A Projection for Bond Location in Chair Cyclohexane and Related Structures A. A. Wwlf Brlstol Polytechnlc, Bristol.
BS 16 lQY, U.K.
Fragments of the diamond structure appear in isoelectronic forms as chair cvclohexane or adamantane structures characterized by the Gesence of puckered rings.'s2 The empirical formulas of some units that occur singly or combined in cyclohexanelike systems are listed in the table. Isomers are possible depending on bond directions external to the , all axial as ring. Some are all equatorial as in ( P p b ) ~others in trihalo-cyclotrithiazenes, whereas in cyclotrisilazenes ( R z S ~ N Hthere ) ~ are cis and trans forms corresponding with all equatorial R's or one axial R. Carbon monofluoride is an example of an extended ring system formed by buckling the hexagon rings in graphite by direct fluorination, an important reaction in the functioning of fluorine cells. An allsilicon ring system is found in CaSiz where calcium ions hold together puckered silicon sheets. Allotropes of Group V elements contain uncharged ring systems. The relation to adamantane structures is seen when the uooer three oxveens in the trimetaphosphate ion are capped b 2 0 3 +to for~%40io. I t is difficult to reoresent in two dimensions the chair forms present in these structures without ambiguity; the conventional views are not wholly satisfactory in showing the true external bond directions. The normal perspective, looking down a t an arbitrary angle on the ring (Fig. la), tilts the axial bonds away from the vertical. As for the equatorial bonds, even when appropriately shaded, their actual directions may not be immediately obvious to the student.3 The Newman projection (Fig. lb), very useful in isolating certain features in a structure,4& a cross section viewed horizontally along an edge or one of the equatorial bonds. The vertically drawn bonds are really inclined a t 19.41°; the equatorial angles are distorted by projection onto a vertical plane. An alternative oroiection is orooosed that views verticallv along a threefoldaxis without's&h distortions (Fig. 2a). ft shows the close-oacked lavers of the diamond structure. a cross section of'which isvillustrated in Figure 2b.5 ~ x i a l bonds rise vertically above C1, C3, and C5 or drop below C2, C4, and C6. The equatorial bonds emerge radially and are inclined downward a t 103.47' from the axial bonds a t C1, C3, and C5 and upward from the other carbons. The "zigzag" around the antiprism edges from C1 to C6 outlines the chair ring. This very symmetrical projection contains all the
information on bond directions in a readily assimilable form. I t is easilv extended to oolvcvcles. in which umer and lower triang1es"are apex joinid, a i d is ieadily transiormed to the conventional view in Figure l a by tilting the triangular planes. Similar simplified projections are suitable for other D,d molecules such as Ss or Sa-,(NH), rings (n = 4) where lone pairs occupy some, or all, the external positions. Table 1.
Unlts In Cyclohexanellke Structures
Discrete rings (38 elring)
Polyoy~ll~ sheets (30 elrlng)
Oxycycllc trlmen (38 elring).
CH2:NR; NF; NCI SIRz: SnR& PR; S RsBNR:RPSR2:Se
CF: Pa SI-; As: Sb: Bl Sic1
S103+ POsSOs
Oxygona counted as 2s. +Rhombohedra1 black allmops.
Figure 1. a. Normal dew of the chalr form of oyclohexene, b. Newman pro]ec(lon:view parallel to 5.4 and 1.2 edges.
'
Woolins, J. D. Non-Metal Rings, Cages and Clusters Wiley: New York, 1988. Armitage, D. A. horganlc Rings and Cages; Arnold: London. 1077
Shaw, D. G. J. Chem. Educ. 1988,45,587. Blackburn, B. K.; Davles. G. G.; Smon, K. N.; Whitlaker. M. Chem. Soc.Revs. 1988. 17, 147. Ho, S. M.; Douglas, B. E. J. Chem. Educ. 1968, 45, 474.
646
Journal of Chemical Education
Figure 2. a. Projectedvlew perpendicular to rlng. (CI, 3 and 5 at level 1: C2. 4 and 8 at level 314: equatorial H's at 314 and 1: axial H's at 0 and 714). b. Relatlve level ol layers viewed parallel to dose-packed planes.
