[CONTRIBUTION FROM THI FRICK CHEMICAL LABORATORY, PRINCETON UNIVERSITY]
THE RELATIONSHIP BETWEEN OPTICAL ROTATORY POWER AND CONSTITUTION O F THE STEROLS SEYMOUR BERNSTEIN, WALTER J. KAUZMANN,* AND EVERETT S.WALLIS
Received December g6, 1940
It is well known that the carbohydrate chemist has made extensive application of the physical property of optical rotatory power in the elucidation of molecular structure. This has been made possible by the discovery, chiefly by Hudson, of several rules relating the structure and rotatory power of carbohydrates. Sterol molecules are also optically active, and it is apparent that the development of analogous quantitative relationships between the structures and the rotatory powers of these substances should be of similar great value to the worker in this field. It is the purpose of this paper, first to investigate the possibilities of the steroid molecule in this connection from the standpoint of modern theories of optical rotatory power, and then to apply the results of this investigation to the establishment of a reliable and general method of calculating the rotatory power of any molecule from a knowledge of its structure and of the rotatory powers of other molecules. Several investigators have already pointed out definite relationships between rotatory power and the constitution of the sterols. In 1936, Callow and Young (l), compiled data to show that when a certain structural element (e.g., a double bond) is introduced at a given position in a steroid molecule, there is usually a definite directional change in the rotatory power. Unfortunately, the changes in rotatory power observed by them were not such as to make their method quantitative, and, furthermore, a sufficient number of discrepancies were found to reduce considerably its value in elucidating structure. Lettr6 (2), by employing the principle of optical superposition to partially dehydrogenated sterol molecules, attempted to correlate the absolute configurations of the hydroxyl group at the CB position in sterol molecules with that in actetrahydro-P-naphthol. Ruzicka, Hofmann, and Meldahl (3) have observed that the transformations of a A5-3,17-diol into a Ae3-keto-17-01 results in an increase in positive rotation (sodium D light) of 140' to 160" in alcoholic solution. In several other investigations (4), use has been made of the sign and magnitude of the optical rotatory power in support of, or in opposition to suggested structures of sterols, and every experi* Present address, The Westinghouse Electric Company, East Pittsburg, Pa. 319
320
BERNSTEIN, KAUZMANN, AND WALLIS
enced worker in this field now has preconceived ideas concerning the magnitude and signs of the rotatory powers of various types of sterols which are based on his every-day experience. It has been shown ( 5 ) that the validity of Hudson’s Rules in carbohydrate chemistry is the result of certain very special conditions to which the structures of carbohydrate molecules readily conform. It is to be pointed out here, however, that steroid molecules in general cannot possibly fulfill these conditions. Therefore, no method of attack in the manner of the principle of optical superposition can succeed except in very special cases such as that considered by Lettr6 (2). Thus, it will not be valid to assign numbers to individual asymmetric carbon atoms and to attempt to calculate the changes in rotations when the configurations about different asymmetric carbon atoms are changed. Indeed, even if such a procedure were valid, it would be of little use to the organic chemist in this field, since one is usually not at liberty to change the configurations about most of the asymmetric atoms in the steroid molecule. Furthermore, the worker in this field is generally more interested in knowing the change in rotation in going from one type of substance to another with or without different functional groups, and as a consequence the principle of superposition is of little use. We conclude, therefore, that little help will be given by attacking the problem from this point of view. In our opinion the most promising starting point is to be found in the following statements of fact: (A) Construction of space models for steroid molecules, as for example cholestane (6), reveals that certain parts of the molecule are widely sep21
CH, I
*O
n
23
24
CH-CHz-CHz-CHz-CH
25
/
tH3
Cholestane arated from one another. Thus, the ring system A B C D does not curl up, but is more or less flat. Consequently positions 3 and 17 are at relatively great distances (more than 8 .%)from one another.
