4d atomic orbitals

There are five 4d orbitals. These are labelled 4dxy, 4dxz, 4dyz, 4dx2-y2 and 4dz2. The 4dz2 name is an abbreviation for 3d(3z2r2). Four of these functions have the same shape but are aligned differently in space. The fifth function (4dz2) has a different shape.

The shape of the five 4d orbitals. Top row: 4dz2; centre row from left to right: 4dyz and 4dxz; bottom row: 4dxy and 4dx2-y2. For each, the white zones are where the values of the wave functions are negative while the red zones denote positive values.

Each 4dxy, 4dxz, 4dyz, and 4dx2-y2 orbital has eight lobes. There are two planar node normal to the axis of the orbital (so the 4dxy orbital has yz and xz nodal planes, for instance). The 4dz2 orbital is a little different and has two conical nodes. In addition, apart from the planar nodes, all five orbitals have a single spherical node that partitions off the small inner lobes. The higher d-orbitals ( 5d, 6d, and 7d) are more complex since they have further spherical nodes while the lower d orbitals (3d and 4d) 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 4dxy 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.