# 5*d* atomic orbitals

There are five 5*d* orbitals. These are labelled 5d* _{xy}*, 5d

*, 5d*

_{xz}*, 5*

_{yz}*d*

_{x2-y2}and 5

*d*

_{z2}. The 5

*d*

_{z2}name is an abbreviation for 3

*d*

_{(3z2–r2)}. Four of these functions have the same shape but are aligned differently in space. The fifth function (5

*d*

_{z2}) has a different shape.

**The shape of the five 5 d orbitals.** Top row: 5

*d*

_{z2}; centre row from left to right: 5

*d*

_{yz}and 5

*d*

_{xz}; bottom row: 5

*d*

_{xy}and 5

*d*

_{x2-y2}. For each, the white zones are where the values of the wave functions are negative while the red zones denote positive values.

There are five 5*d* orbitals. These are labelled 5d* _{xy}*, 5d

*, 5d*

_{xz}*, 5*

_{yz}*d*

_{x2-y2}and 5

*d*

_{z2}. Four of these functions have the same shape but are aligned differently in space. The fifth function (5

*d*

_{z2}) has a different shape.

Each 5d* _{xy}*, 5d

*, 5d*

_{xz}*, and 5*

_{yz}*d*

_{x2-y2}orbital has eight lobes. There are two planar node normal to the axis of the orbital (so the 5

*d*

_{xy}orbital has

*yz*and

*xz*nodal planes, for instance). The 5

*d*

_{z2}orbital is a little different and has two conical nodes. In addition, apart from the planar nodes, all five orbitals have two spherical nodes that partition off the small inner lobes. The higher

*d*-orbitals (6

*d*and 7

*d*) are more complex since they have further spherical nodes while the lower d orbitals ( 3

*d*and 4

*d*) have fewer.

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 5*d** _{xy}* orbital. When either

*x*= 0 or

*y*= 0, then there must be a node and this, is the case for the

*yz*and

*xz*planes.

The Orbitron

^{TM}, 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.