ROTATORY POWER OF T H E STEROLS
321
(B) Introduction of double bonds does not alter this flatness appreciably. (C) Only very few of the stereoisomers theoretically possible are encountered, and these are of such a nature that the major portion of their chemical reactions involves transformations on a fixed framework. For example, cholestane and coprostane, which differ solely a t the Cgposition, have no appreciably differences in regard to the flatness of the molecule. (D) Vicinal actions (ie., the interactions between groups in optically active molecules which give rise to optical activity) decrease rapidly with distance. Therefore, when two centers of asymmetry are far apart, they do not influence appreciably one another’s contributions to the optical rotation. We shall fmd that it is through the careful use of this rule that we can make such quantitative predictions as are actually possible. The question of just how far apart two groups must be before they cease to have significant influence on each other cannot be answered a priori with assurance, but it is very likely that groups as far apart as those attached to Cs and C1, will have little effect on each other. (E) When a group occurs on an open chain, vicinal actions between it and other groups on the chain are much smaller, and decrease with distance much more rapidly than do those between groups attached to a rigid framework (7). This makes the groups on the side chain more independent of the rest of the steroid molecule. The procedure which is to be followed in utilizing the above principles in calculating the rotatory powers of steroids is best illustrated by the following example. Consider the changes in rotation which occur when one goes from ergostane to ergostanone and from stigmastane to stigmastanone : CHI
I
l
u
~
/ C ~ H CHCH‘ ~~ 2
I
CH3
\
CH3
CH3
Ergostane
[MID= +7670° in CHCls [MID = [&X molecular weight (c = 12, H = 1, and 0 = 16). All molecular rotations have been rounded off in the last figure. It is obvious that all measurements shall have been made in the same solvent in order t o reduce disturbances due to solvent effects.
322
BERNSTEIN, KATJZUNN, AND WALLIS
Stigmastane [MID= +10,470' in CHCls
c l g / ; 5 C H z CH3
CH2 CHCH /CH3
I
CzH5
0
/
/
I
\
CH3
H Stigmastanone [MID= +17,000" in CHCla
Stigmastane and ergostane differ from each other solely a t the Csr position, the former having a methyl group, and the latter an ethyl group. This changes the rotation of the molecule as a whole from [MI, = +7670' for ergostane to [MI, = 10,470' for stigmastane. This modification is centered a t a point far distant from the C3 position, and moreover it occurs well out on an open chain. If one considers the side chain and the atoms in the neighborhood of C3as two independent regions of asymmetry,
+
323
ROTATORY POWER OF THE STEROLS
each of which contributes a definite amount to the optical rotatory power of the molecule, then subtraction of the rotation of stigmastane from that of ill give the difference in the contributions to the rotation of a ergostane w methyl group a t the C24 position and its environment, and of an ethyl group a t that position and its environment. Similarly, subtraction of the rotation of stigmastane from that of stigmastanone will give the difference in the contributions to the rotation of a methylene group a t Cs and its environment, and of a carbonyl group at C3and its environment, since the contributions of the side chain regions, which are the same in both molecules, should cancel each other. In the same way, when we subtract the rotation of ergostane from that of ergostanone, the contributions of the side chains cancel one another, leaving again only the difference in rotation of the methylene and carbonyl groups a t the Ca position. Therefore, the difference in rotation between ergostane and ergostanone should be the same as that between stigmastane and stigmastanone. This is, indeed, found to be the case: Ergostanone.. ............ +13,960 Ergostane.. ............... +7,670
