number of polyenes; he found it to be constant and has a value of 2.0 eV. Consequently, eqn. (12) may be used to calculate the wavelength of a polyene if 2.0 eV is used as the value of Vo. However, carbonium ions have a value of V owhich is between the zero for polymethines and the 2.0 eV for polyenes. Since VOfor carbonium ions is closer to zero, eqn. (10) gives a reasonable value for the wavelength. Making simplifying assumptions on the free electron molecular orbital model, Platt (16) has derived a very simple relationship that can be applied to carbonium ions. A,
= 49(n)
(13)
I n eqn. (13), n stands for the number of carbon atoms in the original polyene chain where it is assumed that the carbonium ions are formed by protonation of the polyene chain. Sometimes this is a diicult point to see. Consider the retinylic cation which is pent* enylic; it has five double honds. However, it would have to be obtained from a polyene with six double bonds if protonation were the method of generation. Consequently, six double bonds would represent 12 carbons and n = 12 or X = 588 mp.
Figure 2. Potential energy of a r electmn moving along o conjugated polyene chain.
I
= hc/A
The Experiment
For the first time, the undergraduate will be able to generate and study an often-mentioned, but seldomdetected, reaction intermediate. I n addition, the student will be introduced to some of the techniques used for the stabilization of short-lived intermediates (i.e., the use of low temperatures and rapid mixing procedures). The product of the experimental procedure is a series of absorption spectra for the retinylic cation and retinyl acetate. The absorption curves are then used to determine values for the A,,, E,,, and t.,, for the cation. The experimental A,, value can then be compared t o the value predicted by the free electron model and to the previously reported (9) value for the retinylic cation for the same conditions (594 mp). The retinylic cation decays with time and there is a corresponding change in the observed A,. and E,... Since the A,, shifts with time, it is best to scan the spectrum for each measurement, rather than selecting the A,, of the first scan and taking a series of absorption readings at this wavelength.
Com~arisonof Values for the A.,
of Polyenylic Cations
-Calcnlated , ,X
No. Double Bonds StabilizIng Cat~on
Plrttt Calc. Eqn. (13)
(mu)Modified FEMO Calc. FEMO (V = Calc. 0.69)' Eqn. Eqn. (10) (12)
be prepared and stored in the dark (or in red light).
It should be discarded after 12 hr and a fresh solutiou prepared when needed. A second solution (B) is
BI&, et al.
Sorensen
Obtained from eqn. (12) by using a A,, of 594 mp for the pentaenyhc eatmu. 8 BLATZ,P. E., AND BALASUBRAMANIYAN, V., unpublished data.
Assuming a first-order rate equation, the rate of decay of the retinylic cation is
where kl is the rate constant, c is the concentration of cation, and t is the time. Solution of the dzerential equation a t t = 0, when c =CQ, gives and co kd log = c 2.303
A value for 161 can be obtained from a plot of log A versus time after mixing since the slope of the line is equal to lc1/2.303. Inherent in this relationship is the assumption that the observed absorbance is directly proportional to log co/c. The half-life (t112) of the retinylic cation can then be calculated from
Equation (16) reduces to eqn. (17) when t = t.,, and cQ/c = 2. Since the half-life is dependent upon temperature, reproducibility is poor unless constant temperature equipment is used. The optimum temperature for stabilization, handling, and measurement of the retinylic cation is about -30°C. Equipment to maintain such a temperature in the spectrophotometer is generally unavailable; and so, only a qualitative estimate for the half-life may be made. Procedure
Reagents. Although many solvents and acids have been reported (9, IS) in the literature for the generation of the retinylic cation, 2-propanol and 98% sulfuric acid have been selected for this experiment. Both materials may be used without purification if freshly opened bottles are used. Commercial grade all-trans-retinyl acetate may be obtained from Distillation Products, Rochester, N. Y., and used directly if certain precautions have been followed. The polyene is sensitive to light and moisture and, therefore, must always be stored in a dark, refrigerated place, under reduced pressure. A stock solution (A) is prepared by weighing 1.5 mg of all-transretiuyl acetate into a 5-ml volumetric flask and diluting to volume with cold 2-propanol. This solution must
prepared by diluting 1 ml of A to 25 ml with 2-propanol. An acetone and dry ice bath is prepared in a Dewar flask. I n a large test tube (preferably glass stoppered), 13 ml of sulfuric acid is added dropwise to 12 ml of cooled (approximately -35OC) 2-propanol. The mixture should be continually cooled in the dry ice-acetone bath to keep it below about -25°C. If a t any time, the solution becomes discolored due to degradation of the alcohol, it should be discarded. Three sets of this 2-propanol-sulfuric acid solution should be prepared and stored in the Dewar flask until needed. Because of the instability of the carbonium ion, the rest of the experiment should be performed a t the spectrophotometer. A Beckman DB Spectrophotometer with a recording attachment is adequate for this work. The instrument, equipped with a tungsten lamp, is balanced a t 600 mp using 2-propanol in both quartz cells. A 0.2-ml aliquot of the retinyl acetate stock solutiou (A) is pipeted into a 50-ml beaker. As the solution is stirred rapidly with a magnetic stirrer, a 25-ml sample of the 2-propanol-sulfuric acid solution is added and a timer is started simultaneously. The solution