Bernard E. Hoogenboom
Gustavus Adolphus College st. Peter, Minnesota
Three-Dimensional Models of Atomic Orbitals
A
common source of confusion for the undergraduate student of chemistry is the visualization of the spatial arrangements of atomic orbitals. Physical descriptions of the shapes of orbitals and their relative energies or maximum extensions into space are readily grasped by the student; but the orientations of orbitals due to mutual repulsive interactions are not as obvious. For example, it is difficult to visualize, without models, that the combination of four individually linear sp3 hybrid orbitals will assume a tetrahedral arrangement. Papier-mache1 and Styrofoam2 models have been used to demonstrate the spatial properties of atomic orbitals; but such models do not show the mutual and dynamic repulsions which force the atomic orbitals into their most stable, or lowest energy, arrangements. The use of balloon models of atomic orbitals has been reported briefly, but without emphasis of the principle of maximum separation of orbitals due to mutual repulsive interaction^.^ By tying together two nearly spherically inflated balloons of the same size and color, the two lobes of a single pnre p orbital can be illn~trated.~,'The orientation of p,, p,, and p, orbitals with respect to each other may be illustrated by joining three differently colored balloon pairs of the same size a t their stems. It is usually not necessary to actually tie the balloon pairs together, for once assembled by interlinking the balloon pairs, the aggregate will be stable. The most stable arrangement is orthogonal (Fig. 1). As in the case of atomic p orbitals, the balloons become oriented so that there is a minimum of inter-balloon interference. The repulsive forces which force the balloons, or orbitals, into the most stable or lowest energy state are represented by the compression of the balloons a t the points of contact. The most stable arrangement will resist forces which tend to disturb it. Omitting the smaller lobe for convenience, a single
' FOWLES,G. W. A,, J. CAEM.EDUC.,32,260 (1955). 'LAMBEET,F. L., J. CHEM.EDUC.,34, 217 (1957). POLIAR&F. A,, J. CHEM.EDUC.,28, 607 (1951). 'Scaling of the models to emphasize the different energies of different orbitals may be accomplished by inflating the balloons used to the volume appropriate to the desired shapes, sizes, and maximum extension values of the atomic orbitals. The maximum extension values used are given as bond strengths in PAUL ING, L., "The Nature of the Chemical Bond," 3rd ed., Cornell University Press, Ithaca, New York, 1960, pp. 10&144. These , A., "Valence," Clarendon values are summarized in C o a s o ~ C. Press, Oxford, 1952, p. 201. COAEN,I., J. CEEM.EDUC.,38, 20 (1961). Textbooks eommonly represent pure p orbitals as being either dumbbell shaped or spherical; s. more correct view is that they are more nearly ellipsoidal in shape. 40
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Journal of Chemical Education
linear sp3 hybrid orbital may be represented by a single nearly spherically inflated b a l l ~ o n . ~The three-dimensional orientation of four spS hybrid orbitals can be shown by interlinking two balloon pairs of the same size and color, each balloon pair representing two single sp8 hybrid orbitals. It will be seen that the most stable arrangement of the balloons is tetrahedral (Fig. 2), a condition which corresponds to the ground state of a methane carbon atom in a bonding situation. If three nearly spherically inflated balloons of the same size and color are joined at their stems, it can be shown that the orientation of three sp2 hybrid orbitals is planar. The balloon representing the smaller lobe of each sp2 orbital is omitted for convenience. If another balloon pair of a different color, slightly smaller in size4and representing a pure p orbital, is interlaced
Figure 1 (left). Orthogonal arrangement of p,,p,, and p , orbitals. Figure 2 (center). Tetrahedral orrongerned of four rp3 orbitolr. Figure 3 (right). A p orbitol perpendicular to three planar rp2 0rbitolr
with the three sp2 orbital balloons, the sp2 orbital balloons remain planar and the single p orbital balloon becomes oriented perpendicularly to the plane of the sp2 orbital balloons (Fig. 3). By means of such a model it can be shown that although the p orbitals of adjacent atoms may interact to form a p i bond, the sp2 hyhrid bond orbitals remain planar and separated by angles of about 120 degrees. The balloon model of a pnre p orbital, if inflated to a slightly larger size,' can also be used to illustrate the combination and arrangement of two sp hybrid orbitals. If this linear pair is interlaced with two more balloon pairs of different colors and slightly smaller in size, representing two pnre p orbitals, the bonding situation of carbon in HCN and acetylene is illustrated. The two p orbitals are perpendicular to each other and to the two sp bond orbitals. The octahedral arrangement of six d2sp3 bonding orbitals may be illustrated by interlacing three balloon pairs of the same size and color.
The use of balloon models of atomic orbitals was suggested by Fowles,' hut apparently not pursued because of the short life-expectancy of balloons. This admittedly poor feature of balloons is more than offset by the fact that they are very inexpensive, readily
available, and present virtually no storage problem. The balloon models are simply and rapidly constructed and are ideal for classroom demonstrations. Their simplicity also provides incentive for the student to construct his own models as an effective study method.
Volume 39, Number
I, January 1962 / 41
