GUEST AUTHOR H. Bradford Thompson
Gustavus Adolphus College st. Peter, Minnesota
Textbook Errors, 27
The Criterion for Optical komerism
A
common (and correct) criterion for optical isomerism is that the molecule in question and its mirror image be nonsuperimposable. However, a second criterion has been added, by statement or implication, in a number of standard organic texts:' that optical isomerism occurs if the molecule has no plane of symmetry. Further, it is often assumed that the second criterion follows from the first. This is simply not so, as can be seen by examining the marked cubes in the figure. These cubes contain no plane of symmetry; the two large ones are clearly mirror images of each other yet are readily superimposable. This can be seen easily by comparison with the smaller cube below, which becomes the left cube by a 90" rotation around a vertical axis and the right one by a 180" rotation around a horizontal axis. There can he little question about the first criterion. If a molecule and its mirror image cannot be superimposed, then there are certainly two distinct isomer^.^ As the mirror-plane rule is not a sufficient alternative, one ought, perhaps, to investigate the criteria for superimposability more completely. The Symmetry Elements
A molecule may he idealized as a collection of points (nuclei) in a fixed mutual relationship. Any other molecule with the same arrangement of nuclei will be a molecule of the same chemical substance.3 The combination of internuclear distances and angles determines the physical and chemical behavior of the substance. Such a molecule may be reoriented in space without altering this mutual relationship. It can be shown that any possible reorientation can be accomplished by rotation about some axis. The molecule may also be reflected (that is, changed into its mirror image) while maintaining the same internuclear angles and Suggestions of material suitable for this column and guest columns suitable for publication directly are eagerly solicited. They should be sent with as many details as possible, and prtrticularly with references to modern textbooks, to Karol J. Mysels, Depart. ment of Chemistry, University of Southern California, Los Angeles 7, Calif. Since the purpose of this column is to prevent the spread and continuation of errors and not to evaluate individual texts, the source of errors discussed will not be cited. To be presented, the error must occur in at least two independent standard books. 'It may not seem immediately obvious, however, that optical activity will result. This point is well covered by D . F. MOWERY, JR., J. CHEM.EDUC., 29, 138 (1952). To be sure, electrons play the major role in determining these distances and angles. However, any two ground-state molecules having the same nuclear arrangement will have the same electron distribution.
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distances. If after rotating or reflecting our molecule, we find ourselves with a structure that looks just like the original in its original orientation, we have discovered a symmetry element for this structure.
A first type of symmetry element is a rotation axis. Methyl chloride, for example, possesses as a symmetry element a rotation axis along the C - 4 1 bond. Rotation through 120' brings one to an orientation indistinguishable from the original. If the required rotation is 360°/n, we call the element concerned an n-fold axis of symmetry, and indicate it by the symbol C". Symmetry Elements Involving Reflection
Reflection in a given plane is a possible symmetry element-that is, following reflection one may again find an arrangement indistinguishable from the original. In this case the molecule is said to possess a plane of symmetry, commonly designated 0 . If such a plane is present, the molecule and its mirror image do not differ-that is, they cannot be two distinct species of molecule. The presence of a "mirror plane" is thus sufficient to rule out the possibility of optical isomerism. We have seen by concrete example, however, that the absence of a mirror plane does not necessarily mean that optical isomerism will exist. To cover this case adequately we must observe the possibility of a third type of symmetry element, rotation followed (or preceded) by reflection in a plaue perpendicular to the rotation axis. Such an element is called a rotationreflection axis, 8,. As a simple example, ethane in the staggered rotational position has a sixfold rotation reflection axis along the C-C bond. Rotation through 60' plus reflection brings the hydrogens from one methyl group into the positions formerly occupied by those of the other methyl. If a rotation-reflection axis exists, the mirror image of our molecule is identical with the original reoriented
in space, and distinct optical isomers do not exist. Thus the presence of either a plane of symmetry or a rotation-reflection axis rules out optical activity. The cubes in the figure each contain a fourfold rotation reflection axis. The reflecting plane is horizontal, the axis vertical. The small cube represents the intermediate stage of applying this symmetry element to the large left cube since i t can be transformed into the latter either by a 90' rotation around a vertical axis passing through its center or by a reflection from a horizontal plane passing through its center. That these considerations are not an idle speculation is shown by the fact that McCasland and his colleagues have synthesized molecules having no other significant symmetry element than a rotation-reflection axis,4 such as a pentaerythritol esterified with four optically active methyloxyacetate groups, two of them (+) and two (-) : (+)ROCH,OCOHzC
CHIOCOCHsR(- )
\ / C,
A number of discussions mention the center of symmetry as a criterion for the absence of optical isomerism. This element, sometimes indicated by i , is identical with the twofold rotation-reflection axis S2, and is thus included in the above. In the strictest sense, the mirror plane r is also included, being identical with 8,. For many of us, centers and planes of symmetry are probably best visualized separately from the rotation-reflection axes. Thus optical act,ivity requires the absence of a number of symmetry elements, namely all those involving a reflection either alone or combined with a rotation. Other symmetry elements may however he present M c C a s ~ a ~ G. o , E., (1916); 81, 2399 (1958).
ET AL.,
J . d m . Chem. Soe., 78, 5646
without precluding optical activity, especially the simple rotation axes. Thus the molecules of D- or L-tartaric acid contain a twofold axis. Internal Rotations
The discussion above has been limited to rigid molecules. Molecules with intramolecular rotations present a further problem, rarely adequately covered in elementary texts. While individual rotational conformations may be optically active, optical inactivity can result from equal molecular populations in states that are mirror images of each other.5 For example, meso-2,3-dichlorobutane would be optically inactive although two of its three staggered rotational conformations should be active by the criteria above. The trans rotational isomer contains, of course, a center of symmetry. Summary
The basic criterion for optical isomerism may be stated as follows: Distinct optical isomers of a substance may exist if, and only if, a molecule of the substance cannot be superimposed up011 its own mirror image. The absence of planes and/or centers of symmetry does not produce a criterion equivalent to this one. Nor is the absence of any element of symmetry required. The alternate criterion, to agree most closely with the first, should read in full: Distinct optical isomers of a substance may exist if, and only if, a molecule of the substance has no symmetry element involving reflection. The elements considered must include, in addition to planes and centers of symmetry, the higher rotationreflection axes.
' For B thorough discu~sionsee MOVERY,op. cit., AND NOLLER, C. R., J. CREM.E ~ u c .24, , 600-4 (1947).
Volume 37, Number 10, October 1960
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