Stigmaatanone.. .......... +17,000 Stigmastme............... +10,470
+6,290
+6,530
Again, we should expect increases in the positive rotation of about 6400' in going from cholestane to cholestanone, and from ysitostane to y-sitostanone: CHs
/
CHS CHzCH
\
CHI
Cholestane CH3 I
/
CH3
324
BERNSTEIN, KAUZMANN, AND WALLIS
y-Sitostane
y-Sitostanone
Since an error in the measurement of [a]=of only 2.5" would result in an error of about 1000" in [MI,, we see that in this case also our expectations are fulfilled within experimental error. Cholestanone.. . . . . . . . . . . . +15,840 Cholestane.. . . . . . . . . . . . . . . +9,160
7-Sitostanone.. . . . . . . . . . . . +15,760 7-Sitostane. . . . . . . . . . . . . . . +8,090
$6,680
+7,670
I t is interesting in this connection to point out that in all of the above compounds, the hydrogen a t Cgis conventionally taken to be trans to the
Coprostane
[MID = +9430" in CHCla
Coprostanone
[MID = +14,010 in CHCla
325
ROTATORY POWER O F THE STEROLS
Clo methyl group. A comparison of the above differences with the differences in the rotations of coprostane and coprostanone types of compounds, where this hydrogen is cis to the Cl0 methyl group illustrates what happens when the environment at the CBposition has been altered. Here an agreement is not to be expected in the difference (4580') and indeed is not so found. In order to be able to carry out this procedure for any molecule it will be convenient at this time to set up a system of notation. Let us arbitrarily select cholestane as our reference compound. The rotation of this substance will be denoted by the symbol C (Table I). In the change from cholestane to cholestanone, there will be a change in rotation which will be denoted by the symbol2 K a t ;we can write, therefore, the rotation of cholestanone as C Kat. The value of C is 4-9160, this being the molecular rotation of cholestane itself (Table I). Since the rotation of cholesKst = 15,840, and hence K,, tanone is +15,840, it follows that C = 6680. Similarly, in the change from cholestane to ergostane we change the rotation by an amount denoted by the symbol Erg, and since 7670' it follows that C Erg = +7670, the rotation of ergostane is and therefore Erg = -1490'. Now if we wish to express the rotation of ergostanone precisely in terms Kst Erg e, of these constants, we must write its rotation as C where C , Katand Erg have the values given above, while e is a factor which takes into account the difference in the interactions of the ergostane and cholestane side chains with the carbonyl and methylene groups a t the Cs position. As we have seen, e should be insignificant, so that we can express the rotation of ergostanone as C Kat Erg = 14,350', as compared 13,960'. Thus the neglect of this term, e, with the observed value of under the proper circumstances can be said to provide the basis for the present method of calculation. In Table I there is given a series of constants whose values have been derived in the same manner as that outlined above. Each constant represents the change in rotation which occurs when an indicated change is made in the structure of cholestane. Rotations measured in chloroform have been used in deriving the constants, since this is the solvent most used in this field. Only measurements with sodium D light have been utilized. It should be noted that other solvents and other wave lengths, if used consistently, would, of course, be no less suitable than those selected, but indiscriminate use of solvents and wave lengths obviously is to be avoided. The system used in assigning symbols in Table I is as follows: N and
+
+
+
+
+
+
+
+
+
+
+
+
+
8 This symbol signifies that there is a carbonyl (Ketone) a t the Cs position and that the hydrogen a t CSis trans to the CIOmethyl.