must be warmed slightly until it reaches a point a t which it is pourable, but still viscous. The mixture is stirred until the blue coloration is somewhat homogeneous At this point, the mixture is rapidly transferred to a dry spectrophotometric cell and scanned from 650 mp to beyond the maximum absorption peak of the retinylic cation. The time after initial mixing should be recorded for the maximum point of absorption. The mixture is then rescanned several times over the same wavelength region, recording the times a t which each maximum is reached. The spectrum obtained about 15 miu after the initial mixing is used as the base line. Good results are directly related to the rapidity with which mixing and scanning procedures are carried out. Therefore, the first mixture is usually used to develop the best techniques for mixing and transferring the sample to the spectrophotometric cells. Duplicate and triplicate runs are recommended. After completing measurements on the carbonium ion, it is worthwhile to obtain the spectrum of alltrans-retinyl acetate. A portion of solution B is added to a dry spectrophotometric cell; its spectrum is scanned from 400 to 260 mp using a hydrogen lamp. Retinyl acetate gives an absorption maximum of 325 mp in 2-propanol. The Reporl
In preparing the report for this experiment, the student will make use of the spectra of the retinylic cation and retinyl acetate. The experimental, . ,X for the retinylic cation and retinyl acetate are obtained directly from the spectra. The value reported for the retinylic cation will be that of the initial scan with its time after mixing noted. The, ,A observed by our students varied from 598 to 608 mp. Variations from the published value of 594 mp are due partly to the slow scan speed of the Beckman DB. The value of 594 mp was obtained using a Beckman DK2A Ratio Volume 46, Number 8, August 1969
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515
Recording Spectrophotometer equipped with a Beckman Temperature Regulated Cell Holder and rapid scan capabilities. Also, a slight discrepancy is inherent in the use of commercial reagents rather than those which have been purified and dried. A calof the retinylic cation is culated value for the A., obtained from eqn. (10) and compared with the experimentally determinedvalue. A straight line should be obtained for the plot of log A versus t since it is assumed that the rate of decay of the retinylic cation is first order. A maximum ahsorption value (A,) is then obtained by extrapolating to zero time. The molar extinction coefficient of the cation is then ohtained using the value for A , and the relationship A
=
.be
(18)
where A is the absorbance, c is the molar extinction coefficient, b is the path length of the cell, and c is the concentration of the cation. I n the determination of the concentration of the retinylic cation, it must be assumed that there is a quantitative conversion of retinyl acetate to retinylic cation. Also, the most reliable results for concentration are ohtained by measuring the total volume of cationic solution a t the end of each run-this includes the quantity in the beaker and in the spectrophotometric cell. The published value (9) for c, is 6.7 X lo4 cm2 mmole-'. Students in this laboratory have ohtained values from 6.0 to 7.0 X lo4emzmmole-l. A value for the half-life of the retinylic cation is obtained by using the log A versus t plot and eqn. (17). The values observed in this laboratory by undergraduate students were in the range of from 3 to 5 min. On the whole thc results from this experiment are quite good. The student is forced to recognize that there are discrepancies between theoretical calculations and experimental observations. In the report, it
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Journal of Chemical Education
would he worthwhile to ask the student to list reasons for these discrepancies. Also, t,he student should be asked to search the Meratwe for other conjugated polyenes that could be used for carbonium ion formation. Acknowledgment
The authors would like to express their appreciation to the Public Health Service for its support under Research Grants No. GW1261G and NB-6712 and for its fellowship grant (GR4-31,379) to D. L. Pippert and to the Atomic Energy Commission for its support under Contract No. AT(l1-1)-1693. Literature Cited (1) DENO,N. C., in "Progress in Physical Organic Chemistry," A,, JR., Vol. 2 (Editms: COHEN,S. G., STREITWIESSER, AND T A ~R., W.) Interscience Publishers (a division of John Wiley & Sons, Inc.), New York, N. Y., 1964, p. 129. (2) DENO,N. C., Chem. Eng. News, 42 (40), 88 (1964). (3) OLAH,G. A,, Chem. Eng. News, 45 (14), 77 (1967). H. G., JR., FRIEDMAN, N., HODQE, (4) DENO,N. C., RICKEY, C. U. JR., J . Am. J. D., H o u s ~ n J. , J., AND P~TTMAN, Chem. Soe., 85, 2991 (1963). C. U., JR., AND TURNER, J. O., J . (5) DENO,N. C., PITTMAN, Am. Chem. Soe., 87, 2153 (1965). T. S., Can. J. Chem., 42, 2768 (1964). (6) SORENSEN, T. S., J. Am. Chem. Soe., 87, 5075 (1965). (7) SORENSXN, (8) BLATZ, P. E., PIPPERT, D. L., AND BALASUBRAMANIYAN, V., Photochem. Photobiol., 8, 3M (1968). D. L., J. Am. Chem. Soe., 90, (9) BLATZ,P. E., AND PIPPERT, 1296 (19GR). E. M., CAWLEY, J. D., AND EMBREE, N. D., J. Am. (10) SHANTZ, Chem. Soe., 65, 901 (1943). P.. DULOU.R.. AND VINET.A.., Bull. SOC.Chim. (11), MEUNIER. Bid., 25, 3'71 (1943j. ' (12) BARNHOLDT, B., A& Chem. Scand., 11,909 (1967). P. E., AND PIPPERT, D. L., Tetrahedron Letters, 1117 (13) BLATZ, (1966). (14) KUHN,H., J. Chem. Phys., 17, 1198 (1949). (15) Monm, P. M., Phys. Rev., 35, 1310 (1930). (16) PLAXT,J. R.., J. Chem. Phys., 25, 80 (1956).
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