3d atomic orbitals
There are five 3d orbitals. These are labelled 3dxy, 3dxz, 3dyz, 3dx2-y2 and 3dz2. The 3dz2 name is an abbreviation for 3d(3z2–r2). Four of these functions have the same shape but are aligned differently in space. The fifth function (3dz2) has a different shape.
The shape of the five 3d orbitals. Top row: 3dz2; centre row from left to right: 3dyz and 3dxz; bottom row: 3dxy and 3dx2-y2. For each, the white zones are where the values of the wave functions are negative while the red zones denote positive values.
Each 3dxy, 3dxz, 3dyz, and 3dx2-y2 orbital has four lobes. There are two planar node normal to the axis of the orbital (so the 3dxy orbital has yz and xz nodal planes, for instance). The 3dz2 orbital is a little different and has two conical nodes. The higher d-orbitals ( 4d, 5d, 6d, and 7d) are more complex since they have spherical nodes.
The origin of the planar nodes becomes clear if we examine the wave equation which, for instance, includes an xy term in the case of the 3dxy orbital. When either x = 0 or y = 0, then there must be a node and this, by definition, is the case for the yz and xz planes.
The OrbitronTM, a gallery of orbitals on the WWW: https://winter.group.shef.ac.uk/orbitron/
Copyright 2002-2023 Prof. Mark Winter [The University of Sheffield]. All rights reserved.