Shapes of d orbitals

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For d-orbital (l = 2), there are five possible orientations corresponding to m = - 2, -1, 0, + 1, +2. This means that there are five orbitals in each d-subshell. For 3d subshell, these are designated as 3d_xy, 3d_yz, 3d_xz, 3d_x²_{- y}² and 3d_z²_. These five orbitals are equal in energy but differ in their orientations. The shapes of 3d orbitals are shown in the figure 1.5.

fig 1.5 - Shapes of five 3d orbitals

The shapes of these orbitals are described below:

(i) The three orbitals d_xy, d_yz, and d_zx are similar and each consists of four lobes of high electron density lying in xy, yz and zx planes respectively. These lobes lie in between the principal axes. For e.g., in case of d_xy orbital, the four lobes lie in xy plane in between the x and y-axes.

(ii) The d_x²_{- y}² orbital has also four lobes of high electron density along the principal axes x and y. It may be noted that this orbital is exactly like d_xy orbital except that it is rotated through 45^o around the z-axis.

(iii) The d_z² orbital consists of two lobes along the z-axis with ring of high electron density in the xy plane.