326
BERNSTEIN, KAUZMANN, AND WALLIS
++ ut, ++ ut, ++ + + + + 0+ t+, + +
but,
mwG? mi
t,t,t,t,
4C.l
m. 3
3 4
2. W-
m w m m 3
m
+ + +
t,
t,
b u t ,
2
0,
2
B
00
m
ROTATORY POWER OF T H E STEROLS
A
327
TABLE I1 SUBSTANCE
Pregnane 7-Sitostene Stigmastanol Epi-stigmastanol Ergostanol Epi-ergostanol 7-Sitostanol p-Sitosterol p-Ergostenol al-Dihydrositosterol al-Isodihydrositosterol a-Ergostenol 7-Sitosterol 22-Di hydroergosterol A*:14,n:2aErgostadiene01-3 Ergosterol B3
C C
+B +
Et17
+ y S i t + D5:6
c + N t + Stig C C C C C C C C
~+10230+lo190 1+12770 +lo610 Nt Erg +7430 +6230 Et Erg +9970 +5670 N 7-Sit +7840 +7650 NDsE8 Stig -13940 -14950 NtD14:15 Erg +11630 $8080 NfDs:l4 al-Sit +9660 +4510 NtD14:15 If14880 $17390
+ Et + Stig
+ + + + + + +
+ +
+
C
I
+
+ +
+
al-Xit C
i1-21910 +4700 +5700 -23640
f16.3 -55.1 $24.6 +30.7 +18.5 f24.8 f18.8 -33.7 +29.1 f23.3 +35.9
f19.8 8, 19 17 -59.4 +24.5' 8 8 f25.5 8 +l5.5 8 +14.1 8 +18.4 8 -36.1 8 $20.2 4 $10.9 4 $42
+ NtDs:14+ Erg , +6410 + ND5:e + 7-Sit -16330
+5760 $16.0 +14.4 -17550 -39.4 -42.4 -45110 -43380 -113.3 -109 $0.3 -19.9 +lo0 -7920
1, 8
-63670 -71480 -160.8 -180.5
8, 21
8 8 8
-3060
-19.6
-7.7
8
-23070 -24950
-55.9
-62.7
8, 22
22-Dihydrobrassicasterol a-Spinasterol
-16740 -18520
-41.9
-46.3
23
a-Stigmastenol 7-Dehydro-8-sitosterol Stigmastanone Ergostanone 7-Sitostanone A4-3-oxo-bisnorcholenic acid Cholanic acid Allopregnane-01-3 Allolithocholic acid i-Stigmasteryl methyl ether i-Brassicasteryl methyl ether Stigmasteryl p-toluenesulfonate Brassicasteryl p-toluenesulfonate
f9210 +lo350 $22.5 +25 -42310 -47800 -102.7 -116
-7800
Dihydroergosterol I1 (5:6-dihydroergosterol) Brassicasterol
4-3370
+ B + Chol +Nt + + Et + Chol Etii
c + iCHiO + St'k7
0
+9.3
+
+ Erg C + Ts-Oa-Ds:s + Stig Daz :zs C + Ts-os-Ds:~+ ~CHO
24, 25
8
+41.4 +35.9 +35.6 $61.7
f41.1 4-34.9 $38.0 $60
8 8 17 8
+8260 +7560 $4080 +4870 t10290 +lo904 t17070 +14435
+22.9 f13.4 +27.4 $41.0
+21.0 +16.0 +29 +34.7
8 18 8 23
t13800 +8240 +33.5 f20.0
23
-26350 -26660
-46.6
-47.1
23
-29620 -34000
-53.7
-61.6
23
Dza:za
C
24
f17020 +13960 +15760 +20640
t17150 t14350 t14750 t21220
C C C
0
DZZ : 1 3
Erg Dza :zs
Footnotes to Tables I and I1 In many cases these values represent the mean molecular rotation calculated from specific rotations reported by several different investigators. In many cases these values represent the mean specific rotation calculated from values reported by several different investigators. 0 Represents double bond. a
ROTATORY POWER O F THE STEROLS
329
E refer to the hydroxyl group a t the C) position in the "normal" and "epi" configurations, respectively (Le., cis and trans to the Clo methyl group, respectively). The subscripts c and t refer to the cis-trans relationships of the hydrogen a t the C5 position to the Clo methyl group. D signifies a double bond system, and its subscript gives its position. The meaning of the other symbols is self-evident. In Table 11, these constants have been utilized in calculating the rotations of a number of known compounds whose rotations have actually been measured. Table I1 contains only those compounds for which rotations have been measured in chloroform, and for which the constants of Table I were derived from measurements made in chloroform solution. In Table 11, the calculated and observed molecular rotations usually differ by less than 2000" (the equivalent of about 5" in CY]^), and on the whole there can be little question that the results tend to verify our postulates. -4statement should be made a t this time concerning the theoretical significance of those cases in which large discrepancies occur between observed and calculated results. Thus, in the calculation of the rotation of epiergostanol an error of about 4300" is found. The calculation involves the replacement of a hydrogen at C24by a methyl group, and this region is a t such a great distance from C3 and C5 that it is inconceivable that an interaction term, E , is of such a magnitude as to account for the difference between observed and calculated values. The conclusion is inescapable, that in this case either the compound in question is i m p ~ r eand , ~ consequently an error of at least 10' has been made in the measurement of the rotation, or that the structure assigned to this compound is wrong. Similarly in other cases, inspection of the data and of the assumptions involved in the calculations leads to the same conclusions. In conclusion, we wish to emphasize that it has been our purpose here to indicate a general method of attack rather than to set up a rigid system of calculation. We have left for others the problem of adapting the method to their needs. It should be noted that one can calculate the rotations of many compounds not indicated here. Furthermore, the method may be applied to derivatives of the sterols, such as esters, ethers, oximes, etc., and if proper care is used, to different solvents. SUMMARY
1. An application of the modern theories of optical rotatory power to the steroids has been discussed. 8 In view of the great difficulty of obtaining steroids in the pure state, the occurrence of these discrepancies is not too surprising, and it is likely that the greatest practical obstacle t o the quantitative use of rotatory powers in determining structure will prove t o be just this difficulty of obtaining pure compounds on which to make the necessary measurements.
