Orbital Shape Representations Osamu Kikuchi The University of Tsukuba, Sakura, lbaraki 305, Japan Keizo Suzuki Science University of Tokyo, Kagurazaka, Tokyo 162, Japan Quantum chemistry has become important in the undergraduate education of chemistry students. Correspondingly, physical chemistry textbooks contain various types of representations of the electronic structure of atoms and chemical bonds in molecules. Atomic and molecular orbitals are illustrated in several ways to help students understand orhital shapes. We wish to comment on orhital representations that have been proven beneficial in our lectures. Figure 1shows several representations of the hydrogen Zp, atomic orbital, +zp,, and its electron density distribution, 1+2p,1
+zp, = R ~ ~ ( r ) Y ~ , ( 0 , 6 )
R&) = (1/2&) exp(-rl2)r Y,,(0,4) = ( f i t 2
6) sin0 cosm
A traditional way of illustrating atomic orbitals is by use of two-dimensional polar plot representation of the angular
function YL,(O,+)of the atomic orhital. The radial function R,r(r) is chosen to he a constant, and the plot distance, d, varies with direction. In the case of a two-dimensional polar plot of a Zp, orhital (Fig. l(a)) on the xy plane, where 0 = 90°,the diagram is ohtained by In this case the plot distance O P is proportional to the function value at Q which is located along the O P direction and on a circle of a given radius. The polar plot diagram of the density function of the Zp, orhital, Figure l(h), is obtained similarly by The polar plot diagrams are not contour lines.
Figure 1. Hydmgen 2pXatomic orbital and its electron density distribution. (a) Polar plot of & ,on the xyplane. The OPdistance is propanimal to Icos$l. The pasitive region means that cosB 0 in this region, and the negative region means that cos6 0 in this region. (b) Polar plot of (+2,)2 on the xy plane. The OPdistance is propational to lc0sd1~. (c)Contour lines af + . , o n xyplane. Solid lines were used for Me poshive function values end dotted lines far. the negative function values. The values cited are in units of ad-'". (dl Contour lines of (+z,)~ on the xyplane. The values cited are in units of a.u.r3. (e) Pseudo-threedimensionalplot of The function values calculated on the xy plane were plotted along ths r axis (f) Three-dimensional contour surfaces of +2px, The solid-line surface corresponds to +2p, = +O.Ol while the dotted-line one corresponds to = -0.01 a.(1.-3'2.
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