Rule of Thumb for Predicting Optical Activity
To the Editor: In my recent article entitled "Criteria for Optical Activity in Organic Molecules" which appeared in THIS JOURNAL [46, 269 (1969) 1, a general rule of thumb for predicting optical activity was stated to be "the absence of a rotation-reflection or alternating axis of symmetry in the molecule or any of its conformations produced by bond vibration or rotation including ring alternation." This was stated as the "most general rule of thumb," and it was not intended that this be accepted as an absolute criterion but only as an easier test than comparing mirror images, which might be used in a majority of cases. It should have been pointed out, however, that this rule of thumb fails with certain classes of compounds. A compound falling into one of these classes is (+)menthyl (-)-menthy1 2,6,2',6'-tetranitro-4,4'-diphenate prepared by Kurt Mislow [Trans. of A'. Y. Acad. Sci., (2), 19, 298 (1957)l and described on p. 93 of "Introduction to Stereochemistry" [W. A. Benjamin, Inc., New York, 1966, p. 931. A molecule of this compound has no alternating axis of symmetry in any of its conformations, but is, by rotation of the central diphenate grouping, identical with its mirror image and therefore optically inactive. JR. DWIGHTF. MOWERY,
High School Courses
To the Editor: I noted with interest John Troland's letter [J. CHEM. EDUC., 46,124 (1969) I on the chemistry content of high school courses and am in general agreement with his sentiments, although a t the same time stressing that we must not go too far the other way and'lose sight of the interests of the few per cent future chemistry specialists. The problems with which all beginners in chemistry are faced are the differences between elements and compounds, the size and indeed the very existence of atoms, etc., etc. Such problems are often carried over well into the period spent studying chemistry a t university level and in some instances are never resolved. A student's initial surprise a t being told, for example, the incredibly small size of an atom can eventually lead to a situation in which he puts his mind "in neutral" and thereafter helplessly accepts all he is told without attempting to understand it. I n my experience of teaching chemistry at all levels I have found that if raw beginners are allowed to establish for themselves some of the facts early in their study, they are better oriented towards accepting (not uncritically) the subsequent and inevitable mass of theories and data. For example, again considering atomic size, by making a dilute solution of sodium chloride and then seeing how small a drop will still impart a yellow color to a flame, they can set an upper limit cm) to an atomic radius. Analogously, 700
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Journal of Chemical Educofion
ionone can be diluted with air to the threshold of detection by smell. A simple calculation then sets an upper limit to the particle radius of 10-4-10-5 cm. A cubic micron of fluorescein solution (1 in lo8) shows fluorescence under a microscope: radius limit 10-%m. No originality is claimed for these methods which can readily be extended. Their significance lies in the fact that they can be understood by laymen, to whom they are convincing. There is no need for the common authoritarian approach in which it is baldly stated that an atomic radius is cm. Time, of course, does not permit this heuristic approach to he applied to all chemical facts, but the students do at least begin to sense that the subject is not artificial. They experiment for themselves from the start and can see that chemistry has a practical basis. A. G. BRIGGS
Normalization of MO's
To the Editor: I n the July, 1968 issue of THIS JOURNAL [45, 465 (1968)l Drs. Reiter and House, Jr., presented a computer program for calculating clectron density contour maps of Hz+for an electron in the lowest bonding and antibonding molecular orbitals. More meaningful comparisons of these density contours would be possible if both of these molecular orbitals are normalized which was not the case in their program. The normalization problem is extremely simple [PITZER,KENNETHS., "Quantum Chemistry," Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1953, p. 1311, the respective bonding (B) and antibonding (A) factors being
+ 2A)-'/a
NB
=
(2
NA
=
(2 - 2A)-I/.
where
in which rp, and rps are the normalized hydrogen atom 1s wave functions about nuclei a and b, respectively, R,b is the internuclear separation, and a. is the Bob; radius (0.529 A). For the Hz+ ion with R a p 1.06 A, A = 0.5864 and the bonding densities given in Figure 3 of the Reiter-House article should all be divided by 3.17 while the antibonding densities given should be divided by 0.827. These factors can of course be put into the computer program. An important qualitative aspect of the difference between bonding and antibonding densities becomes more apparent after this normalization. The antibonding orbital has a higher density for an electron to be found in those regions of space (as for example on the internuclear axis beyond or below both nuclei) where its presence actually tends to separate and destroy the molecule. CHARLES E. HECHT