330
BERNSTEIN, KAUZMANN, AND WALLIS
2. A method of calculating the optical rotatory power of steroids has been developed. PRINCETON, N. J. REFERENCES
(1) CALLOW AND YOUNG, Proc. Roy. Soc., (London) A, 167, 194 (1936). (2) LETT&, B e y . , 70, 450 (1937). HOFMANN, AND MELDAHL, Helv.Chim. Acta, 21, 597 (1938). (3) RUZICKA, (4) See e.g., BERNSTEIN AND WALLIS,J . Am. Chem. Soc., 61, 2308 (1939). (5) GORIN,KAUZMANN, AND WALTER, J. Chem. Phys., 7, 327 (1939). KAUZMANN, in preparation.
(6) For a picture in space see STRAINin “Treatise of Organic Chemistry,” Edited by Gilman, Vol. 11, John Wiley and Sons, N. Y. l9S9, p. 1252. (7) KAUZMANN, WALTER,AND EYRING,Chem. Rev., 26, 339 (1940). EYRINGAND KAUZMANN, J. Chem. Phys., 9, 41 (1941). “Chemistry of the Sterids,” The Williams & Wilkins Co., Baltimore, (8) SOBOTKA, 1938. (9) WINDAUS AND ZUHLESDORFF, Ann., 536,204 (1938). (10) LINSTEAD, J. Am. Chem. Soc., 62, 1766 (1940). (11) HEILBRON et al, J. Chem. Soc., 1940, 1390. AND WALLIS,J . Am. Chem. Soc., 69, 1415 (1937). (12) FORD (13) STRAIN,“Organic Chemistry,” Vol. 11, John Wiley and Sons, N. Y., 1958, p. 1220. (14) WINDAUS,LINSERT,AND ECKHARDT, Ann., 534,22 (1938). (15) SCHENCK, BUCHHOLZ, AND WIESE,Ber., 69, 2696 (1936). AND NAGGATZ, Ann., M ,204 (1939). (16) WINDAUS 2.physiol. Chem., 176,269 (1928). (17) BONSTEDT, GOLDBERG, AND HARDEGGER, Helv. Chim. Acta, 22, 1294 (1939). (18) RUZICKA, Helv. Chim. Acta, 21, 161 (1938). (19) STEIGERAND REICHSTEIN, (20) BERGAND WALLIS,unpublished. (21) HAUSSLER AND BRAUCHLI, Helv.Chim. Acta, 12, 187 (1929). AND STAVELY, J . Am. Chem. Soc., 61, 142 (1939). (22) FERNHOLZ A N D RUIGH,J. Am. Chem. Soc., 62, 3346 (1940). (23) FERNHOLZ AND MOORE, J . Am. Chem. Soc., 61,2467 (1939). (24) FERNHOLZ (25) FERNHOLZ AKD RUIGH,J. Am. Chem. Soc., 62,2341 (1940).
