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Atomic orbitals: 5d

The shape of the five 5d orbitals. From left to right: (top row) 5dx2-y2 and 5dz2 (bottom row) 5dxy, 5dxz, and 5dyz. For each, the red zones are where the wave functions have negative values and the green zones denote positive values.

For each atom, there are five 5d orbitals. These are labelled 5dxy, 5dxz, 5dyz, 5dx2-y2 and 5dz2. Four of these functions have the same shape but are aligned differently in space. The fifth function (5dz2) has a different shape.

Each 5dxy, 5dxz, 5dyz, and 5dx2-y2 orbital has 12 lobes. There are two planar node normal to the axis of the orbital (so the 5dxy orbital has yz and xz nodal planes, for instance). The 5dz2 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 partitions off the small inner lobes. The higher d-orbitals such as the 6d orbitals are more complex still since they have further 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 5dxy orbital. Clearly when either x = 0 or y = 0, then we must have a node, and this by definition is the case for the yz and a xz planes.

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Document served: Wednesday 21st October, 2020