3d atomic orbitals

There are five 3d orbitals. These are labelled 3d_xy, 3d_xz, 3d_yz, 3d_x²-y² and 3d_z². The 3d_z² 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 (3d_z²) has a different shape.

The shape of the five 3d orbitals. Top row: 3d_z²; centre row from left to right: 3d_yz and 3d_xz; bottom row: 3d_xy and 3d_x²-y². For each, the white zones are where the values of the wave functions are negative while the red zones denote positive values.

The five 3d orbitals. Use the previous and next icons to see other views

The five 3d orbitals including orbital nodes. Use the previous and next icons to see other views

Nodes of the five 3d orbitals. Use the previous and next icons to see other views

Each 3d_xy, 3d_xz, 3d_yz, and 3d_x²-y² orbital has four lobes. There are two planar node normal to the axis of the orbital (so the 3d_xy orbital has yz and xz nodal planes, for instance). The 3d_z² 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 3d_xy 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.